This document is an HTML version of the thesis. The full PDF version is available on the Web. Some of the Appendices have been modified in this version due to their size.
I wish to acknowledge the helpful assistance and suggestions given me by my adviser, Professor John D Cowan, Jr, without whose help this dissertation would not have been possible. I also wish to thank David M Shupe and Edward M, Kennaugh for their help in developing the basic idea of the spheroidal radiator. The Numerical Computation Laboratory of The Ohio State University (OSU) granted much of the necessary computer time required. Albert Farha of the Columbus Division of North American Aviation supplied the FORTRAN subroutines for the SC 4020 that were used as a model for development of the SCATRAN programs and also allowed time on North American's SC 4020 to check out the many subroutines that were developed or SU's computer-operating system. Above all I wish to thank my wife, Lois Ann Groves, for her support, encouragement, and typing of this dissertation.
The work reported in this dissertation was supported in part by the National Science Foundation through the National Committee for Electrical Engineering Films of Educational Services, Incorporated of Watertown, Mass. whose technical services were also appreciated,
The purpose of this work was to see if computer-generated motion pictures could be applied to the analysis of electrical engineering phenomena. This subject was broken down into four parts which are described later in this chapter and which comprise Chapter II through Chapter V.
What are computer-generated motion pictures? They are a small branch of computer-graphics, one of the fastest growing fields in electrical engineering today. Computer-graphics, or the science of producing pictures with computers, is part of the attempt to cope with the most serious problem affecting these machines today. As computers become faster and larger, communication with them on the part of the human being becomes more difficult. Not only do the rules for programming inputs become more involved, but the mass of output tends to overwhelm the researchers when they try to interpret uhat they have created,
The solution to this problem is to use a graph to show the various relationships that are hidden in the mass of figures that constitute the average program, and computer-graphics uses the machine to draw these graphs directly instead of plotting them by hand.
The usual output device used for this purpose is the microfilm plotter. It consists of a computer-controlled cathodo ray tube and a camera that can record the face of the tube on film. The computer causes lines or characters to be plotted at any desired location on the tube. When a complete picture has been drawn, the film is advanced to a new frame and the next picture is constructed.
Generally, each frame is independent, but when a computer-generated movie is produced, the information plotted in each frame is incremented from the one before it, so that the final result when the film is run through a projector is an animated motion picture. These movies differ from a regular one in one respect. A regular movie is exposed in real-time and run at the same rate to give the proper motion, while computer-generated movies are created frame by frame. This means that the computer can take as long as it wants to calculate each picture in a sequence, and it is the calculated increment in position that causes the motion.
The first problem considered in this work was how computer-generated motion pictures could be applied to increasing understanding in electrical engineering. Chapter II discusses how the advantages of the technical training film could be combined with the computer's ability to handle large masses of data in order to illustrate physical events that are usually expressed mathematically. Many of the subjects in electrical engineering are of this type and the equations explaining what is happening are usually accompanied by a still drawing. The tremendous advantages of the computer-generated motion picture are that the motion in either time or space can be shown and the limitations of the amount of data that can be handled are removed. The exact solution can be plotted and described as easily as the approximate one. The main requirements are that the subject be mathematically complex and that motion be an essential component to understanding.
A number of different topics are discussed and it was felt that electromagnetic fields are undoubtedly one of the best subjects that can be found to which these techniques can be applied, The degree of abstraction of the mathematical concepts contained in Maxwell's equations, for example, make it a difficult field to understand from the student's point of view. When solutions are known to the field equations in a certain case, the complex equations and mass of numerical output detract from complete understanding of the problem. This is particularly true when other than steady-state fields are considered and it is important to see time as an element of understanding of the problem.
Therefore, a number of topics in electromagnetic fields are discussed with regards to how they might be helped by the production of a computer-generated movie,
The next problem encountered was how to give OSU the capability to make movies using their IBM 7094 computer. It was decided fairly early to center this effort around the SC 4020 microfilm plotter made by the Stromberg-Carlson Corporation. This machine is an off-line plotter that uses magnetic tape to drive a cathode ray tube that is matched to an automatic 35 mm camera, It was chosen because it was almost the only machine available on the market at the time this work was begun and because a body of subroutines was available from North American Aviation in Columbus, Ohio for use on their SC 4020. Although OSU's computer center is not equipped with an SC 4020, there are enough of them at other colleges and in industry that time can be obtained fairly easily, either for research purposes or by contract. Also, the machines that are coming on the market at the present time generally follow the same organization as the SC 4020 so that when OSU obtains a microfilm plotter, the capability demonstrated in this work can be transferred to the new machine with very little effort.
There were, however, a number of problems that had to be solved before a movie could be produced. These included determining the capabilities of the SC 4020, organizing the available software to find out what was useful and what was not, overcoming a computer language difficulty between OSU and the outside world, and finally, writing subroutines that would permit any programmer at OSU to produce movies of electrical engineering phenomena merely by adding the right subroutine calls to a main program describing this phenomena.
In order to solve these problems, the subject of computing software had to be considered in relation to the requirements of the SC 4020. A general description of how these problems were solved is given in Chapter III. This turned out to be a very complex subject with a great many details that would be of interest only to a programmer who was attempting to actually use the subroutines developed in the course of this work to produce a movie. Therefore, the details are described in the first three appendices of this work covering the differences between FORTRAN and SCATRAN computing languages, the SCATRAN operating system, and the FORTRAN system respectively. Chapter III ends with an example of how a programmer would use the system to produce a scene in a movie from a very simple program.
Chapter IV describes the details of a motion picture that was produced using the technique developed in the preceding chapter. A number of different subjects were considered from the field of electromagnetics, such as plane waves and wave guides, in addition to the field pattern that was finally chosen, but it was felt that a coherent movie covering one subject thoroughly would be more interesting to the viewer than a number of bits and pieces. Therefore, a script outline was written and from this a three-minute motion picture entitled The Resonant Spheroidal Radiator was produced. The movie pictures the antenna that was chosen, and then demonstrates several facets of the field produced by this antenna.
This chapter covers the mathematical theory behind the programming, describes each scene and discusses a number of problems that ware encountered and solved. The biggest problem was what to show the viewer in order to get the point across. Therefore, the description of each scene also attempts to outline its purpose. The final effect can only be judged by seeing the movie itself, rather than the illustrations in this work.
For the sake of completeness, the program listings for the movie are included in Appendix D.
In the course of making the movie example, it became apparent that although the availability of the SC 4020 dictated the use of this device, the use of a computer-driven plotter expressly designed for producing computer-generated movies would ease the task of the programmer. Therefore, Chapter V examines the plotting devices that are now on the market and also makes a survey of the various types of computer-graphic equipment now in the laboratory stage to see what trends might be of help in this area. The main problem would seem to be one of cost. The hardware and programming techniques are available today so that the actual programming and computing of a movie could be almost completely automated, but so far they have not been put together.
The chapter concludes with some suggestions that could be considered should the effort be made to reduce movie-making to where the human being can communicate with the machine on his terms rather than on the computer's. This would free the programmer to apply himself completely to the ideas behind a particular movie instead of getting bogged down in the computer programming details.
Training films are considered to be very effective in the educational process, but they are usually used only to extend the teacher's effectiveness. This is especially true in such fields as electrical engineering where the subject matter is mainly expressed in mathematical terms. One solution to this problem is the use of computer-graphics to make movies of mathematical representations. Several subjects in the field of electromagnetics are discussed.
In the last twenty years, movies have come into their own as a training device. When one looks at the catalogs of available films, the number seems limitless. A representative list put out by the Instrument Society of America has almost two hundred titles that would interest engineering students ranging from Accelerometer Calibration to X-ray Crystallography. These films come from universities, industrial corporations, laboratories, advertising agencies, and professional educational film companies. When all the sources are added up, the sheer volumne indicates how helpful films are considered to be in the educational process [1].
However, ninety-nine per cent of these movies have one thing in common. The film is used only to extend the range of the teacher. They save a great amount of time and effort, particularly when an experiment needs large and complicated equipment, but in general movies are used only to bring the instructor to the student and not in their own right to increase the student's knowledge and understanding.
Taking all of the available films and determining which ones would be suitable for graduate instruction, movie after movie is dropped until very little remains. This is particularly noticeable in research, with the notable exceptions of time lapse photography and Harold E Edgerton's high-speed strobe motion pictures. It is obvious that the motion picture camera is a valuable instrument, especially where the motion is impossible to observe, as in the above cases, but until now it could only be applied to the real world. The camera saw only the action, and philosophical approaches were handled by letting the expert lecture to the camera instead of the class. The only advantage was that the audience could be far greater and a good lecture could be given many times.
The main difficulty seems to be that although education experts are unanimously agreed that training films are effective teaching aids, no one seems to know why or even how effective they are.
An indication of this lack of knowledge is shown by a current study being financed by Britannica Films and Bell and Howell, and conducted by the School of Education at OSU. Two schools, one in a poor area of Washington, D C, and another in Shaker Heights, Ohio, have projectors in every classroom and have been given a complete library of 2000 movies and filmstrips. The hope of the study is to determine whether the quality of education can be raised by unlimited use of the educational movie.[2]
The pat answer is that movies are effective because if one picture is worth a thousand words, then a thousand pictures are worth that much more. However, before one can really answer the question, How effective are movies in education?, one must answer the question, How do people learn?. In the education library at OSU, there are over 500 titles under the heading of Psychology of Learning and yet as one reads through this massive body of literature, the impression is given that we really know very little about the learning process. Even the definition of a good teacher seems to cause lots of difficulty, although it is easy to pick out such individuals on the campus. The learning and teaching process does not seem to be one that can be specified on a rating form.
Electrical engineering as a field suffers particularly because most of the communication is in the form of mathematics. The information to be presented is contained in the form of symbols and conventions that must be understood before the information can be transmitted. As the user of mathematical tools gains more familiarity with his subject, he finds it harder to communicate with those who do not have the same depth of background that he has. Tensor analysis is a particularly good example of this in that by the time the notation is thoroughly understood, many problems are easily solved, but the results can be explained only to someone who also knows the notation.
This already complex problem is intensified when one considers the change brought about by the introduction of the digital computer into the educational process. It is becoming a dominant force in shaping the trends of the future, particularly in the sciences.
The digital computer represents one of the great revolutions of our time. It has already affected our daily life to a far greater extent than most people realize and the changes that it is responsible for are occurring at a faster and faster rate as time passes. Nowhere have more changes occurred than in the academic and research fields so that now one man, aided by the digital computer, can find solutions to problems that would have taken a lifetime of effort without it.
At the present time, an undergraduate student can easily solve problems assigned for homework in the course of a week that could not be solved by hand over several months. The solutions are more likely to be correct because of the lack of human error, and the number of calculations can be far greater. This is because the machine can execute a program a hundred times as easily as once with the same amount of effort on the part of the human programmer. In fact, these features of the digital computer can also lead to difficulties that are unique to this new age. The use of the computer has a tendency to guide research in the directions where computer solutions are the easiest to obtain and therefore some promising avenues of exploration are not pursued. Along with this, the output of a computer is tremendous and because anything as expensive as this has to be kept busy at all times, we may end up buried in our own paperwork with pages of figures that have no meaning because there is no time to have a human being analyze the forest for the trees.Computers are becoming bigger and faster at an increasing rate every year. However, the advantages in this increase cannot be utilized to their fullest extent because one area has lagged far behind the rest in computer technology. The input-output area where the human must communicate with the machine is still approximately the same as it was when digital computers were invented. At the start, the already invented teletypewriter was used to print out numbers stored electrically in the machine. Almost the same method is used today with an increase of about an order of magnitude in the speed at which the numbers can be printed. The storing of numbers in machine codes on magnetic tape has helped in increasing tho rate of flow from the computer, but the information stored is in a form that is inaccessible to the user until the tape is printed out on paper.
If the statistician or engineer wishes to make sense out of a jumble of figures, he draws a graph. It seems to have occurred to people only fairly recently that this is tedious and time-consuming and if the computer could take over the work of drawing graphs rather than presenting numbers, a dent could be made in the vast output that pours from these machines every day. The area of computer graphics has just started to move. At the present time, one cannot pick up a technical journal in this field without seeing at least one article on the subject. And yet very little hardware exists for putting these ideas into practice. Although many analog X-Y plotters have been adapted to accept computer output and translate it into visual material, these plotters are even slower than the printer. What is needed is a device that can work at computer speeds and at the same time reduce a mass of numerical data into an easily understood picture.
With the advent of computer controlled display systems that can be recorded on film and combined with high speed plotting devices, the result is that time can be added to the parameters of space already available. Better understanding will result even for those who already have a thorough knowledge of the problem when a motion picture can be made easily of a process that could be described only mathematically.
There are many phenomena particularly in the field of electrical engineering which, although they are physical events, can only be explained on the basis or mathematical theories. As The Ad Hoc Committee for Demonstration Films in Electrical Engineering stated:
Electrical engineering teachers have a peculiarly difficult task because electrical phenomena arises from invisible submicroscopic charged particles that can interact through empty space, in contrast with mechanical, chemical, and other physical phenomena normally involving visible matter undergoing changes of state..... Films which show well-designed demonstrations of physical phenomena and relate the phenomena to the applicable electromagnetic field or circuit theory will enhance and broaden the comprehension of those who are inclined to view the world as a geometric structure covered by a set of equations. Such film can point up where simplifying or restrictive mathematical assumptions must be made in order to have a tractible mathematical field or circuit theory. The emphasis here should be on the natural phenomena and the visual images of the abstract concepts of theory which interpret it,...[3]
It is in this area that computer graphic movies can serve as an instrument for explaining and understanding electrical engineering phenomena so efficiently that every university will have its own means of producing these movies. The users will wonder how they ever got along without them in the same way that it would now be impossible to get along without the computer itself.
The number of subjects in electrical engineering to which this equipment can be applied is very large. The main requirements are that the subject can be expressed mathematically and the element of motion has to be important enough so that a movie can show concepts that would be missed in ordinary text book pictures.
Among the many topics that could be investigated even with the limited equipment at hand are convolution, root locus methods, energy levels in quantum mechanics, and Fourier analysis. But the overwhelming choice would seem to be electromagnetic fields.
Maxwell's equations consist of a set of coupled first-order partial differential equations relating the various components of electrical and magnetic fields. They can be used to explain all electrical phenomena from antennas and wave guides to circuit theory and Ohm's Law. Since Maxwell's equations have both time and position as basic parameters and represent a vary abstract concept of physical events that are hard to illustrate, they are the ideal subject to use to demonstrate the ideas expressed in this work.
The equations for propagation of waves on a transmission line are well known. [4] However, in the classroom, the student is generally concerned with the behavior of a transmission line when the voltage and current present are a steadily applied single frequency. Transient phenomena is usually considered only for an open or short circuited loss-less line.
The use of computer generated motion pictures to show the signals on a transmission line opens up a whole new region where the student can accurately see what happens to a pulse or step applied to the line under various conditions of terminal impedance and different parameters of the transmission line itself, For example, consider a pulse traveling down a line terminated by an inductance. When the pulse first hits the inductance, it acts as an open circuit because no current can flow through the coil. Therefore, the pulse is reflected, but, as time passes, the inductance changes to a short circuit because of the current it is drawing. The problem can be further complicated by having a termination that is part resistance and part inductance or capacitance and by having the pulse reflected at both ends of the line.
The transient behavior of a transmission line can become extremely complicated if it is not distortionless, and as a consequence, most texts treat only that class of line. The differential equations of a line with distortion can be solved [5], but the solutions are usually in the form of infinite series that make it hard to understand exactly what is happening to the shape of a wave traveling down the line. Here is an ideal subject for a computer-generated movie. The computer can be used to solve the differential equations in series form, with enough terms to give good answers, at different points on the line at different times and then the movie producing subroutines can complete the job by showing what is actually taking place.
The study of time varing electromagnetic fields usually starts with the plane wave. The E and H fields are derived from Maxwell's equations, and a drawing (Figure 1) attempts to show the relationship between these two vector fields.
As one author puts it, when referring to this drawing:
To show the wave as it exists in three-dimensional space would require a combination of these diagrams, with the distribution of the electric and magnetic fields shown throughout many planes. Even this would be only an instantaneous picture of the wave and would fail to show its motion; for a complete picture the imagination must be called upon to visualize what cannot be drawn on paper. [6]
This sums up very neatly the usefulness of computer generated motion pictures. The limitations of drawings on paper are released and what can be shown is limited only by the programmer's ingenuity.
An interesting movie could be produced covering the following subjects as a unified topics plane waves radiating in space, the concept of parallel and perpendicular polarization, waves hitting an infinite dielectric interface, Brewster's angle and total internal reflection, waves propagating through a dielectric slab, wave propagations in a semi-conductor, and finally, wave behavior at the surface of a conductor.
A program has already been written that calculates the field of a perpendicularly polarized plane wave hitting an infinite dielectric interface as an example of what can be done. The standing wave due to reflection and the waves propagating in the dielectric are shown by means of the stream function. Lines of constant potential in the electric field are calculated, and the final result can show the variations in the field due to changing both the angle of incidence and the dielectric constant.
Wave guides are another area where the drawings showing the electromagnetic field in the guide have become stereotyped. Generally, a cross section and a longitudinal section are shown with solid lines for the electric field and dashed lines for the magnetic field. Almost any reference on the subject of wave guides will give an example of these drawings.[7]
Using a rectangular guide as an example, the requirements that there be no tangential electrical field at the sides of the conducting wave guides, in addition to satisfying Maxwell's equation, causes the field to assume a certain form. The drawings show this form but do not explain why this should be so.
The movie-making technique described in this work can be used to great advantage. A number of things could be shown that could not be demonstrated in any other way.
The requirements to be met in the wave guide can be filled by showing two plane waves traveling in the guide at the same time following a zigzag path with multiple reflection from the walls of the guide. These two waves combine in such a way to give a zero electric field at the walls at all times while propagating down the guide.
This effect could be explained in a movie by showing a cross section of the guide. The differences between wave and group velocity could be shown due to the zigzag path and the dimensions of the guide could be changed to show the effect of cut off at a particular frequency.
The ultimate example would be a cut away perspective view of the wave guide in which the components of the wave could be shown one at a time and then the combined effect of all of them. Occasionally, drawings of this type appear in texts, but without motion, much of the effect is lost.[8] A perspective view would be much easier to program if a subroutine were written that would take the three x, y, and z coordinates and convert them into the two-dimensional x-y coordinates of the perspective view. Such a subroutine would not be difficult to write and it would allow the programmer to think and calculate in the three-dimensions of the wave guide. One of the features of this subroutine could be to suppress any points or lines outside of the cut out in the wave guide.
The extension of these ideas to higher order modes and wave guides of different shapes is obvious. Another application in research could be the determination of fields in a wave guide that had minor distortions of the shape, such as a stud inserted in one side that would alter the field. Of course, this method is limited by the fact that the mathematics of such a field would have to be known before the field could be computed, but it is possible that this could be handled by a perturbation method where the basic field would be corrected by the distortion before movie subroutines were called. [8]
Antennas would seem to be one of the best candidates for a movie of the field pattern in so far as their mathematical properties are known. A complete description of one such field is given in the spheroidal radiator example which was produced as a demonstration of a computer generated movie. The discussion will be limited in this section and the reader is referred to Chapter IV for further details.
In general, the field of a radiator can be divided into three zones: the surface of the antenna, the near or induction field, and the far or radiated field. An interesting movie could be made showing the difference between these two fields for the same antenna. The scale would be different because the induction field is only up to about a wave length away from the radiator, while the far field exists to infinity. In the example of Chapter IV, only the far field is shown because at resonance all of the power is radiated and there is no inductive near field.
The solution to a radiated field problem that is going to be used as a subject can be handled either as a boundary value solution to Maxwell's equations, as in the example, or as a diffraction and scattering of optics. In either case, once the decision has been made as to how the field is going to be represented; the movie subroutine can be used to calculate the picture on the screen.
Only one area in electrical engineering has been discussed, and that only briefly. Still, it can be seen that the number of areas even in this one field is great and a lot of work is waiting for someone who can translate mathematical calculations into motion pictures, especially for the benefit of the electrical engineering student. However, as a glance into Appendix D covering the program for the spheroidal radiator example will show, there is a large amount of work between selecting a subject and having the film in hand. The ideal researcher would be one who combines a thorough knowledge of the mathematics of the chosen subject with an excellent grasp of computer programming, and such people are hard to find.
The SC 4020 Microfilm Plotter was the main device used to produce the motion pictures described in the dissertation. This chapter describes the construction and operation of this plotter and explains that there are eighteen command words that can control the available operations when they appear on a magnetic tape used to feed data to the plotter.
The concepts of software and programming languages are briefly discussed and the importance of software in expanding the above eighteen codes is explained, The languages in use at OSU are defined and the steps taken to overcome a conflict between the original SC 4020 programming system and the OSU operating system are outlined. Finally, the place of the SC 4020 plotter in the overall system is explained and the subroutines available to the programmer for making movies are given. An example of how these calls would be added to a main program defining a movie scene is given so that the actual mechanics of placing the desired SC 4020 command words on tape is accomplished with very little effort on the part of the programmer.
The actual details of the SC 4020 operating system are expanded at great length in Appendix B for those who would be interested in actually using the subroutines developed for making movies. This chapter covers only the general outlines of the work done in programming the SC 4020.
Most of the visual materials used as examples for this dissertation were produced with an SC 4020 microfilm computer recorder manufactured by the Stromberg-Carlson Corporation. The SC 4020 is representative of a number of devices that are used to translate digital commands into visual images, such as graphs or printing. It is important to understand that this device is not an analog machine where the characteristics of the input signal are related directly to the output. In a television receiver, the magnitude of the video signal is directly proportional to the degree of brightness seen on the screen. In contrast to this, a digital machine such as the SC 4020 uses the numerical information contained in its input commands as the visual material to be produced. The input signal can be represented as a number which, if it is within the set representing the machine's operating instructions, tells the machine to perform a particular operation. For example, a single number will instruct the SC 4020 to plot a dot at a certain location on its screen.
Because the SC 4020 was the prime research tool used in this study, it !s desirable to go into some detail as to the construction and operation of this device.
The heart of the SC 4020 is a seven-inch cathode ray tube of a special design called e CHARACTRON. This tube consists of an electron gun, a set of deflection plates, a matrix consisting of a metal plate with sixty-four alphanumeric characters cut in it, a second set of deflection plates, and finally a phosphor screen for viewing the image.
The first set of deflection plates locate the electron beam so that any desired character cut in the matrix can be illuminated. As the electron beam passes through the small hole in the shape of a particular character, it assumes the shape of the hole. For this reason, the CHARACTRON tube is often known as a beam shaping cathode ray tube. The second set of deflection plates positions the shaped electron beam on the face of the tube where it can be photographed. In general, two options are available for the output of the SC 4020, either a nine by nine inch hardcopy is produced on oscillograph paper or a thirty-five millimeter camera is used to produce microfilm. This camera is special in that it has to be fitted to the face of the cathode ray tube and controls must be provided to operate the shutter and to advance the film frame by frame upon receipt of an electrical command.
So far, the cathode ray tube can be considered as an analog device much like a television tube. However, it should be noted that the first set of deflection plates must be energized in such a manner that only sixty-four precise locations corresponding to the sixty-four holes in the matrix are illuminated by the beam. This converts the CHARACTRON tube to a discrete device in which a digital signal consisting of six bits processed through the proper logic circuitry can select any one of sixty-four different characters. Forty-eight of the sixty-four available characters correspond to the standard IBM BCD alphanumeric code[9]. In each case, the octal number used by IBM for each character in the forty-eight character set is identical with the one used by the SC 4020 in the sixty-four character set. There are sixteen codes not used in the IBM set that are used by the SC 4020. They are given in Table 1.
| OCTAL CODE | SYMBOL | Name |
|---|---|---|
| 12 | ∂ | Partial Derivative |
| 14 | " | Quote |
| 16 | δ | Delta |
| 17 | α | Alpha |
| 32 | π | Pi |
| 35 | β | Sets |
| 36 | ± | Plus or Minus |
| 37 | ? | Question Mark |
| 52 | . | Plotting Dot |
| 55 | γ | Gamma |
| 56 | ∼ | Similar (Tilde) |
| 57 | d | Differential |
| 72 | ° | Degree |
| 75 | ∫ | Integral Sign |
| 76 | Σ | Sigma |
| 77 | □ | Alignment |
The second set of deflection plates determine the position of the beam on the face of the tube. These can be energized in both a discrete or continuous manner. In order to translate the location of the beam into a finite number of digital bits, the face of the tube is divided into a matrix of 1024 cells down by 1024 cells across. Each address of an X location (across) or Y location (down) can be specified by ten bits and therefore with twenty bits of a thirty-six bit control word 1,048,576 different locations on the face of the tube can be specified. The addition of two more bits used for this purpose in the control word would multiply the number of addressable locations by four, but this is not necessary nor desirable.
The size of the face of the tube compared with the size of the beam will show that all of the available resolution is gained with the 1024 divisions. Two dots plotted in adjacent cells will overlap, two plotted one cell apart will just touch. In order to plot discrete vectors or points, they should be at least three cells apart. The second set of deflection plates can also be used in a continuous manner to plot either vectors or axes. A discrete location signal or address will determine the start of a vector and the beam will be swept in the desired direction to form a line. Vectors are limited in length but axes can be swept for any length.
Associated with the CHARACTRON shaped beam tube is a certain amount of logical hardware that is used to translate the input commands into the necessary voltage signals used by this tube. The complete SC 4020 package also includes an input buffer for matching the data transmission rates to the logical hardware. Although this buffer is generally driven by a magnetic tape unit, it is perfectly possible to use the SC 4020 on-line with a large computer. Strictly speaking, the SC 4020 is not a computer but is only a peripheral device which produces data in response to input commands. A computer has the power to alter its operation based on past responses to its programs; the SC 4020 does not. It can only take each command word and perform the operation specified by that command.
It is important to understand that in the discussion which follows the commands referred to are hardware commands and not part of the SC 4020 software. A hardware command can be equated to the throwing of a switch to turn on a light, while a software program can be equated to a routine that calculates when and how the switch is to be thrown. There are two reasons why the programmer should be able to utilize the machine commands even though he will not refer to them again once all the required subroutines are operational. The first is that the available SC 4020 subroutines were developed by North American Aviation, Inc. to meet a specific need and unfortunately the production of a movie was not one of the desired goals. Although liberal use was made of these subroutines as a model, many new subroutines had to be written. In order to write subroutines for the SC 4020, it is essential to understand the capabilities of the machine, and this can best be obtained by analyzing the machine commands available to the programmer. The second reason is that as programs are written to produce scenes in a movie it is necessary to have a convenient check on the output. The best way is to make a tape of a particular scene and then run it on an SC 4020. However, this may not be convenient. A subroutine is available that prints out the control words as data from the IBM 7094 computer and knowledge of the codes used by the SC 4020 will enable the programmer to check his work directly.
The SC 4020 uses eighteen different operation codes which can be conveniently divided into four categories: performance, vector, plotting, and typing commands. Each command occupies a thirty-six bit word even if not all the bits are used for a particular function. A thirty-six bit word can be represented in octal notation by twelve digits with three bits to a digit.
For example, the command word to advance the frame of either the film or hardcopy can be expressed in octal notation as:
460000000000
These eighteen codes are expressed in some detail in Appendix B of this work. Also given in this appendix are two examples, the output of two different tests, showing what the SC 4020 command words look like when they are printed out by the computer.
It is the software programs associated with the SC 4020 that make it possible for the programmer to produce movies. Since the command words are in a one to one correspondence with machine operations and some movie frames contain over sixty thousand points to be plotted, it would be impossible for the programmer to use these hardware commands directly even if he had a method of determining what numbers to use in the control word from a series of points expressed in X and Y coordinates. With the software, the single call:
CALL SUBROUTINE()=APLOTV.(N, X, Y)-
will do all of the work necessary to place N points at different X and Y locations of a programmer's coordinate system on magnetic tape in the form of command words matched to the SC 4020's raster grid. The only limit is the size of the computer's memory.
At this point, it is necessary to digress somewhat and discuss the general concepts of software as opposed to hardware. A data processing glossary definition of these two terms [10] is:
H E Kosters et al, Automatic Data Processing Glossary (Washington U S Government Printing Office, 1961.
Hardware has long been with us. It is all that is really necessary in order to compute with a machine as anyone can attest who has used a desk calculator. Since the birth of the digital computer in 1944 (a relay machine called the Mark I), a great deal of effort has gone into making computers bigger, better, faster, and as a consequencs, far more complicated.
The term software has a relatively more recent origin and the importance of software is newer still. For several years, many computer experts were against any form of what has come to be called software. To quote one such author as late as 1958:
There are, on the other hand, people who will have nothing to do with any form of conversion. (A very crude form of software - BRG.) They believe that a programmer does best to write his orders in a form as near as possible to that which they will take inside the machine - in the case of a binary machine this means the use of the scale of 8, 16, or 32 - the input operation consisting of a simple transfer of digits to the store to form words ... the establishment of such a scheme absorbs a great deal of programming effort and they suggest that this effort could better be directed towards solving problems. No sooner, they say, does someone get good at programming than he stops doing real programming and starts making programs to make other programs.[11]
To show how far we have come since 1958, in 1965 IBM spent more money on having people make programs to make other programs than they did to manufacture all of the hardware that was sold in that year. One of the reasons that IBM is the giant of the computing world is that their software has generally been ahead of that of their competitors.
It is software that makes the digital computer such a powerful tool. The key word in the definition of software is the word extend. Without software, the digital computer is nothing more than a glorified adding machine. With software, each person's efforts add to the foundations of already solved problems and techniques so that the final result is a complex structure that no one person can hope to understand completely. The total of all software for a particular computer installation is known as the operating system. The tremendous extension in the computer's capabilities comes about by the fact that it is not necessary to understand how the operating system works. It is only necessary to understand how to enter the system and record the desired results. The software keeps track of the literally thousands of details that are required to process the program in addition to calculating the results of a problem from the input data. For example, when the programmer specifies that a number is to be used, the software not only has to convert that number into a binary number and store it in the computer's memory, but in addition, it has to give the number a name and then record where the number was stored so that it can be found again. This of course is a trivial example, but when it is multiplied a million times, it gives an idea of the magnitude of the operating system. The main job of software is to shift as much of the work in programming as possible to the machine and make it as easy as possible for the programmer to do his work. This requires that the machine take the programmer's language and convert it into the ones and zeros that are the only language the machine understands. The ultimate operating system would allow a person to communicate with the computer as he would with another person, but this seems far in the future.
It was stated above that the main purpose of software was to shift the burden of necessary details to the machine as far as possible so that the programmer would not have to know how they were done. Unfortunately, when writing an extension of an operating system, the exact reverse is true. It is a requirement that the software programmer know as much as possible about the system that he is going to extend, because his subroutines must dovetail with all the other programs that have already been written and that are going to be used to support the extension. For example, the proper calls must be made to the already existing input-output subroutines.
The following discussion in this chapter covers a body of software that was developed to write magnetic tapes for the SC 4020 and BL 120 microfilm plotters. These subroutines were written to operate under the OSU Numerical Computation Laboratory operating system and in their entirety they are suitable for running only at that location. However, the foundation for these subroutines comes from a set written by North American Aviation for the IBM 7090 series computer. Therefore, they could be adapted to any system using this series of computers with a smaller amount of effort than would be required to write a new set of subroutines for this purpose. The tapes that are produced can be run on any SC 4020 available to the programmer subject to the input buffer limitations mentioned in Appendix B under program running operations.
In the discussion on software which follows, the word language can have several different, although precise, meanings. This is because a language as applied to computers can operate on one of several different levels depending on how close the programmer wishes to be to the machine. In general, the language is the system of rules for communicating with the computer and for combining various statements to build up a program that can be executed. The two main levels of language are object language and source language. The source language is the language that the programmer uses to prepare the program. The object language is the output language of some routine after the machine has operated in the source language. Generally, the object language is very close to the language that the machine uses in actually solving the problem (usually a series of binary numbers), but it is entirely possible to have the object program from one step of processing become the source program for another step. Unfortunately for programmers, as for the world, one language is not enough. Someday there may be a universal computing language (a new language called PL-1 is said by its writers to be all things to all men), but at the present time there are several hundred well known computer languages. If this were not enough, every operating system grows away from its original source so that there are thousands of different varieties, all called by the same name, Just as an example, at a computer conference, the following languages were discussed:
ALGOL FORTRAN MIMIC APT GPSS PERT AUTCODE HELP PLACE COBOL ICES QUICKTRAN COGO INTERCOM SAINT CPM JOSS SCATRAN DYSAC MATHLAB SIMSCRIPT FAP MIDAS SNOWBOL
However, this is not the place to go into great detail on computer language. There are many references that cover areas in this field but none that cover it completely or adequately. [12]
Before discussing the language used at OSU, it is necessary to explain the difference between an assembler and a compiler. An assembler operates on an object program and changes it into a machine program. The programmer, in writing an object program, usually follows the general outlines of the machine operation, but he specifies the various commands and variables by means of a relocatable program: i.e., one in which a piece of data is not assigned a definite place but is assigned only in relation to all the other pieces of data in the program. Because each piece of information is given a name, this is often called a symbolic program. The assembler is a software program added to the programs placed in the computer by the programmer that makes certain that everything has a place. The assembly program is not part of the program that is used to compute the desired output and is used only the first time a program is run. As a general rule, the object program is assembled by the assembler and then punched on cards in machine language. This is known as an object deck and is the most basic form used. When the object deck is placed in the machine, an additional small software program called the loader gives each machine instruction the right address so that it can be found again. It also checks all subroutine names called in each program. If any name is missing, this subroutine checks the library of subroutines that are on call in the operating system. The library consists of subroutines that are so popular that it would waste time if the programmer had to write his own each time he wanted to use one. A good example of this is the square root subroutine (SQRT) which is a subroutine in its own right and not a machine function like addition.
All of the above remarks apply to a compiler as well as an assembler, but a compiler resembles an assembler as a Model A Ford resembles this year's Cadillac. The machine language is the Model T. At the start (in 1950), all programs were written in machine instructions with each operation located in the machine by the programmer as he came to it. The assembler was born when the machine operations were coded but the written program was still tied to a particular machine. The great advantage in using a compiler is that not only does the programmer not have to know how a particular computer works, but he does not even have to know what computer is going to be used to run his program.
The programmer writes in a source language that is procedure oriented rather than in an object language that is machine oriented. Each machine will have a different compiler that translates the source program into an object program for that particular machine. The compiler is an extremely complicated piece of software because it effectively replaces the skilled programmer by the computer. In fact, when IBM began to write the first compiler, many people felt that it would prove to be an impossible job. With a good source language, a person who has never run a problem on a computer can do so after several hours of instruction; after several weeks, they are able to routinely use the computer in their work. A goad source language resembles the mathematics that the user is accustomed to and all the rules are in a book. One can construct a program by looking up the various pieces. The most difficult thing about a source language is to have it flexible enough to be really useful and at the same time have few enough rules that they can be easily understood. As the two goals of flexibility and simplicity are met, the compiler grows until it is the dominant part of the operating system. At the present time, it is almost impossible to sell a computer without compilers operating in the more popular languages because there are not enough programmers around who can write programs in machine language for a new machine.
For that matter, the "third generation" of computers has been delayed by several years because there are not enough programmers who can write compilers. The only person harder to find is the system analyst, a man who not only knows all there is to know about a particular computer, but also knows the field to which it is going to be applied.
It would be perfectly possible to have a universal source language except for two influences. The most important one is the fact that a source language is written in the terminology of the field in which it is going to be used. Most computer programs can be divided into two classes: scientific and data processing (business), and so at least two languages are needed. The most popular ones are FORTRAN II (FORmula TRANslator) and COBOL (COmmon Business Orientad Language) respectively.
The other reason is that a language is never fixed. At some stage, a name is given to a language, hence the II in FORTRAN II, but people keep changing the language under the same name or write a completely new one that has the features they want.
SCATRAN is a good example of this. It is a new language that was developed at OSU to overcome a serious deficiency present in FORTRAN II under the type of computing load expected at a large university. The computing load consists of a large number of small student problems with a very short execution (calculating) time. Most of the time on the machine is spent in compiling the incoming programs so a language with a vary fast compiler speed is needed. SCATRAN is at least an order of magnitude faster than FORTRAN II, so ten times as many programs can be run in the course of a working day. If the execution times for each program were on the order of fifteen to twenty minutes instead of several seconds, there would be no need for the faster compiler. But at OSU, the computing load could not be handled without the SCATRAN language.
Far out in left field are the source languages developed for a special purpose. By developed, I mean that a set of rules have been set up and a compiler written to translate a program according to these rules into machine language or into another source language. An example of this that is available at OSU is SNOWBOL. It was originally written to determine authorship of anonymous passages by word count and analysis of style.
There are two source languages and two versions of one object language in use at OSU. The two source languages are FORTRAN II and SCATRAN. The object language is FAP (Fortran Assembly Program). I am not going to attempt to describe all of the features of these three languages, to do so would require several books (see Bibliography under SCATRAN, FORTRAN and FAP). In the bibliography, there is a list of the essential texts that are needed to use these languages. In general, these books will not show you how to write a good program because that comes only with experience. However, they do list the rules that are to be used and give some examples on how they are to be applied. What the books do not tell you is how to make everything work together, and the purpose of this section is to try to tie up some of the loose ends between the three languages.
Most of the subroutines for producing SC 4020 plotter commands are written in FAP. There are actually two FAP operating programs at OSU. One is the original FAP assembler language used when running main programs under the FORTRAN II operating system. The other is called OS-FAP and is used when running programs under SCATRAN. It can be shown how close the two are by the fact that the object deck output from either assembler can be run under the other operating system. In the near future (1967), both FORTRAN and SCATRAN will be combined into one operating system using one FAP assembler. At the present time, it is immaterial which system is used to assemble a subroutine. The advantage of the FORTRAN assembler is that the diagnostics are better and the statement listings are followed by an index giving the locations of every variable being defined and their locations. This is a help chiefly when trouble shooting a long, complex subroutine or trying to understand one somebody else has written. It is recommended that if a library of subroutines is being constructed, the final version be assembled under the FORTRAN system to obtain the more complete statement listings. This will help the people who are going to use them whether in FORTRAN Or SCATRAN. The advantages of the SCATRAN assembler are that it is faster than FORTRAN (of importance only when a large number of subroutines are to be assembled) and programs run under SCATRAN are returned to the programmer much sooner. This is because SCATRAN is the primary language used ar OSU. It is running most of the time while FORTRAN programs are run only at certain times of the day.
However, when writing a main program to produce movies, the programmer will generally use a compiler language and add the calls to the subroutines in that language to make the tapes. There is no choice between FORTRAN and SCATRAN in this case. SCATRAN is the preferred language by far because it will compile more than ten times faster than FORTRAN. Since compiling uses up most of the time in test runs to check out the written programs, almost ten short programs can be run in SCATRAN in the time of one FORTRAN program. Another advantage is that since SCATRAN is the preferred language at OSU, the turn around time is a matter of hours while for FORTRAN it is at least one day.
However, using SCATRAN brought up a very troublesome problem. The foundations for the SC 4020 subroutines were written by North American Aviation as a corporate effort involving the work of many people. At North American, the main languages are FORTRAN II and FAP, This meant that these subroutines were designed to be called from the FORTRAN language. SCATRAN calls in a main program resemble FORTRAN calls, but the operating procedure of the SCATRAN compiler makes it impossible to call a FAP program that was originally written under the FORTRAN system. Therefore, one of the major jobs that had to be done was to write new subroutines, using the old ones as a guide, that could run in SCATRAN. The results of this conversion are covered in great detail in Appendix A.
It is apparent from the foregoing discussion that the subject of computing languages is an extremely complex one. A review of which languages are used where in the course of producing an SC 4020 tape may be helpful. Figure 2 shows the process in block diagram form.
The programmer writes the main program in a source language such as SCATRAN, The computer uses the system compiler to reduce that into an assembly language called FAP which is very close to the IBM 7094 machine language.
The SC 4020 subroutines called by the main program are originally written in FAP. This is because the programmer-oriented languages have a very extensive set of rules, but if a case comes along that does not fit these rules, there is no way the job can be done in that language. One sacrifices flexibility for the advantage of easier programming.
FAP has an entirely different structure from this. The language consists of approximately four hundred different operation codes such as CL, SXA, etc. Each one of these is completely independent and it is up to the programmer to string them together to form a program that will do what he wants. There are no rules other than the fact that the program has to have continuity so that it can be entered, executed, and left. In fact, the programmer does exactly the same job that the compiler does in the machine but because human programmers are not limited like the compiler, there is no limit in flexibility in writing a FAP program.
The command words for the SC 4020 ara constructed bit by bit from the input data. This requires that a very large number of logical operations be performed for every arithmetical operation. In FAP, it is very easy to operate on each individual bit in a thirty-six bit word. In SCATRAN it would be very difficult to operate on the individual bits because the language is not machine oriented. Also, the SCATRAN compiler is very inefficient and a compiled subroutine would have many more words than a hand-written one, thus requiring more room in the memory for any given program.
One subroutine was originally written in SCATRAN and the compiled FAP version is used. This is the subroutine that writes the magnetic tape and handles the tape file in general. This is because the input-output functions are so intimately tied in with the SCATRAN operation system that it is better to use SCATRAN statements to open and close files and set up the output buffers. These calls could be written in FAP but not much would be saved by doing so.
When the program is actually run, all the FAP programs are converted into IBM 7094 machine language by the assembler. The program is then executed. All machine language instructions can be considered as thirty-six bit binary words (usually written as twelve digit octal words), but a very limited subset of these instructions can be considered as an SC 4020 machine language. This language has only eighteen words in it and most of these will not be used in making movies.
The reason that the SC 4020 language is so limited is that the SC 4020 does not have software to extend its capabilities. Each of the eighteen words in the language correspond to a hardware function and if a word is put on tape that is not recognized, the only thing the machine can do is record that an input error has occurred.
In summary, this very large mass of software has only one purpose: to enable the programmer to state in relatively simple terms, plot a point or draw a line here, using my coordinate system. The computer does the rest, ending up with one of a few words that the SC 4020 will understand, which are repeated millions of times on magnetic tape.
The SC 4020 microfilm plotter is only one link on the end of a long chain that is necessary if one is to have a successful motion picture result from the programmer's efforts. Figure 3 briefly shows the elements in this chain in a block diagram. The diagram and the description of the overall system can be divided into two sections. One is labled IBM 7094 and the other SC 4020, The magnetic tape containing the information necessary to generate the movie makes a good place to separate the system, not only because the two machines are actually separated, but also because two different approaches are being used on each side of the dividing line. The IBM 7094 computer is used to create the necessary information, the SC 4020 to transfer this information onto film or hardcopy.
The first, and by far the hardest, job to be done by the programmer is to decide what should be shown in a particular scene. This is because the relationship between the programmer, the subject, and the audience is greatly interdependent. Once the human factors aspects have been satisfied, the main program can be written.
In this case, one scene from the spheroidal radiator will be used as an example to illustrate the overall systam. It was desired to show that a particular antenna is in the shape of an ellipse. Most of the viewers of this movie would have seen an ellipse drawn with two focal points and a loop of string, so it was decided to draw the ellipse by first showing the focal points and then connecting them to a point that would proceed to circle around, drawing the ellipse after it. A coordinate system was scaled and 196 equally spaced points were calculated on the desired ellipse. Up to this point, all calculations were done on the computer using SCATRAN. A check was run by printing out the X and Y values of the points and this is the first possible output in the block diagram.
In the description which follows, it must be remembered that the SC 4020 has a limited number of commands. In fact, in this scene, only two will be used, the drawing of a line between two points and the command to advance the film.
The next thing is the forming of the commands to draw the focal points. The points consist of three short, straight lines that form an asterisk. These are created when the programmer follows the dotted line in the block diagram and uses the SC 4020 subroutines directly to form a symbol. Without going into details, the programmer can use the subroutines to specify that a symbol (the asterisk) should be drawn to a certain size in a certain location in his coordinate system, The subroutines look up the symbol in a table, determine that three lines are to be drawn in a relationship that will look like an asterisk, check the size and location, and then form three control words, one for each line, that will be understood by the SC 4020 hardware. These words are placed in an output buffer reserved in the computer memory and the program proceeds to calculate the second focal point in the same manner. These control words are described in Appendix B. They will eventually be placed on the magnetic tape, one at a time, in the order in which they were placed in the output buffer. These words can be printed out in the course of a run and can be used to check that a tape is being generated which the SC 4020 will recognize. This is the second possible output in Figure 3.
The next thing is to draw the string. A LINE subroutine is used to draw lines from one focal point to the other, and from each focal point to a specified point on the outside of the ellipse. This point is the first location in an array containing the 196 X and Y locations around the ellipse. Since the SC 4020 can only draw lines that are limited in length for each control word, the subroutine may have to generate several words which, when interpreted by the plotter, will draw short lines end to end to cover the desired distance. These words are placed in the output buffer. This completes the first scene, so the programmer specifies that an advance film command is to be placed in the buffer and the magnetic tape writing subroutine is then called.
This subroutine takes all of the words that have been placed in the output buffer and writes them on a magnetic tape as thirty-six bit binary words. Six bits are placed in one row with six rows containing a complete word., When all of the words have been recorded, the tape is moved ahead three-quarters of an inch to form a record gap. The record gap can be used to find where information was placed on a tape.
After writing the tape, the subroutines return control to the main program which calculates the same scene over again with one difference. The second point on the ellipse is used for the lines from the focal point and a line is added from the first point to the second point. This is repeated point by point with an advance film command after each set of calculations. The final effect when these commands are recorded is the string swinging around the two focal points, leaving the ellipse behind it. With the proper use of DO loops in the SCATRAN program, the number of statements the programmer has to write is very small.
Most of the work is done by the software. The SCATRAN subroutines calculate the desired X and Y values and also write the magnetic tape. The SC 4020 subroutines translate the information generated by the SCATRAN program into control words that can be recognized by the SC 4020. The main program, which is the only one written by the programmer, merely serves as a control that keeps track of the jobs to be done and transfers control from one subroutine to another.
Another form of output can be obtained at this point. After the magnetic tape is returned to the programmer, he can have a dump printed out. This will show exactly what is on the tape before it is sent to the SC 4020.
The SC 4020 reads the magnetic tape word by word and does the job specified by each one. In this case, each word will first position the cathode ray tube beam at a certain location. The beam will then be turned on (unblocked) and moved in the desired direction for the desired length. This process is repeated for each word on the tape. The advance frame command moves the film at the proper times and the programmer can control either one of two cameras to receive back either film or 9 × 9 inch hardcopy.
The subroutines mentioned above form the SC 4020 library. The purpose of a library in an operating system is to make life easier for the human programmer. He can concentrate on writing his main program and leave the details to the library. He can use calls that will perform a specified operation without further effort on his part. For example, there is no reason why sines and cosines have to be calculatad by the main program each time they are needed. A call to the SIN subroutine will not only save the programmer's time needed to write the statements for the calculations, but he also has the assurance that the SIN subroutine will work every time while his own program might have mistakes in it.
The operating system library can be extended by the programmer himself through the use of a subroutine deck. This deck will contain any subroutine written by the programmer and will be placed in the back of the main program to take care of the calls in that program. The operating system is very accommodating in that if the programmer wishes to use his own subroutines rather than the system library, the system will choose the same name in the deck over the one in the library. Another reason for using a subroutine deck is that there may be very little call for a particular subroutine. Since each subroutine occupies space on the system tapes, it is better to have the few people using the SC 4020 use the necessary subroutine decks rather than to occupy this space permanently. When OSU acquires a microfilm plotter, these subroutines will become a permanent part of the system library.
The available SC 4020 subroutines are described and listed in Appendix B, but a brief review will be given here. There are four groups of subroutines that are of interest in the production of movies. They are as follows:
The setup subroutine for producing SC 4020 tapes will open up a tape file, start a clock running to time the program, and write an ID frame to identify the run with only one call in the main program. Another call at. the end of the program writes a closing ID frame, either rewinds or dismounts the finished tape, reads the clock and prints out the time taken by the program, and calls ENDJOB to close the run. This subroutine also handles the necessary buffers to store information that is to be written on tape and generally keeps track of all the details such as when to wwrite an advance frame command on the tape.
The routines to plot points are very useful to draw smooth curved lines by plotting a series of touching points along the path of the line. This can be done with a single call if the X and Y locations of each point have been calculated and placed in an array before the call.
The LINE subroutine will draw a line between any two specified points. This is done by using limited length end-to-end vectors to fill up this space. Routines are also provided to draw either an X or Y axis with a single call.
Some of the most useful subroutines for generating computer animation are the ones used to generate variable sized symbols. They allow the programmer to specify the shape, size, and location of any symbol completely independent of each other. In addition, a writing routine allows the programmar to use variable sized letters, one after the other, for titles and subheadings in his movies by only specifying the text that is to be used. Several examples of the use of these subroutines are given in this work. They include the titles, the generator symbol, and the ruler discussed in the spheroidal radiator movie example and complete details are given in Appendix B.
As an illustration, we will consider a very simple program and then add the required calls.
DIMENSION (X(6),Y(6))-
START DO THROUGH S1, J=0,1,J.L.50-
D0 THROUGH S2, K=0,1,K.L.6-
X(K):COSF.(THETA)-
Y(K):SINF.(THETA)-
S2 THETA=THETA + 1.0472-
S1 THETA=THETA + .1256-
CALL SUBROUTINE()-ENDJOB.()-
END PROGRAM (START)-
This program has two DO loops. The inner one, using K as an index, calculates the position of six evenly spaced locations on a unit circle. The outer one, using J as an index, calculates fifty different sets of the six points after moving them one-fiftieth of the way around the circle between each set. The final result, if made into a movie, would be one cycle of six equally spaced dots moving completely around a circle.
The statements needed to call the SC 4020 subroutines are now added to the above program in order to translate the point locations into command words on magnetic tape. The new program is listed below with the original statements underlined.
DIMENSION (X(6),Y(6))-
START CALL SUBROUTINE()=OUT.(4)-
CALL SUBROUTINE()=CAMRAV.(9)
DO THROUGH S1, J=0,1,J.L.50-
DO THROUGH S2, K=0,1,K.L.6-
X(K):COSF.(THETA)-
Y(K):SINF.(THETA)-
S2 THETA=THETA + 1.0472-
CALL SUBROUTINE()=APLOTV.(-6,X(0),Y(0),
1,1,1,44,ERROR)
S1 THETA=THETA + .1256-
CALL SUBROUTINE()-ENDJOB.()-
END PROGRAM (START)-
The first thing to notice is that the statements for calculating each scene (in this case, the inner DO loop with K as an index) are unchanged.
Two statements have been added at the top of the program and one at the bottom outside of any of the DO loops. Subroutine OUT. determines the form of the output (printed or magnetic tape) for this program. Subroutine CAMRAV. opens the tape file and writes the ID frame on it. At the bottom, subroutine CLOSTP. prints out the time used, closes the tape file, and transfers control to the subroutine ENDJOB .. This call was eliminated from the original program.
The two subroutine calls FRAME. and APLOTV. are added inside the beginning and end of the DO loop that generates each frame. The FRAMEV. call writes an advance frame command on the tape and closes the record. The APLOTV. call generates the necessary command words to plot the dots from the X and Y data arrays.
In addition to adding these statements to the main program, it is necessary to add eight subroutine decks to the back of the main program deck. Also, certain data cards have to be added at the end of the complete deck in order to supply the necessary information to scale the X and Y points into SC 4020 command words and fill out the ID frame with the date, programmer's name, etc. Complete details are given in Appendix B.
The final result is a reel of magnetic tape containing the necessary control words to write each specified scene and advance the frame between each one. If this tape was run on an SC 4020, the programmer would receive back fifty frames of hardcopy containing six asterisks each plus an opening and closing ID frame.
It was decided to make a full length (three-minute) movie utilizing all of the available computer techniques. Any difficulties that might show up in using the SC 4020 software could be corrected before the subroutines were released, but, more importantly, it would be a demonstration of the effectiveness in using the computer to generate a mathematically complex moving picture both in research and in the classroom.
When properly presented, a motion picture presentation should be understood even by viewers without a full mathematical grasp of the solution being presented. It is hoped that this example will illustrate these concepts.
The subject matter chosen was the resonant spheroidal radiator. This antenna consisted of a surface formed by rotating an ellipse about its major axis. A certain current distribution was assumed to exist both on the surface and in the interior of the antenna. The choice of these particular currents then determined a radiated field which satisfied both Maxwell's equations and the values on the boundaries of the system. The field produced by such an antenna is described in the next section of this chapter.
Some of the considerations that went into making the movie are discussed. This is followed by a brief outline of the script used for the movie.
The mathematical basis of the electromagnetic field lies in both the coordinate system chosen and the solutions to the differential equation generated by Maxwell's equations. Both of these are discussed and a derivation of the actual formulae used for the movie is given.
The programming and a description of what was being attempted for each scene is included along with some of the problems encountered. Finally, a short criticism of the finished product ends the chapter.
One of the advantages in using the resonant spheroid as an example is that the field it produces is axially symmetric. Therefore, all of the information available from a pictorial field representation can be shown in two dimensions instead of three. A typical display of the field pattern for the resonant spheroid is shown in Fig. 4. If the entire set of lines is rotated about a vertical axis, the result will be a series of curved toroids that move outwards from the center spheroid. Each toroid has a nest of smaller toroids inside it.
A three-dimensional axially symmetric field is ideal when one is limited to a two-dimensional display because any cut made along a plane containing the axis is identical with any other cut. Therefore, all of the information available from a pictorial field representation can be shown in two dimensions instead of three.
Each one of these toroidal surfaces represents a stream-surface which has no current flowing across it. This can be determined from Ampere's Law:
where Id, and Ic, are the displacement and conduction currents enclosed by the path of integration. If, due to rotational symmetry, the H field is independent of the angle about the vertical axis and the integration path is a circle of radius S about this axis, then
If Id and Ic are set equal to a constant then the above equation describes a surface of revolution. Each of the streamlines in Fig. 4 are calculated from a different constant. It can be shown by applying Ampere's Law to a surface area that the net current flow across a stream surface is zero. Therefore, if no conduction currents are present, the displacement current across the surface must be zero.
Assume that a plane cuts a family of stream surfaces normal to the axis of symmetry. Any two surfaces that intersect this plane form two concentric annular areas. Since no displacement current flows across a surface, the current in one annular area must be equal to the current flowing in the other area but opposite in direction. Therefore, the motion of the displacement current is a rolling one around the center of each nest of toroids. The motion reverses between each set so that there will be no discontinuities in the field. It can be seen that the current density across an area normal to the flow between two toroids depends on the position of the area. Obviously, the current density is greater on the X-Z plane than at the top of the toroid and this is shown by the density of the streamlines at that point.
I wish to give full credit to David M Shupe of the Department of Electrical Engineering, OSU, for his work in the development of the streamline model that was used to represent the resonant spheroidal radiator from the electromagnetic field equations. [14]
Once it was decided to produce a movie with continuity, rather than separate scenes that would just demonstrate the computer generating techniques that have been developed, a plan of action was needed. Before starting, two limitations were imposed.
In view of the fact that it was basic policy to have the computer and display device do as much of the work as possible and to have as little photographic work required other than the developing of the basic film, it was natural to reject sound as one of the techniques that could be used to explain the pictorial context of the film. Therefore, the movie would have to be complete in itself without the aid of narration to explain the motion.
The other limitation was that since this film was to be only a prototype and not a finished product, a length limitation would be set to use one hundred feet of sixteen millimeter film. The film comes in hundred foot lengths with the next larger size being 400 feet. The nominal speed of sixteen millimeter is twenty-four frames a second with each frame being three-tenths of an inch long. Therefore, a hundred feet of film will result in a movie that has approximately four thousand frames and runs for 167 seconds or two and three-quarters minutes.
It was decided not to use photographic stretching for any part of the movie. Photographic stretching is a method whereby only one frame is generated by the computer for each scene. Photographic means are then used to generate, in the case of titles, etc., a large number of frames in a row to give the viewer time to read the text. Any animated motion that is cyclic in nature can be extended by producing only one cycle on the computer and running the one cycle over and over again to generate photographically the required length of film. This method has great advantages in that costs are far less expensive per minute of film due to the difference in cost between computer time and the cost of having the photographic work done. In fact, up to this time, all of the computer generated movies that have been produced used this technique in one form or another.
However, after consulting with the animation experts at Educational Services, Inc (Phone calls to Mr Como, ESI, during May and June 1966), who had produced several computer generated movies in another field, it seemed better to absorb the greater computer costs and not use photographic stretching. The main problem is in the registration of the film in the camera. When a movie is produced, each frame on the film has to be exactly in the same position as the last one when the shutter opens or the motion will flicker or jump when the movie is shown, This is no problem when ordinary movies are filmed because the film is always moving smoothly through the camera at a constant rate.
An entirely different situation exists during the transport of the film in a microfilm plotter. The film is moved into position and the shutter is opened, The amount of time that then elapses depends on how much information there is to be plotted in that frame and can be as long as twelve seconds. Since each frame is independent, there is no requirement for accurate registration and therefore the average camera in use on these plotters has very poor registration from frame to frame.
When attempting to use the average camera for making movies, the picture jumps so much that the result is practically useless. In the demonstration movie, the SC 4020 was equipped with a snap action camera built in the 1920's. This camera moved the film with a sprocket mechanism that hit a plate at the end of its stroke so each frame was very precisely positioned before the shutter was opened.
Once a cycle is photographed (50 to 90 frames) by this type of camera, it would be possible to lengthen the film by photographic stretching as mentioned above. But the same problem of registration is present after this first cycle has been copied, The original film then has to be moved back to its starting point and the registration with the copy is lost. This causes a jump each time the film is cycled in making the copy. This is not a problem, of course, if the complete run is generated on the computer. The fact that the registration of the snap action camera is good enough to give good animation from frame to frame guarantees that the animation from cycle to cycle will be just as good.
One other decision was made which, at the time, was thought to increase the amount of computing time needed to run the example, but proved, in the long run, not to have increased the necessary time at all. There are two ways of drawing a line with the SC 4020 software, either using the LINE subroutine which draws a straight line between two specified points, or by plotting dots along the path of the line. The position of the dots are calculated so that each dot touches the one next to it to form the line.
The LINE subroutine breaks up the distance between the two specified points into vector commands. If the points are more than sixty-four raster counts apart in either the X or Y direction, a separate vector command is required for each sixty-four count section. Of course, if the distance is less than this, only one command is needed. Since dots plotted in every other cell will make a continuous line due to the size of the dots, the maximum distance that can be covered by a single vector command would require at least thirty-two dot plotting commands. In addition to the time required to place these commands on tape, time is also required to calculate the positions of each dot so it would appear that to draw lines by this method would increase the computing time required by quite a bit. In fact, all of the computer plotted drawings appearing in the literature have used the lines drawn between points as the method used to create the desired figures.[15][16]
However, the decision to use a dot-plotting technique to draw lines turned out not to require any excessive amount of time over the line-drawing method. As long as the subject matter is composed primarily of straight lines, the line-drawing method would be faster, but the spheroidal radiator example contains only curved lines. In order to obtain smooth enough curves, the end points of each line would have to be close enough together that almost as many points would have to be calculated as in the dot-plotting method. Since a certain amount of time has to be spent in the LINE subroutine to generate the vector command, the final result is that the two methods use approximately the same amount of computer time.
Because the plotting dots are round and do not overlap completely, the line drawn is not completely smooth but has a minor roughness along the edges. This is offset by the fact that a continuous curve can be drawn without any of the sharp breaks that appear when using line segments, no matter how short.
Although each scene will be described in turn later in this chapter, something should be said about the overall goals of the example movie. First of all, it should be remembered that this is a prototype showing the use of the SC 4020 plotter and is not a finished product. It undoubtedly has as many things wrong with it as right, but at the same time, it is only supposed to show the way forward.
The first efforts to achieve a coherent text in the time allowed resulted in a few short major scenes with the great bulk of the time being spent in text that tried to explain what was going on. By the time the viewer had been given enough time to read a complete text, most of the time had been used up and very little was left for any action. One of the main purposes of this work was to demonstrate the usefulness of short movies in the electrical engineering classroom. The result of so much text and so little activity would have been an effort that could better be duplicated by an instructor explaining from a book.
Professor W H Huggins of Johns Hopkins University [17] has suggested that the classroom animated film will be fully effective only when the dependence on the text is removed. The concepts expressed should be demonstrated using only pictorial images that would have some meaning to anyone who viewed them regardless of their background.
It is easy enough to have the computer generate text, and several examples are included in the example for completeness. However, the results are a waste of the computer's abilities especially in view of the fact that much better effects can be achieved photographically. It is the computer's capability to display large amounts of mathematical data pictorially that is going to justify the use of expensive computer time and make this method such a useful tool in the understanding of electromagnetic field theory.
Therefore, the spheroidal radiator example has very little text, only one scene in fact other than the title and credits, and tries to show the development of an idea by means of pictures. The film starts out by showing only two points (asterisks) that will be the focal points of an ellipse. An ellipse is drawn much in the same manner as using a piece of string and two thumbtacks. The ellipse is rotated by changing the perspective to show that a three-dimensional object is being shown. It is then shrunk to a smaller size and a generator is added in the interior. This is followed by a dark fringe on the surface of the ellipse that varies both in position and time in proportion to the magnitude of the current that would appear on the actual antenna. The electric field streamlines begin to radiate from the spheroid until they fill the screen. The motion is stopped and a ruler is used to compare the distances between the focal points with the distances for one-half cycle of the radiated wave. The final scene shows the direction of motion of the displacement current by means of moving segments added to the streamlines. The motion reverses for each half cycle. A more complete description of each of these scenes will be given when the programming is described.
I wish to thank Professors Cowan and Kennaugh for their help in developing a script for this movie. Many of the scenes were the result of suggestions by them. Some additional suggestions that were not incorporated into the movie due to lack of programming time but which would have resulted in an improved version of this example are described later in this chapter.
The main sequences in the film example show the radiating field from a prolate spheroidal antenna at resonance by means of the stream function. Maxwell's equations are used in a boundary value problem to determine the differential equations that specify the conditions of the radiated field. In this case, the internal structure of the spheroidal antenna is unimportant. It is assumed that all generators are completely enclosed by the surface of the antenna and the only thing of interest is the current flowing within and on the surface of the spheroid.
The coordinate system is very important in solving the boundary value problem. The details of the spheroidal coordinate system are as follows.[18]
A family of confocal spheroids are located on the γ axis at the points ±f. Points on these surfaces are defined by the orthogonal coordinate system η, ξ, φ where η is the radial distance outward, ξ is the angular coordinate upward, and φ is the rotational coordinate about the vertical axis. This system can be defined in terms of a cylindrical system r, φ, z by the parametric equations
This transformation is very useful in making the movie. When φ is set to zero, the r-z coordinates become the X-Y coordinates of the standard cartesian set used by the SC 4020 software. The development of the equations will show that there is no dependence on φ and therefore the field can be expressed in two dimensions instead of three. Figure 5 shows the two systems used when φ is set to zero.
The fact that the coordinate system and the field both have rotational symmetry can be used to advantage in solving Maxwell's equations. [19]
Since the field has the same symmetry as the coordinate system, the components are independent of φ. The two equations:
Δ × E - i ω μ H = 0
Δ × B + (i ω ε - σ) E = 0
can be broken up into their components and when the differentials of φ are set to zero, the following differential equation results:
where:
It is obvious that the differential equations can be attacked by means of the separation of variables into two equations that are functions of η and ζ respectively:
This equation was dealt with extensively in: Robert M Ryder, "The Electrical Oscillations of a Perfectly Conducting Prolate Spheroid", Journal of Applied Physics, Vol. 13, May 1942, pp. 327-339. This paper suggested a solution to the above differential equation. However, Ryder assumed that a plane wave was incident on a perfectly conducting spheroid and then solved for the current induced in it. The present work assumed a current present on the spheroid that will lead to the desired solution. This current is only a theoretical concept and does not represent any particular configuration of the interior of the spheroid.
where C is a separation constant. If we let C=t2k2 the two equations reduce to ones that have the following solution:
From the boundary values of the field, Q2(ζ) must vanish when ζ=±1 and Q(η) must have the form ejρκη for large η, therefore: [19]
and
where ρ is an integer corresponding to a particular harmonic. The equation that was used set ρ=1 where the interfocal distance (2f) is equal to one half of the wave length of the radiated signal. The value of AB is determined from the boundary conditions of this particular problem.
The assumption is made that the spheroid has a surface current flowing on it equal to:
and a current flowing internally equal to:
These currents were chosen in order to give a simple solution for the constant AB and do not represent any particular configuration of generators in the spheroid. In the movie, the interior current was replaced with a generator symbol just to indicate that an active source is required to energize the antenna.
Using Ampere's Law
for this field. Therefore:
At the interior surface of the spheroid:
The current on the surface can be divided by the circumference to give the current density:
One of the boundary conditions states that
where the two magnetic fields are on either side of a surface current density K. The magnetic field at the outside of the speroid surface is equal to
AB can now be determined:
Therefore:
The requirement that the tangential components of the E field be continuous is used as a check. The tangential E field can be determined from the potential ψ [18]
From above:
and these are obviously equal.
Therefore, the equations that were used for the field are:
Multiplying these euations by ejwt to give the time dependence and taking the real part:
For ease of computing the following transformation was made:
and the final equations were:
In the calculations for the movie, the term
For each nest of streamlines. Therefore, V can be determined from U by the formula:
and these in turn can be transformed into the X-Y coordinates by the relation:
The movie starts with a single frame containing a conventional identification frame which serves to both identify the run and to check the correct operation of the SC 4020 plotter.
The next ninety or so calls produce the titles, credits, and text. These four scenes are shown in Figure 6. The lettering is generated by the use of the variable sized symbol subroutines.
Most of the lettering is centered on the screen when producing titles, so equations were developed to make it easier to determine some of the calling parameters in the calls:
CALL SUBROUTINE()=CHSIZS.(IX,IV)-
CALL SUBROUTINE()=RITSTS.(ISPACE,IROW,TABLIV.)-
CALL SUBROUTINE()=RITE2S.(X,Y,IEND,90,1,N,-1,WORD, IRE)-
that are used for titles. ISPACE, which generates the space between letters, can be determined from IX, the lattice space used for tables, by the equation:
ISPACE = 5 × IX + K
The addition of K prevents crowding the letters when IX is reduced to the smaller values and is usually set at three.
X and IEND can be calculated from the number of letters in a line when centered lettering is desired.
X = (N-1)(2.5 × IX +.5K)(SCALE) IEND = 512 + (N-1)(2.5 × IX + .5K) + 3 × IX + K
where N is the number of characters in a line including blanks. SCALE is the value of each cell expressed in the programmer's grid. This method of determining position can be used with offset lines if the right number of blanks are supplied at the beginning and end of each line.
TABL1V is used because it contains the standard alphanumeric set. As long as a standard keypunch is used to punch the cards for the format statements (F statements), then TABL1V will match the desired letters or numbers. CHSIZS and RITSTS do not have to be called each time if the size of the letters is not going to be changed between calls. The starting position of a group of letters is set by the call RITE2S so if it is desired to center a line of text, separate calls have to be made for the lines containing an even and odd number of letters. This is why separate calls had to be made for THE and RESONANT SPHEROIDAL RADIATOR in the title scene.
The titles show the largest size letters that can be produced with TABL1V. Larger letters could be produced but a table would have to be written to break up each vector in these letters into a number of pieces.
The SC 4020 tapes were produced with 1024 words in a record. Since the number of words required for each of these scenes was less than this, it was necessary only to calculate each scene once. The following order of calls was used over and over again with minor variations:
CALL SUBROUTINE()=STORE.(X,4)
DO THROUGH (LABEL),N0,1,N.L.M-
CALL SUBROUTINE()=STORE.(X,3)-
LABEL CONTINUE-
CALL SUBROUTINE()=STORE.(X,1)-
The call to subroutine STORE with a calling parameter of 4 adds the advance film command. The DO loop writes the scene on tape M number of times. The last statement writes the scene one more time and then resets the buffer to zero. The amount of text determines the number of times the scene should be called. Enough time should be allowed to read the text through easily for each scene at twenty-four frames per second.
An interesting effect was created with very little programming effort when the names at the bottom of scene two were calculated. One of the calling parameters in RITE2S determines the number of letters in the text to be printed. Even if there are more letters in the text, the subroutine ignores any after this number is reached. Instead of fixing this number at fifty-six, the number of characters in these names, a variable N was used for the calling parameter. This same variable was used in the DO loop that called the scene. The effect is that the first time the scene is written, only one letter will appear. An inner DO loop writes this scene four times to give four frames and then control is returned to the outer loop. This time N is 2 so two letters are written in the next four frames. This is repeated until N reaches fifty-six and the DO loop is terminated. When the movie is run, the names will appear as if written letter by letter across the screen.
The complete listings for the titles, etc, shown in the four scenes given in Fig. 6 are listed from the start through the statement just after L106 in Appendix D.
The text scene shown in Fig. 6 has one error in it. It should have said, The moving segments in the streamlines represent the displacement current., rather than the D field. This could be corrected merely by changing one final statement in the program that produced the titles.
The movie starts with two asterisks being shown near the top and bottom of the center line of the screen. The program then calculates forty-eight evenly spaced points that lie along the path cf the ellipse that is to be drawn. The position of these points are all in the first quadrant. The rest of the points are calculated by first interchanging -X with X and the -Y with Y so that the final result is 192 points positioned evenly around the ellipse.
The ellipse is drawn by using the LINE subroutine to draw a line from one focal point to the other and from each focal point to point M when M runs from 0 to 191 by means of a DO loop. Another DO loop inside of this loop draws a line between each point to the one next in line up to point M. M is increased by one between each frame and the total effect is the same as that of a string looped around the two focal points with a pencil stretched to draw the ellipse. The motion starts at the right hand center side and swings all the way around counter-clockwise to return to the starting point. The complete ellipse and the two focal points are shown for several more scenes.
The statement listings run from L106 through L112.
The ellipse is next rotated by means of a perspective view through the vertical center line. Each of the X distances of the points on the ellipse is multiplied by the use of the linear increment of time and the ellipse is then drawn using the new points. For each complete cycle the ellipse will shrink in the X direction only to a thin line and then expand to full size again. The effect is that of looking head on to an ellipse of wire that can be rotated into the third dimension about the vertical axis. The idea behind this scene is to show the viewer that what he is seeing is not a two-dimensional figure, but is a plane section of a three-dimensional figure. One of the improvements that could be made is to keep each ellipse as it is drawn and to use overstroking of certain ellipses to draw a shaded three-dimensional perspective figure of the spheroid. However, this would add more complexity to an already large program and the rotation and shrinking described next were accomplished with only thirty-three statements.
Statement listings L112+2 to L120+1.
In all of the above scenes the ellipse almost fills the screen. When the ellipse is used as a radiator, it is much smaller and occupies only the center of the screen with the field pattern filling most of the rest of the space.
Therefore, each point on the ellipse is multiplied by a reducing factor and the ellipse is redrawn with the LINE subroutine. The reducing factor is incremented downward between each frame so that when the film is run, the ellipse will appear to shrink from its original size to the size it assumes for the rest of the movie.
Up to this point, the ellipse representing the spheroidal radiator has been drawn by calculating equally spaced, widely separated points along the path of the ellipse and then connecting each point by using the LINE subroutine. In the main scenes, lines are drawn by plotting touching dots along the path of the line, and to make this program compatible with the ones to follow, the drawing of the ellipse is converted from line segments to dots. The position of each dot is calculated by an iterative process that calculates each position, along a line determined by the equation of the desired ellipse, from the last calculated position. The details are not given here because the program used is fully explained in the section on how the field pattern is calculated.
Statement listings are from just below L120 to L399 along with a call to APLOTV just below statement L121.
The last twenty statements in this program (the movie was run in sections of which this is one) form the current generator symbol in the interior of the spheroid and place a dark fringe on the outside surface in proportion to the current distribution. An explanation of the program is given here but it is much easier to see the final result in Figure 8.
The current varies according to the equation
where U is the angular coordinate in the confocal spheroidal coordinate system being used. Since the surface of the spheroid is fixed, the above equation can be converted into one that uses Y as a single variable rather than U. The cartesian coordinate Y is related to the spheroidal coordinates by the equation
Y = f . U . V
Statement listings are from just below L120 to L399 along with a call to APLOTV just below statement L121,
where f = .25 is the focal distance and V = 1.2 is the radial dimension of the spheroid. Therefore,
Y = .3 U U = 3.3333 Y
and the current on the spheroid can be expressed as
I(Y) = sin [π/2 (1 - 3.3333 Y) ] cos wt
This value is calculated for a particular value of t and for each value of Y corresponding to the points calculated along the ellipse. This value is scaled so that it will occupy a distance of ten raster counts when Y and t are zero. This increment is added onto the X value of each point to form a new point and the subroutine LINE connects the two points. Four calls to LINE have to be made in order to cover the four quadrants. The points on the ellipse are touching so all of the lines drawn are side by side and form a fringe on the ellipse. A call to GENSYM with the proper parameter to give the correct magnitude and direction of the current arrow completes the scene. The current symbols and current distribution complete several cycles to show that the antenna is going to be driven by an alternating source.
This scene brings up a far more difficult problem to answer than how a particular movie is going to be programmed. In a nutshell, the question is, Under the limitations of the computing techniques used, what should be shown to communicate the desired idea to the viewer?. The chapter on conclusions will discuss this question in some detail but it is asked here because this scene caused more discussion than any other over what the spheroidal radiator example is trying to show. The result is an example of what can be done and is not a finished product by any means.
The only way to resolve this problem, especially with regards to movies that are to be used in the classroom, would be to try out as many ideas as possible and then show each one before a typical audience. A test given to the viewers afterwards would determine the most successful presentation.
Most of the remainder of the movie used the same basic program to produce variations on the radiated field.
The program starts by reading in a number of variables for the data card on the back of the input deck. This gives the program a good deal of flexibility because, although the basic equations being used remain the same, the result can be altered quite a bit for any run. The number of cycles, the number of lines in each cycle, and the time between each frame are among the factors that can be preset without changing the program.
Only the first quadrant of the radiated field is calculated. The PLOT subroutine is constructed to fill in a mirror image for the other three quarants after all the points have been determined. The first quadrant is shown below. All of the lines appearing in the final result are calculated in exactly the same manner so a detailed explaination of how one line is calculated will serve for all the others. Only the input data as determined by a number of DO loops is different.
The coordinate system used for the calculations is a set of confocal ellipses for the variable V = constant, and two sets of confocal hyperbolas for the variable U = constant. The calculations are executed in this coordinate system, then a transformation is made to cartesian coordinates before the points are actually plotted. The transformation is:
x = f . sqrt [(1-U2)(V2-1) ] Y = f . U . V
where f is the focal distance from the origin. At large distances from the origin, the U-V system approaches a polar coordinate system with a nonlinear angular measurement.
The program determines the ellipse by setting the parameter V to a constant. This constant is called the spheroid index and it can be changed by means of a data card. If the spheroid index is set equal to one, the resulting field pattern would be that of a dipole, and as the index is increased to larger values of V, the pattern approaches that of a sphere.
The positions of the dots plotted to make a line are all calculated by the same method, but it is easier to see how this is done for the ellipse than for the field.
The variable V0, is set to a constant value, as determined by the spheroid index, and the variable U is set to zero. This determines the first point to be plotted (a in Figure 9).
The next point is calculated by incrementing U and then calculating the distance back to the first point. If this distance is within preset limits, the X and Y values are stored; if not, the increment in U is adjusted by the amount of the error in distance and the point recalculated. When the value of U reaches one, equivalent to being on the Y axis (point b), the program jumps to the next section.
The spacing of these points is very important. A series of plotting dots will overlap to form a line if they are plotted in every other cell. The scale the programmer is using determines the distance between the dots and the size of each cell determines the amount of error in this distance that should be allowed, The error should be as large as possible because the iterative process used will require less passes to be within the error. At the same time, if the error is too large, it is possible to plot a point that is far enough away to have a gap in the line being drawn. Figure 10 was used to determine how big the error should be. The asterisk is the center of the dot that has been plotted and the cross shows the centers of any dots that will be plotted if the calculated point falls anywhere in the particular cell. The error shown in the figure was chosen so that two cells side by side would not be plotted. There is a small chance that a call three spaces away on the disgonal will be plotted, resulting in a small gap in the line, if the calculated point falls in the crosshatched area. Assuming that the next calculated position can fall anywhere in the error band with equal probability, approximately three per cant of the dots will fall in this category.
The rest of the program can be divided into two steps that are repeated as many times as necessary. In Figure 9 point c is calculated and U is incremented upwards until point d is reached. At that point, a sine term in the field equation is shifted by 180 degrees and U is incremented downwards to calculate the points lying on the line from d to e. When U reaches zero again at e, the input data is changed and a new line is calculated.
In the section on the mathematical basis of field patterns, the equation for the streamlines was developed in terms of the U-V coordinate system. The final result for the streamline calculations was
For the purpose of computing the points along a streamline, K is set to a constant and the above equation is solved for V.
The value of K determines the particular streamline in a cycle. The different cycles are computed by adding 2n (n positive integer) onto the value of V for the first cycle. n is the number of cycles away from the origin. V also contains the information as to the time in the cycle of radiation. The position of a point on a streamline at any time in the cycle can be determined by adding the time increment to V before the transformation to cartesian coordinates. The time variable in the computer program is labled DTME and appears in the expression for V.
Point c is calculated by setting U to zero, calculating V, adding the time to it, and then calculating X. Points are calculated in the same manner as described for the ellipse. It is easy to tell when d is reached because at that point
and the arcsine cannot be calculated. If the last point calculated is close to the maximum point of the curve, the program switches to the next cycle of the arcsine. If there is enough distance left on the curve, a few more points are calculated to fill in the top before the suitch is made.
This occurs at statement L17.
The rest of the program increments U downwards and calculates that the next line is ready to be computed.
If a streamline is being computed that is close to the spheroid, it may enter the spheroid rather than returning to U=0. In this case, the program immediately jumps to the next line.
When all of the points have been computed for a particular scene, a call to APLOT computes the necessary SC 4020 commands to plot each dot. Subroutine PLOT generates four plotting commands to fill the four quadrants for each set of X's and Y's and places them on tape.
The basic program described above was used for the next four scenes in the movie.
The scene demonstrates how the streamlines are formed. Only the generator symbol and current distribution on the spheroid shows. The streamlines emerge, one by one, until the screen is filled. It was computed by generating four cycles (enough to fill the screen) but by starting at a negative time. This negative time was large enough when added to V that even for the fourth cycle the total V was smaller than the spheroid index. Therefore all four cycles fall inside the ellipse and the streamlines are not computed. As time is increased between each frame, V gets large enough to let the streamlines appear one by one. As they flow outwards, more are generated until all four cycles appear.
In this scene, time is not incremented between frames. Therefore, the field pattern does not move. Instead of the generator symbol appearing in the center of the spheroid, two rulers appear. One is vertical and measures the distance between the focal points, the other is horizontal and measures one cycle of streamlines at the right of the screen. The idea is to show the viewer that there is a relationship between the size of the spheroid and the wave length and that the wave length is in fact greater near the spheroid.
The concept of resonance is another area where ground has just been broken. Several suggestions were made to have clocks to show the idea of frequency and wave length in this example but there was not time enough to try out these ideas. Again, the hard part is not the programming but how to get the concept across to the viewer.
The main program was run with the time limits set to give a complete cycle moving out from the spheroid. This section was actually computed in two sections, one with five cycles of streamlines, the other with four. By doing this, it was possible to cut down on the computing time while still filling up the complete screen. In the moving segment part of the movie, the switch in the number of cycles used was made automatically by the program so that a whole cycle of motion could be made at once and time would still be saved by having as few off scale points as possible to compute. If this scene were to be done again, it is suggested that this feature be added.
The displacement current moves in a direction always tangent to the streamlines. The motion was implemented by placing segments in the streamlines that moved around a center in each group of lines. This motion is independent of the outward motion of the radiated field as far as the program is concerned.
The missing segments in the streamlines were created by omitting certain dots when the plotting commands were placed in the buffers in the STORE subroutine prior to placing them on tape. As each line is computed, the dots are counted. Twenty-four dots are plotted and the next twelve are skipped so that each streamline consists of a section followed by a gap that is half as long. Motion is generated by properly positioning the gaps between each frame so that the breaks appear to move along the streamline. The problem is complicated by the fact that the motion has to reverse direction between each group of lines.
The basic program computes the spheroid for each frame and then computes each set of lines. Between each set, a call to APLOTV puts the dot commands on tape. When the specified number of groups of lines have been computed, the program returns to the start to compute a new frame. As the X and Y values of each point are computed, it is stored in an array until the call to APLOTV.
The key to the moving segment program lies in the fact that all points that are computed always lie in the first quadrant.
The value of X and Y is always positive so that when the array is called by APLOTV, the control word sent to the (PLOT) subroutine has the following characteristics:
00 1xxx 52 1xxx
Plot X Dot Y
Op Code Value Value
The two zeros are the operation code for plotting and the 52 is the code for a dot at tha specified location. The call positions run from 0000 to 1777 (octal) with 1000 falling on the centerline. The (PLOT) subroutine manipulates the X and Y values to give command words that will plot the other three quadrants.
It was decided to let (PLOT) count the dots that had been plotted to determine if a line or a gap was present and therefore if the dot should be plotted or not. Since the number of dots required for each line depends on its length which is an unknown quantity, the main program has to determine when a line starts. It would have been possible to call (PLOT) directly to start the counting, but another method was used instead. In addition to the values of the position computed by the main program, some values were included that resulted in points plotted in the second quadrant. The (PLOT) subroutine was rewritten so that instead of plotting these words, they would serve as controls to start the counting of the dots along the line. Therefore, this problem can be broken up into two sections. The first is the additions to the main program to create control words and the second is the use of these words in the (PLOT) subroutine.
A brief outline of the main program is:
START
DO EACH FRAME TO L14
COMPUTE SPHEROID
DO EACH SET OF LINES TD L16
DO EACH LINE TO L9
COMPUTE LINE
L 9 CONTINUE
CALL APLOTV
L16 CONTINUE
CALL FRAMEV
L14 CONTINUE
ENDJOB
The array that stores the data as it is computed is labled Q(N) for the X values and R(N) for the Y's. The following statements were added to the main program.
START
DELDOT = -.00332
SET1 = -.00166
DO EACH FRAME TO L14
Q(0) = -1.69502
R(0) = -.066406
SET = -1.69834
SET2 = -.00664
COMPUTE SPHEROID
DO EACH SET OF LINES TO L16
DO EACH LINE TO L9
Q(N) = SET
R(N) = SET 1
COMPUTE LINE
L 9 CONTINUE
CALL APLOTV
SET= SET - SET2
SET2 = =SET2
L16 CONTINUE
CALL FRAMEV
SET1 = SET1 + DELDOT
L14 CONTINUE
ENDJOB
The original statements are underlined. Each one of the values above were chosen so that when APLOTV was called the command word produced by XSCALV through APLOTV would have a certain format that can be recognized by (PLOT).
The first X and Y values to be read into the array at the beginning of each frame are
Q(0) = -1.69502
R(0) = -.066406
This will result in a command word as follows
00 0001 52 1012
The 00 and the 52 are constant throughout. However, notice that the third digit from the left is a zero. Since any command word that is to be plotted always has a 1 in this position, the presence of a zero indicates that this word is to be used by (PLOT) to set counters and not plotted.
The 1 in the sixth position from the left is used as an indicator that all the dots in a line are to be plotted. If a zero appears in this position, it indicates that the segments should appear and move counter clockwise in the first and fourth quadrant. The presence of a two reverses the direction of motion. The reason for plotting all the dots at this point is that the spheroid should not have any segments in it.
At the start of the first line, the following values appear:
Q(N) = SET = -1.69834
R(N) = SET1 = -.00166
These two values will be combined to form the word
00 0000 52 1000
The first underlined zero indicates that this is a control word, The second zero indicates that the motion of the segments should be counter clockwise. The last two zeros are used to set the counter and will cause the segments to move between each frame.
The above values are in the innermost loop so the control word appears at the start of each line.
When all of the points in the first line have been computed, the above word is repeated for the next line. When all of the lines in a set have been computed and the values read into APLOTV, the value of SET is changed by the statement
SET = SET - SET2
The sign of SET is changed for the next cycle and a new set of lines is computed. This time the value of
Q(N) = SET = -1.6917
R(N) = SET1 = -.00166
will result in the word
00 0002 52 1000
The zero has been changed to a two so the motion of the segments will reverse. For each set of lines, the sixth figure from the left will alternate between a zero and a two for as many cycles as there are in a frame.
When a new frame is to be computed, the value of SET1 is changed by adding DELDOT to it. SETA has a value of -.00166 to start. DELDOT changes this by a negative increment of -.00332 which results in one being added to the last two digits of each control word. For example
00 0002 52 1000
should become
00 0002 52 1001
00 0002 52 1002
00 0002 52 1003
and so on for each succeeding frame.
These controls are interpreted by the (PLOT) subroutine.
Called 4-QUAD(PLOT)#2
This subroutine divided the plotting area into a top and a bottom. Two index registers are used to count the number of dots that have been plotted using modulus "thirty-six" as a base. If the tested index register contains zero to eleven, the dot is not plotted. If it contains twelve to thirty-five, the dot is plotted. If it contains thirty-six, it is reset to zero. After each set is plotted, the index register is increased by one.
The subroutine tests the incoming control word,and if the two highest order digits (six bits) are not zero, the word is not a plotting command and it is placed directly in the buffer contained in STORE.
If the two highest order digits are zero, index registers IR1 and IR2 are loaded with the numbers they held when this call was last made. The incoming word is next tested for the presence of a one in the third highest order bit. If a one is found, the dot command is to be plotted. IR2 is tested and if higher than eleven, a dot is plotted in quadrants I and II. 1R1 is tested to see if quadrant III and IV should be plotted. Both index registers are raised by one, reset to zero if they read thirty-six, and the contents stored for next time. Control then returns to the calling program. This portion of the program occupies about the first half of the statements on the subroutine.
If the incoming word starts with two zeros and the third digit is also a zero, the plotting determination is skipped and the second half of the subroutine comes into play.
Figure 12 shows how the dots would look near the center line of the field pattern for ten frames in a row if the right-hand segments are moving counter-clockwise. The small numbers are the magnitudes that have to be placed in the index registers at the start of each line in order to make the segments move properly.
For example, in the fifth frame a 32 is placed in IR2. This causes four dots to be plotted and then the next twelve are omitted. IR1 has a 16 placed in it to start. The tuanty dots plotted before the gap match the four plotted above the line to fill out the twenty four dot line segment crossing the center line axis. Another graph identical to Figure 12 can be made up in which the segment moves down instead of up.
The subroutine places the correct starting count in the index registers by analyzing the incoming words that start with three zeros. If the sixth number is a 1, the indexes are set to twenty and not incremented. This causes all of the dots to be plotted for the spheroid. A zero or a two in the sixth position in combination with the last two digits are manipulated to give the proper number in each index register. All of the segments in any one group of lines move together and the left-hand side of the pattern is a mirror image of the right.
Off scale dots have to be counted also or the segments would jump as the lines move off the edge of the screen. The subroutine XSCALV has been modified to call (PLOT) and insert the word
00 0000 60 0000
into the (PLOT) subroutine. Under normal conditions, this word has no effect because it plots a blank at zero-zero. However, the segment generating (PLOT) subroutine will increase the count in each index register by one upon receipt of this uord,
One complete cycle of outward motion requires twice as much time as the steady state scene because two complete cycles have to emerge from the spheroidal radiator instead of one. This is due to the fact that the motion of the segments reverses between every group of lines. The group of lines has been referred to as a cycle several times in this work but actually the complete cycle of a spheroidal radiator is represented by two groups of streamlines.
Another timing factor has to be considered if the one computed cycle is to be run through the SC 4020 several times in order to make several minutes run time for this scene. The position of the lines in the last frame has to match those of the first, but also the segments have to have just finished moving across the center line to match the start. This requires that the number of frames in a cycle be divisible by thirty-six to make this match. Figure 13 shows the segments inserted in the spheroidal radiator. END scene.
TABL5V was written to place the block letters
THE END
in the center of the screen by using RITE2S. The program for this scene changes the size of the letters from minimum to maximum in steps between each frame. The effect when the movie is run is that of the letters coming towards the viewer out of the screen.
Table 2 summarizes the computer time required, length of magnetic tape, number of frames, and running time for each scene in the spheroidal radiator example. The movie was calculated in several segments which were then combined during the copying process. The final result was three reels of tape.
The finished product had a few minor faults due to programming errors and a major difficulty during the running of the magnetic tape on the SC 4020.
The minor errors were of a sort that can be corrected easily. ror example, the ellipse did not shrink properly from the large drawn one to the center of the radiator. A change of one variable in a calling parameter could correct this. However, this points up the fact that each scene should be checked by hardcopy production before the computer time is invested in the final run. Also, the hardcopy gives the programmer an actual representation of his work that cannot be visualized from the numbers alone.
The major difficulty was that even though great care was taken in recording the magnetic tape (see the section on program running operations in Appendix B) there was still false information seen by the SC 4020 that resulted in many blank frames in the finished movie. Also, some of the information was lost resulting in a spotty picture.
| TAPE | FILE | SCENES | TOTAL 7094 TIME (mins) | TOTAL WORDS | RECORDS | FEET OF TAPE | FRAMES | TIMES TO RUN | TOTAL FRAMES | MOVIE RUNNING TIME (mins) |
|---|---|---|---|---|---|---|---|---|---|---|
| I | 1 | 598,084 | 1869 | 655 | 1869 | 1 | 1869 | 1.29 | ||
| 2 | 1,338,889 | 1351 | 1289 | 88 | 1 | 88 | 0.06 | |||
| 3 | 241,746 | 245 | 246 | 35 | 7 | 245 | 0.17 | |||
| II | 1 | 887,937 | 880 | 854 | 25 | 12 | 600 | 0.42 | ||
| 2 | 884,396 | 872 | 850 | 25 | ||||||
| III | 1 | 880,359 | 884 | 848 | 72 | 12 | 864 | 0.60 | ||
| 2 | 8,581 | 132 | 16 | 132 | 1 | 132 | 0.09 | |||
| (Totals) | 4,840,000 | 4758 | 3798 | 2.63 | ||||||
There are a large number of companies that make visual output devices to be used as peripheral equipment associated with a digital computer. However, most of these are not of interest with regards to this work because they have no provision for permanently recording their output.
The devices described below do produce permanent records and therefore can be used to make a movie of computer-generated output. They ware chosen because they are representative of what is actually commercially available and of what is being developed in the computer manufacturer's laboratories. They cover the range of available tools that can be used to produce movies today.
The CALCOMP digital incremental plotter manufactured by California Computer Products, Inc. is a mechanical plotter that produces paper output in the form of graphs. Like most computer-graphic equipment, it was designed to create engineering output and not pictures. It is limited to drawing lines under computer control although quite a bit of software programming has been developed to create symbols, label graphs, and scale plotted points. The OSU computation center is equipped with one of these plotters. A body of subroutines is available as part of the computer library.
The CALCOMP plotter is useful when it is desired to plot out single frames of electromagnetic fields. It was originally planned to use this type of plotter to make the spheroidal radiator example using the following technique. The mathematical description of the radiated field would be used to calculate the field streamlines at one particular time. The commands for the particular plot would be punched on cards by the IBM 7094 and these cards would be used to drive the plotter. The plotting would be repeated at different times to complete the cycle and the total number of scenes would be animated using regular film techniques. In fact, a length of film was produced in this manner but it was not satisfactory for several reasons.
Because of the limitations on mechanical plotting speeds, up to forty-five minutes of computer time was required for each picture. The time increment to give smooth motion without jumps was in a range that meant at least thirty-two different plots had to be made for each scene. The film animation techniques proved to be very time consuming and difficulties were encountered in accurately placing each frame as it was photographed to give proper register when the movie was shown,
Another disadvantage is that this is an incremental plotter and therefore the commands generate a specified step length in only eight directions at forty-five degree angles. This puts a severe limitation on the amount of resolution that can be obtained unless the drawings produced are very large. Even with the first two by two and one half foot drawings, this resolution limitation could be clearly seen. The newer plotters are better in this respect (twenty-four steps instead of eight) but it seems difficult to imagine producing any volume of film with a mechanical plotter.
The second commonly available device is the SC 4020 microfilm plotter, manufactured by Stromberg-Carlson, Inc., which reads magnetic tape or computer output to produce graphical, pictorial, or alphanumeric output directly on film. Since a complete description of this device is given in this work, details are not covered here. The heart of this device is a cathode ray tube that can be photographed directly with both the display on the face of the tube and the camera being controlled by computer output.
Because a cathode ray tube, whose beam is without inertia for all practical purposes, is used to perform the actual plotting, the limitations in plotting speed are not determined by a mechanical movement. Instead, the speed limitations is set by the rate at which the computer can transmit information from one place to another. As this transmission is being performed at computer speeds, the increase in plotting rates over a mechanical recorder is appreciable. In the spheroidal radiator example, some of the drawings took approximately forty-five minutes each. When the same plots were duplicated using the SC 4020, the total time to complete each scene was about five seconds.
Two other machines have recently come onto the market, one of which is a serious contender for the spot now held by the SC 4020. The CALCOMP 835 electronic digital plotting system is a new plotter that is meant to complement their mechanical plotters rather than replace them. The digital logic has been constructed to make the cathode ray tube operate as an incremental device with the direction and position specified for a preset step size. The interesting thing about this plotter is that it is compatible with the current software programs available at OSU for the mechanical plotter. The only difference is in speed, up to 100,000 steps per second instead of 200 steps per second achieved at present. This unit has another advantage in that it is the least expensive unit now available ($76,000) that could be considered for making movies. Unlike the other plotters described, it does not produce hardcopy, so the 35 mm film has to be developed before a print can be made.
The B-L 120 plotter manufactured by the Benson-Lehner Corp. is almost a direct replacement for the SC 4020. Its design was obviously influenced by the other because magnetic tapes made for the SC 4020 can be run on the B-L 120 providing one minor precaution is observed.
A record gap (a blank space on the tape) has to follow an advance film command on tapes that will be run on the B-L 120. This is not necessary with the SC 4020.
According to the manufacturer, this plotter has approximately twice the speed of the SC 4020 and in addition, logic is provided to check for tape errors. This is the ability to run a record over again if the machine hits a command that it does not recognize. The SC 4020 under similar conditions puts an error mark on the edge of the film and then skips to the next record. This error can occur if the magnetic tape was produced in the presence of noise so that the bit levels on the tape are obscure. All of the description in the chapter on the SC 4020 also applies to this unit. One detail is interesting, the announced price for the B-L 120 ($100,000) is approximately one-fourth that of the SC 4020. This may be a reflection of the fact that the SC 4020 has been the only machine of its type in the market and if so, a drop in price should occur.
The DD 80 microfilm plotter manufactured by Control Data Corp. of Minneapolis is a good example of a third generation machine. The SC 4020 and the B-L 120 can be considered as a second generation, and the CALCOMP plotter as a first generation. As such, the DD 80 hae all of the features of the other plotters, but it has in addition several advance options that make it especially attractive for making movies. Its control logic operates on a different principle that results in much less data being transmitted for the same amount of information to be recorded. This is significant in movie making where the computed data is liable to be voluminous and the cost of the computer time is far greater than that of the plotter.
In the SC 4020, a single input number of thirty-six bits is used to represent both the operation and the location where this operation is to take place on the screen. In a third generation device, the operation code and the position codes are separated. An operation code is sent to the machine that tells it to perform this operation until another operation code is received. For example, the code might be to plot a dot on the screen. Thereafter, until the receipt of another operation code, all information fed to the display device will be location only. Some idea of the time that is saved by using this method can be gained from the fact that in the spheroidal radiator movie some scenes contained fifteen thousand dots plotted in sequences. In the SC 4020 the status, namely that a dot was to be plotted, had to be determined for each of the fifteen thousand commands. On the other hand, where the operation code is used to set a status, three locations can be stored in each of the following command words. This compression of information plus the fact that the operation code does not have to be interpreted each time will result in a four-fold increase in speed at a minimum using the same hardware. Actually due to increased machine speeds and better information transmission handling methods, the increase in speed is more likely to be twenty times as fast. The SC 4020 will plot about twelve thousand characters a second, and the BL 120 about twenty thousand characters a second. In contrast to this, the DD 80 will plot up to two hundred thousand characters per second.
Another vary important feature of the DD 80 is that it has a dynamic memory rather than an input buffer. An input buffer is a temporary store that only holds information for a short period of time. If the information is not recorded immediately, it is crowded out by new information coming in and is lost as far as the recorder goes. On the other hand, the dynamic memory allows the programmer to accept a certain amount of information, depending on the size of the memory, and hold it in store while writing it out on the face of a cathode ray tube display. Each command in the memory is cycled at a rate to keep a continuous picture on the CRT display. By placing several frames in the memory and cycling the full amount of information present, a scene from a movie can be checked before the film is recorded.
If an error is discovered or the programmer wishes to make a change in a scene, there are three methods available to insert changes once the data has been placed in the dynamic memory. The first is a teletypewriter that can be used to modify any command word in the memory. The effect of any changes made can be seen immediately on the large CRT display. The other two methods are similar and only the means of actuating the display are different. The display comes equipped with both a light pen and a trackball. The light pen has a two position detent switch mounted on it. The first position turns the light on to form a spot on the screen. When the switch is pressed into the second detent, the position of the spot is inserted into the memory and the last action that was typed in takes place at that location. The light pen can be used to delete or replace characters, draw lines, and do general editing before the scene is recorded. The trackball is a phenolic ball mounted in the desk in front of the display screen. The top of the ball sticks slightly out of the top of the desk and is connected to two digital encoders that keep track of the X and Y movement of the ball. When a switch is thrown, a circle with a point in the canter appears on the screen corresponding to the X and Y encoder positions. As the ball is moved, the circle will follow. Another switch serves the same purpose as the second detent in the light pen.
It is obvious how helpful these features would be in the production of a movie. If the dynamic memory were big enough, not necessarily the case with the DD 80, each scene of the movie could be edited before it was recorded without the time and expense of having to compute the entire scene over to correct a few minor mistakes.
The trends of the future can be clearly seen in the computer graphics equipment that now exist in prototype form at both the university and the computer manufacturer. Table 3 summarizes some of the efforts in this area. In each case, these have to be considered as prototype efforts because, unlike the DD 80, they are not being offered as a commercial item by the people involved. There are undoubtedly other systems in existence but these have received the most publicity.
| NAME | FULL NAME | SPONSOR | COMPUTER INPUTS | MANUAL INPUTS | FILM OUTPUT |
|---|---|---|---|---|---|
| DAC-1 | Design Augmented by Computer | General Motors | ON LINE (2-7094s) | Light Pen, Electric Pencil, Keyboard, Card Reader | Yes |
| Graphic-1 | Graphic 1 | IBM-Bell Labs | ON LINE | Light Pen, Keyboard | No |
| MAGIC | Machine for Automatic Graphics Interface to a Computer | NBS-NASA | ON LINE | Light Pen, Switches, Keyboard | No |
| GPOS | General Purpose Display System | System Development Corp | ON LINE | Light Pen, Rand Tablet, Keyboard,Teletypewriter | Yes |
| COED | Computer Operated Electronic Display | Bendix | Magnetic Tape | Track Ball,Switches | No |
| Sketchpad | Man-Machine Graphical Communication System | MIT-Project MAC | ON LINE (Special Purpose Computer, Paper Tape | Light Pen, X-Y Knobs, Many Switches (not key board) | Yes |
Two trends are evident. The first is that efficient systems, whether they are just for research or can also make movies, will have to be run ON-LINE in real time with a computer that has a very large memory in order to try the effects of different inputs as the results are being produced. One of the main difficulties to date is that with even the largest scale systems (GM's two 7094's, for example), the response is very slow because of the vast amounts of information that have ta be moved from place to place in the computer.
Some idea of the difficulty can be obtained from BEFLIX [20], a computer language that has been developed by Ball Telephone Laboratories for the production of animated movies by a computer. In this particular language, the cells on the screen of the SC 4020 are treated as a television raster with a location reserved for each cell in the IBM 7090 being used. Two complete frames take up the entire storage, so a large disk file had to be added where up to 440 frames can be stored. When peripheral equipment such as disk or tape is involved, the needed time is increased by a far greater amount.
The solution to this problem may be found in the concept of parallel processing now under investigation at the University of Illinois. Instead of having only one central processor which does one arithmetical or logical operation at a time, this computer would have a hundred or more processors so that large increases in throughput speeds can be obtained without a corresponding increase in hardware speeds.
The other item common to most of these systems is the light pen used to edit and modify displays on a cathode ray tube. A control of this type would seem to be a necessity when making movies to save on the amount of programming effort required to make changes.
An interesting variation on the light pen is the Rand Tablet. This is a plate with 1024 × 1024 wires embedded in it with just the ends showing. When the circuit is completed by running an electric probe over the surface, the computer stores the circuits which were completed and controls the cathode ray tube to follow the path of the probe. Therefore, it is very easy to insert lines and curves into a display, but they will not have the linearity of a programmed line. In addition to the Rand Tablet, software is needed to make lines straight and circles round after they have been drawn.
The spheroidal radiator example was produced by very conventional methods of programming. A program for each scene was written, typed on cards, debugged by several runs through the computer, and then joined to the larger program being constructed. In each run, the feedback to correct a program was delayed by hours spent waiting for it to be returned.
As the Sketchpad engineers have pointed out[21], a display system with a cathode ray tube allows one to communicate with the machine by means of line drawings instead of written words. It is obvious how much time can be saved when an object can be drawn rather than described. Since computer generated movies involve highly complex and abstract pictures, a visual display would seem to be almost essential in order to determine the program being made.
By using a type of input-output where there is very close cooperation between the man and the machine, the burden is placed on the programmer to write software that is man oriented rather than machine oriented. This, of course, will aid the movie producer because he can now concentrate on what the scene should show and not on the programming or debugging details.
However, there are still many unsolved problems. The one of speed was mentioned above. Although the display device is essentially a two dimensional one, several people are experimenting with three-dimensional movies, either by using perspective views or a stereoptican process where the viewer wears polarized glasses. The newer SC 4020's are equipped to plot dots with eight different shades of gray. This means that the programmer could get away from the type of drawing that can be produced on a blackboard and into drawing where halftones are important. For example, the direction of motion of an object could be shown by leaving a trace that slowly fades out after the object has passed.
Another area that has not been touched is that of color. One way that this could be handled would be to have a wheel in front of the movie camera with filters containing the primary colors in it. The camera would be loaded with color film and each scene would consist of several exposures, one for each color. The program would control the position of the color wheel and the result would be like that of color printing.
At the present time, movies are produced by having one computer do the necessary calculations and another expose the film. Consideration should be given to have the camera as an integral part of the computer. It would serve as the final storage for information being generated. Particularly in the case of recurring or cyclic motion, the scenes for one cycle could be stored in a disk memory associated with the computer and then recorded over and over again to produce the required footage of film. Both disk and tape have very fast access times if the information is going to be read in serial form so that the unit does not have to go through a search procedure. The disk would be preferable where modifications were going to be made via a CRT and light psn because the response time to place changes on the disk would be faster then that of tape.
Unfortunately, the cost of implementing these ideas would be very high. The hardware, in large parts, exists today, but the programming effort would incur an amount of time and money that is beyond the reach of most organizations. Perhaps the cost of such a machine could be justified by the production of movies in many fields and not just electrical engineering. In any event, a university would seem to be the ideal place in which to have such an endeavor considering that experts would be available in all necessary fields from antennas to human factors.
The use of microfilm plotters to produce computer-generated motion pictures has opened a new area in explaining electrical engineering phenomena. The technique described in this work will be especially useful in the classroom in helping the student understand the reasoning behind the mathematics placed on the blackboard, and it can also be of assistance in research where the movies produced would serve to reduce pages of figures to a few clear pictures.
The computer is beginning to play a dominant role in electrical engineering education and research, and while the labor that the computer replaces allows for more complicated problems to be handled, the output is in a form that tends to overwhelm the researcher who is trying to interpret the results. It is hoped that this work will help reverse the trends that the computer has sat in motion and that computer-generated movies will find common use in the classroom and laboratory. It is especially applicable to electromagnetic fields and the applications described were primarily in that area,
The technique consists of using a large computer (such as an IBM 7094) to calculate the desired results, such as the points of constant potential in the electromagnetic field produced by an antenna, and then converting these points into commands that can be interpreted by a high speed microfilm plotter. The parameter time is varied and the data is plotted frame by frame for each time increment. The final result is a series of plots on sixteen millimeter film that can be run as a movie to show the motion involved. Up to now, the researcher had two choices: either cartoon animation, or a still frame showing the subject at one instant in time while the associated text described the motion. As some of these motions are complicated, there are times when even a lengthly description does not get the point across. It is in these cases that being able to.produce a motion picture would be invaluable to the student.
The number of subjects in electrical engineering to which this method could be applied seemed to be greater in the area of electromagnetic fields, so the possibilities were considered mainly from that field. These included transients on transmission lines; plane waves of different polarizations hitting a dielectric slab at various angles; fields in wave guides; and the radiation from antennas, diffraction, and scattering.
In order to study the concept of computer-generated movies, a three-minute example entitled The Resonant Spheroidal Radiator was programmed! This was a complete movie from the title to THE END and it was an attempt to show both what the subroutines could do and more importantly, what the techniques could do for electrical engineering.
In the course of writing programs that resulted in the movie example when run on the SC 4020, many limitations were encountered that were due to the machine and not the programming. For example, it was impossible to edit any pictures before committing them to film. Therefore, the computer-graphic equipment now in prototype form was investigated to determine what future trends might help the computer movie programmer.
One point should be made. The particular programmer cannot use these subroutines to support his own lack of understanding of the problem on which he is working because the input data to the subroutines must be the correct solutions to the problem being considered. However, under this limitation, it should be able to accomplish a helpful trend in electrical engineering. At the present time, most effort is directed towards determining the mathematical model from the physical theory until the reality of the system is lost in the mathematical details. When one is going to program a movie of physical action from the mathematics, one is forced to think back to what one is actually trying to explain. This should help greatly in eliminating the confusion that can easily arise between mathematical analysis and experimental evidence,
The first conclusion reached in the course of this study is that computer-generated motion pictures have a definite place in electrical engineering. The mass of formulas and figures presented to the student in the classroom may be meaningless, but if a movie can be shown that illustrates the physical aspects of the mathematics, a greater understanding and appreciation of the reasons behind them can be gained. The main requirements are that the subject can be expressed mathematically and that the motion be important enough that a movie will show things that would be missed in still pictures.
The importance of motion can be expressed in two ways. The first of these is motion in time. For example, this motion can be used to express the form of electromagnetic fields far more affectively than by any other method. In fact, this seems to be one of the best subjects for these computer-generated motion pictures.
The second consideration is to use the motion to explain the effect of a parameter other than time in a system. A good presentation would be to show the effect that varying the position of the poles and zeros in a root locus diagram has on the stability of the system under consideration.
In electrical engineering research, the methods developed in this work can be used to gain time in the processing and understanding of results that can be checked by the computer. For example, a motion picture of a plasma field might be compared to a motion picture of the mathematical model of the same field to sea if the analog is correct. Hand plotting would take far longer and would not be nearly as effective.
The second problem that was solved in this work was how to give programmers at OSU a working system to produce motion pictures from computer output. Although the future holds great promise in the developments in computer-graphics, at the time the movie example was being produced, the available graphic output equipment was pratically limited to one device the SC 4020 microfilm plotter by Stromberg-Carlson. This device was originally designed to produce engineering graphs or tabulated data in the form of thirty-five millimeter microfilm or 9 × 9 inch hardcopy. Therefore, an extension of the OSU Numerical Computation Laboratory operating system was written so that the SC 4020 could be used to produce movies at 0SU. This extension consists of about fifty subroutines that enable a programmer to concentrate on programming of the movie itself and not on the details of how the SC. 4020 operates.
The main reason that such a device can be considered for making movies is the speed with which it plots. It can draw vectors or plot points at 12,500 a second, so in the course of about fifteen minutes an amount of film can be produced frame by frame that would take days of animation by any other technique.
The SC 4020 has a limited range as a computing device and in fact the only thing it can do is either plot a character at a specified location or draw a vector from that location in a specified direction. Since it was assumed that the people using this device to produce movies would know how to program the desired results but would not necessarily know how to use the SC 4020, software was written and debugged to remove this chore from the programmer's hands. Therefore, one of the accomplishments of this work is a body of subroutines that will accurately create the desired pictures. All that the programmer has to do is calculate touching points along any line to be drawn or, if straight lines will suffice, the end points of these lines. The subroutines will take care of the rest from calculating the proper plotting commands to writing the magnetic tape used by the SC 4020.
One difficulty overcome in writing these subroutines was a computing language conflict. A subroutine library existed in FORTRAN II for producing engineering output and it was desired to use this as a model for the movie-making subroutines. Using this library saved several man-years of programming, but a conversion had to be made to SCATRAN, the language used at OSU. The input-output routines were completely rewritten due to the difference in handling magnetic tape between the two systems and conversion programs ware written so that the available FORTRAN subroutines directly useful in movie making could be used. In addition, details are given so that the programmer can construct any desired symbols or figures out of straight lines without the bother of having to calculate the position of each break-point in the drawing.
The final result was extremely successful. At the present time, OSU not only has the capability of producing a magnetic tape that can be processed by any SC 4020, but several other plotters are coming on the market that use the same command code words. The BL 120 by the Benson-Lehner Corp. will run SC 4020 tapes subject to the minor restriction that any advance film command be followed by a record gap.
The complete programming and subroutine system for this plotter is described in great enough detail in Appendix B of this work that it would be possible for a programmer to duplicate the system without difficulty.
During the programming of the example described before, a number of problems were encountered that could not be foreseen. To save grief and difficulty on the part of those who might use these subroutines, a section on program running operations was included in this appendix,
In addition to the operating system described in Appendix B, the listings for the necessary changes so that these subroutines could be run under FORTRAN have been included in Appendix C. This would be a great convenience to someone trying to use them outside of OSU. Finally, there will undoubtedly be plotters coming on the market that use a different code than the SC 4020. Evan though these could not be used directly in that case, they can still be used as a useful guide as to what is required for making movies.
The next problem to be solved was to show first that the body of subroutines was capable of actually producing a movie and, more importantly, proving that computer-graphics have a definite place in the production of movies of electrical engineering phenomena. The final result was a three-minute movie entitled The Resonant Spheroidal Radiator which was made to serve as a demonstration of both the use of these programs and of the basic ideas behind them.
The spheroidal radiator as a radiating antenna has been investigated in some detail by Stratton, Chu[18], and Ryder[19] , but their final results left something to be desired for the average reader. Therefore, this seems to be an ideal subject, namely, it was mathematically complex, time was a basic parameter, and, at resonance, the streamline equations gave an interesting picture without an excessive amount of programming. Incidentally, all of the programming was done by one person, and therefore it is also a good example of what a researcher interested in a particular function of antenna design could do without a team effort.
Up to now, this effort has resulted in endeavors that are primarily of interest in the classroom, but the above example is just a start on something that could show the usefulness of computer-generated movies in electrical engineering research. The resonant case was picked for the spheroidal radiator because the solutions that were available ware reasonably tidy in closed form. However, the authors who have investigated this problem also give series solutions to the differential field equations for all frequencies and it would be extremely interesting to see what the near field, in particular, looked like as the antenna was driven by a range of frequencies passing through resonance.
The last scene of the movie was particularly interesting because it shows the results of two different motions at the same time. The lines indicating the field are calculated from lines of constant potential and also show when the magnetic field has constant phase. In addition, the displacement current is shown by means of segments that move along the streamlines. They reverse for each radiated cycle to indicate the alternating field. It is felt that this concept could be extended to a number of different cases in electro-magnetic fields where it would be desired to show both the electric and magnetic fields by means of the displacement current streamlines.
The movie was successful except for soma difficulties in processing. These were the fault of the particular SC 4020 used and not the programming, but it would be necessary to make certain that all errors and noise are removed before a perfect copy could be achieved.
When the scenes in the movie are compared with the mathematical formulas used to develop them, it is felt that this demonstration definitely proves the value of computer-generated movies in the human interpretation of exceedingly complex electrical engineering phenomena.
The fourth problem arose as a result of the work on the demonstration movie example. It was found that the SC 4020 is extremely limited in concept because it was originally meant only to make microfilm documents from computer tapes. Even with the addition of extensive software tailored for producing movies, there were a number of features that could have been desired to help the programmer. Therefore, a number of computer-graphic display systems were examined to see what was in the future as far as the present state-of-the-art is concerned. The conclusion reached was that it would be possible to build a device that could accept programs, display the result frame by frame, and then immediately produce an animated movie, but such a device would have to have both a bigger and faster memory than any machine on the market today.
Display equipment is improving rapidly, but no displays have yet been offered that are expressly made for producing movies. It was found in the course of this work that the ordinary microfilm plotter would not be sufficient, principally because of the registration problems with the film camera. It was felt, however, that even with the small survey that was made, computer-graphics will become one of the fastest growing fields in the area where computers and education meet.
In conclusion, the computer is swamping electrical engineering researchers and students with its output, and the production of computer-generated movies would seem to be one of the best ways that a balance can be restored. The technique developed and demonstrated in this work will serve as a valuable accessory in promoting understanding in both electrical engineering classrooms and research.
Quite a bit of the detail in the Appendices are less relevant due to the demise of FAP, SCATRAN and the SC 4020. The Appendices have been shortened with more appropriate detail where relevant.
This appendix gives the details for solving a conflict in programming languages that occurred when SC 4020 subroutines written to be called from FORTRAN main programs were used as a model for subroutines that were to be called in the OSU SCATRAN language. Both FORTRAN and SCATRAN use FAP (FORTRAN Assembly Processor) as a basic machine language but there are enough differences between the two systems that a subroutine written to be called in one language cannot be called in the other. A brief description of the FAP language is given covering only those areas that are affected by the above differences. Two programs are then compared so that the calling structure to the subroutines can be determined. Finally, a sample conversion program is described to enable the programmer to run subroutines written outside of OSU under the SCATRAN system.
The FAP language is a basic machine language used by the IBM 7094 computer. No matter what source language is used, the compiler will eventually write the program in FAP so that it can be loaded into the computer. Because it is an assembly language and not a compiler language, it is extremely flexible and therefore preferred for writing subroutines that are going to become a part of the operating systems library. Also, the average programmer who is thoroughly familiar with FAP can write a tighter program than is possible by using a source language and having the computer do the compiling into FAP. This is especially important where there are a great many subroutines to be loaded and the core space may be limited by the size of the main program.
A detailed discussion of the FAP language will be left to the programming manuals, but some of the features of this language must be discussed in order to understand both the operation and the difficulties encountered in writing the SC 4020 subroutines. Two features will be discussed in some detail, namely how an entrance and exit is made from a FAP subroutine and the principle of indirect addressing.
At the beginning of each FAP subroutine there is a list of entry names to that subroutine. Any of these names can be used in another program to call the subroutine.
The next item in the statement listing lists any subroutine names called by this subroutine. Every subroutine name has six letters (including enough blanks) that are referred to as a transfer vector. The loader takes all of the transfer vectors and compares them one by one with the BCD name associated with an entry point address. When a match is found, the transfer vector is replaced with a transfer command to the address in that particular subroutine. For example the transfer vector 74 41 46 22 45 34 equals (JOBN). This BCD twelve digit number represents one 36 bit word when the program is loaded in the computer, but it is not the number that appears in that location when the problem is ready to be run. Instead a transfer to the current entry point appears. If the subroutines are shuffled into new locations, the next time the program is run the loader will supply the new addresses as easily as it did the old.
The programmer does not have to specify the transfer vectors for each subroutine the way he does for the entry points. He refers to the subroutine name by either one of two calls:
CALL Subroutine name - 6 letters or less TSX Subroutine name - 6 letters or less
The word CALL is equivalent to the word TSX (transfer and set index) and it is a matter of individual preference as to which one the programmer uses. However, when the TSX is used, the subroutine has to be prefixed with a dollar sign so that the assembler will know that the name is not an undefined variable in the program on which it is working. The assembler will automatically set up the correct transfer vectors at the start of the program.
It was stated above that the loader attempts to match the transfer vectors with the entry points on a one-to-one basis. If the loader does not find an entry point in the list obtained from the input deck, it looks in the OSU system library and loads the subroutine it needs from there.
Once the entry point has been called, it is necessary to be able to return to the called point after leaving the subroutine. This is accomplished by means of storing the calling address in an index register, namely index register IR4.
There are three index registers available in the IBM 7090 computer: IR1, IR2, and IR4. IR3 is used for a book-keeping function. The IBM 7094 computer has twice as many available, but these subroutines will run on either machine because they were first wwritten uith only three index registers in mind.
It is obvious that a subroutine can be left by calling another subroutine and then exiting through the transfer vector, but a more common method is to return to the next instruction in the main program after the subroutine call. This is made possible by the fact that either CALL or TSX, stores the address of the transfer command in index register four before the transfer is made.
Therefore, IR4 can be used to determine the return from the subroutine. One of the powerful features of the FAP language is the ability to tag an address. Consider the FAP statement that occurs quite frequently at the termination of any FAP subroutine:
TRA 1,4
The one refers to the number that is going to be placed in the address of this instruction when the subroutine is loaded, and the four is placed in what is known as the tag bit. Since TRA is a transfer, this statement would be read as transfer to address one tagged by four. This means that the contents of IR4 are added to the address one before the transfer is made. Assume that the subroutine was called from location 15455. lhen the above statement is executed, the transfer is made to location 15456. Notice that the subroutine had no knowledge of where it was called from. Address 15455 could have bean any location in the computer.
Very often it is desired to use index register four in a subroutine when calling yet another subroutine, and the calling address may be lost. Since the address in IR4 is the only way the subroutine has of knowing where to return in the main program, it is necessary to save this address before using IR4, Therefore, very often.a typical subroutine will have the following form:
ENTRY SXA (X4),4
- - - - - - - - - -
subroutine statements
including use of IR4
to call other subroutine
- - - - - - - - - -
(X4) AXT **,4 AXT is address to index, true
TRA 1,4
END
ENTRY is the name of this subroutine. The first operation (SXA) saves the contents of IR4 in the address (X4).
At location (X4) there are two asterisks in the position for specifying the address. This means that the address is to be supplied by a statement earlier in the program, namely the SXA.
The subroutine is then executed including any calls to other subroutines that will alter the contents of IR4. When (X4) is reached, the address in this location is placed in IR4. Since this is the address of the calling statement, the TRA then transfers to the next statement after this. Both the subroutine and the calling statement can be at any space in the computer store and neither has to know the location of the other in order to communicate between the two.
In order to understand how the data of one subroutine or program can be used in another subroutine, it in necessary to understand how indirect addressing works. Approximately half of the operations permitted on the IBM 7094 (about 200) are of a type that requires the machine to do something with the data that is stored either in a particular location in storage or in the accumulator or multiplier registers. For example, the instruction
CLA ALPHA
in a program clears the accumulator and then places the information in location ALPHA into the accumulator.
When it is desired to use the indirect addressing feature, any of the above commands can be modified by the addition of an asterisk to the three letter operation code. For example,
CLA* ALPHA
performs an entirely different operation than the previous command. In this case, the computer instead of taking the data in ALPHA and placing it in the accumulator looks for the address stored in ALPHA. It then performs the clear and add operation, not in ALPHA, but on the data stored in the address stored in ALPHA. Hence the name indirect addressing. This characteristic extends the capabilities of the computer by a tremendous amount because very often it is not known where a piece of information is stored but the location of the address of the data is known. A perfect example of this is in a data array where a series of numbers are stored in the computer's memory. By placing the address of the first word of the array in a specified location, any word in the array can be located merely by adding the number of the word to the address. Assume that the first word of the array is in address 14401. If this address plus the number of the desired word are placed in address 14400 (i.e., for word 22, 14423 would be placed in 14400), it is only necessary to apply an operation code followed by the asterisk to address 14400 to use data in 14423. Without indirect addressing it would be very difficult to write a compiler that could handle subscripted variables in the source language. It is this capability and that of being able to modify addresses with a tag that separate the large computer from the small one. Indirect addressing and index register tagging are two ways to increase program speed by an order of magnitude without increasing hardware speed.
However, indirect addressing is of vital concern to the programmer in another area uhen he is writing subroutines that either use or supply data to the main program. Needless to say, most of the SC 4020 subroutines are of this type. In order to explain how indirect addressing is used to transfer data into a subroutine, it is necessary to explain the use of calling parameters. They are also called the arguments of a subroutine because they are written in the same fashion as the arguments of a function. Consider the following statement in a SCATRAN source program:
CALL SUBROUTINE()=EXMPLE.(X,N,1,TABLE.)-
The name of the subroutine is EXMPLE.. The period after the subroutine name is the SCATRAN. method of keeping track of subroutine names for the transfer vectors between programs. Any symbol in the brackets is a calling parameter; X, N, 1, TABLE. are all arguments of the subroutine EXMPLE.. It will be noticed that they can be floating point numbers (X), fixed point numbers (N), literals (1), or even subroutine names (TABLE.) subject to the limitation that a subroutine cannot call itself. This notation for calling parameters is quite general for different computing languages as will be shown when SCATRAN and FORTRAN are compared.
In order to understand why indirect addressing is important in this case, it is necessary to look at how the compiler would handle the above statement. It would appear in a core dump of the storage as the following set of words:
0074 00 4 14415 0000 00 0 27540 0000 00 0 27541 0000 00 0 14401 0000 00 0 14414
The 0074 is the operation code for transfer to the address IN this word (14415) and set an index register to the address OF this word (TSX). The index register to use is given by the tag of 4 for IR4, Address 14415 is the location of the entry point for subroutine EXmPLE. and the following four addresses specify the locations of the variables X, N, the location of a word containing the literal 000000000001 and the location of the entry point to the subroutine TABLE. respectively.
Note that only the address of the data is given, not the data itself. Since only the address is given and since the address of the calling statement is not known but has been placed in IR4, it can be seen that both tagging and indirect addressing will have to be used to obtain the required data once the subroutine has been entered. To continue this example, the subroutine EXMPLE. might be written as follows:
Address in Machine Word FAP Language Statement COMPUTER 14415 0500 60 4 00001 EXMPLE CLA* 1,4 14416 0601 00 0 14425 STO ALPHA 14417 0500 60 4 00002 CLA* 2,4 14420 0601 00 0 14426 STO ALPHA+1 14421 0500 60 4 00003 CLA* 3,4 14422 0601 00 0 14427 STO ALPHA+2 14423 0500 60 4 00004 CLA* 4,4 14424 0621 00 0 14430 STO ALPHA+3 14425 0020 00 4 00005 TRA 5,4 14426 0 00000 0 00000 ALPHA PZE 14427 0 00000 0 00000 PZE 14430 0 00000 0 00000 PZE 14431 0020 00 0 00000 TRA **
Each of the CLA*'s operate in the same manner. The tag 4 means that the number in the address of the instruction is added to the address in TR4. The asterisk means to clear and add the word whose address is in the address specified above. For example, the first instruction is CLA* 1,4. A transfer is made from the main program to the address of EXmPLE.. The data in the address given by the next machine instruction (27540) is placed in the accumulator. The STO stores it in location ALPHA. The fourth CLA is not used for indirect addressing because it is the address itself, i.e., the address of the entry point to TABLE, that is desired. The following STA stores this address in the third location after ALPHA. The last command in the subroutine is a transfer (TRA) that will jump back to the address in IR4 plus five locations. This is the next instruction in the main program when the four calling parameters are accounted for. The final result after going through the subroutine is:
ADDRESS CONTENTS 14426 Value of X 14427 Value of N 14430 000000000001 14431 0020 00 0 14414
and control has been returned to the main program. An additional set of commands could operate on the stored data with the aid of another subroutine call. The reasons for the emphasis on this particular area of programming will be shown when the differences between SCATRAN and FORTRAN are discussed,
There were three main difficulties with using the North American subroutines at OSU. The first one was that the North American operating system has an extensive bookkeeping program that is tied into all of their subroutines. When their computer executes an SC 4020 program, in addition to generating the desired output data, it counts the number of frames of hard copy made, the number of frames of film, the programmers name, the date, department number, time on the computer, etc. Since all of these items were handled in different places in North American's library, when an attempt was made to run them at OSU over forty loose ends showed up that prevented the program from being run at all. Therefore, the first job was to uproot the bookkeeping functions from each subroutine while making sure that the removal did not destroy the continuity of the subroutine.
The second difficulty involved the input-output equipment available at North American versus that at OSU. Since input-output equipment is vary expensive, the tendency is to buy just what is needed at a particular installation. In this case, North American has an IBm 7090 computer and OSU has an IBM 7094. The 7094 is a larger machine but it is also compatible with the 7090 so that any program written for the 7090 will run on the 7094. However, this is not true with regards to the available input-output equipment. Although North American has a similar computer, the nature of their computing load requires that their input-output equipment be far more extensive than that of OSU's larger computer. The final result was that when the basic subroutines were run at OSU, the computations were performed, but the first time a piece of data was to be written on an output tape, a tape unit was called for that did not exist at OSU. The program would halt at that point and because the computer had entered the IOS (input-output supervisor) subroutine of OSU's operating system library and not in one of the subroutines that had been supplied to it by the programmer, the reason for the machine halt was very well hidden. This was one of the many troubles encountered in this area.
The third difficulty was by far the most serious one. It was stated above that two compilers are in use at OSU, namely SCATRAN and FORTRAN. As the subroutines had been written originally for FORTRAN calls, it was decided to use this language to develop the operational software for producing tapes at OSU. This objective was accomplished very successfully from the point of view of producing a tape that would run on any SC 4020 but certain obstacles appeared that detracted from this success.
In theory, the two available operating systems are equal in computing capacity with SCATRAN noted for the flexibility of its program statements and FORTRAN for running programs written elsewhere. However, in practice, SCATRAN is the language preferred by the Numerical Computation Laboratory and the difficulties in running FORTRAN programs were found to be almost insurmountable. The many minor ones include the fact that only a limited amount of FORTRAN runs are made each day and that very few consultants in the computing department are interested in FORTRAN or able to give advice on problems that the individual programmer may be having.
The minor difficulties could have been ignored but a major obstacle led to the decision to abandon FORTRAN as a language and to write subroutines that could produce SC 4020 tapes under the SCATRAN operating system. In addition, it was decided to keep the FORTRAN features of the subroutines as far as possible so that the programs could be run in FORTRAN if it was desired to do so in the future.
This major obstacle was the time that it took to process a program under FORTRAN. A test program was developed in order to check out the operating system when using the SC 4020 subroutines, It consisted of an ID frame and a series of frames (usually four) of asterisks in concentric circles that rotated between each frame. This program was run under identical conditions in both FORTRAN and SCATRAN using the identical FAP object decks for the SC 4020 subroutines. Incidentally, these FAP decks were assembled under the FORTRAN operating system so that if there were any incompatabilitias they should favor the FORTRAN system. In the case of SCATRAN, the program took 5.46 seconds total execution time. The same program when run under FORTRAN took from a minimum of five and one-half minutes to a maximum of just over seven minutes. In SCATRAN the computer keeps track of the time being used for each seperate stage of processing a problem and this is printed out after the problem is completed. In FORTRAN, this item was recorded manually by the operating personnel at the computer center and no breakdown could be obtained as to what was taking up the time in the FORTRAN as opposed to the SCATRAN run.
Although it could not be determined definitely as to why FORTRAN programs should take so much longer than SCATRAN, I believe that the great bulk of the time is used in two areas. First, the FORTRAN compiler is extremely slow compared to SCATRAN. This does not matter at most computer installations where a program will only be compiled once and then loaded from an object deck afterwards, but at a university installation most jobs take considerably less than a minute to run and several minutes of compiling time for each progrem cannot be tolerated. SCATRAN was written with the most emphasis on compiling speed and as a consequence, SCATRAN will compile an amount in one second that would take FORTRAN about one minute.
The other reason is due to the way a non-system file (the SC 4020 tape returned to the programmer) is handled under FORTRAN as opposed to SCATRAN. Under each system, a message is printed out for the computer operator to dismount a tape and return it with the program. At this point SCATRAN immediately goes into the next program and stops charging to the previous job. In effect, having the tape dismounted is free under SCATRAN. In FORTRAN however, the computer stops after printing out the message. You are being charged while the operator reads the message, finds another tape to replace yours, locates which tape unit is being used, replaces the tape and then starts the computer again manually to accept the next job. In each case, this procedure can take several minutes but in the case of SCATRAN it does not show up as very expensive IBM 7094 time charged to the job.
The seriousness of this situation can be shown by comparing the IBM 7094 computer time needed to make a hundred feet of movie film. In 100 feet of 16 mm movie film, there are 4000 frames. If under SCATRAN five frames took 5.46 seconds, then the 4000 frames could be computed in about 1.2 hours of IBM 7094 time. These five frames would take about five minutes under FORTRAN, For 100 feet of film, this would require approximately 67 hours. This would be impossible from both the point of view of obtaining time on the computer and of the cost incuread in making only small amounts of film. For this reason, although the subroutines were operational under FORTRAN, the decision was made to run all future programs in SCATRAN.
The major task in the conversion was to determine the differences between the FORTRAN and the SCATRAN operating systems. These differences are due to the way the compiler is written and cannot be removed. The compiler operates as a total system and any changes that would be required had to be made in the subroutines under the programmers control and not in the operating system.
Although there are many differences between the two operating systems, fortunately there are only two areas that will effect the operation of the FORTRAN based SC 4020 subroutines when they are called in SCATRAN. Both systems use FAP as an object language so that the problem is, one: finding where the input and output data is stored in the main program and, two: the form of this data, particularly integer numbers.
Two identical programs were written for the two systems that have no function other than showing the differences that must be considered when using a FORTRAN object deck with a SCATRAN program.
A detailed description of the programs and code generated followed in the thesis with listings that are quite difficult to read so have not been included here. There was also a section concerning a program to convert from FORTRAN to SCATRAN.
Two identical programs were written for the two systems that have no function other than showing the differences that must be considered when using a FORTRAN object deck with a SCATRAN program.
Figures 14, 15, 16 and 17 give a SCATRAN test program and lower core dump followed by the same program and core dump for FORTRAN. Each program has four different subroutine calls that show the use of different calling parameters.
SOURCE LANGUAGE STATEMENTS
C TEST PROGRAM FOR SCATRAN @
DIMENSION(X(3))@
START NR=1@
IR1=1@
IR2=496@
XR4 = 35.367@
X(NR)=3.5@
CALL SUBROUTINE()=EXAMP1.( )@
CALL SUBROUTINE()=EXAMP2.(X(NR),NR,TABLE.)@
F NAME BRENTON R. GROVES@
F DEPT ELECTRICAL ENGINEERING@
F DATE 7/15/66@
CALL SUBROUTINE()=EXAMP3.(NAME,DEPT,DATE)@
CALL SUBROUTINE()=EXAMP4.(IR1,IR2,IR3,XR4)@
CALL SUBROUTINE()=ENDJOB.()@
END PROGRAM(START)@
GROVES, B. R. JOB FGJ500 09/13/66 089010 PAGE 7
SYSTEM DUMP 14400 TO 14536 AC OV OFF MQ OV OFF DVCK OFF M TAG ON FTRAP ON FTRAP OFF
AC 0+000000014426 MQ +000000000000 SI 266621642360 SSW6 U LITI 04123 LDDI 00000
IR1 77777 IR2 00001 IR3 76510* IR4 63250 IR5 61641* IR6 62225* IR7 61641* (0) 00000 REL REG 00000
-00001 -77777 -01270* -14530 -16137* -15553* -16137* PROT REG 77400 14400
14400 202700000000 206432737166 000000000760 000000000001 002100014532 002100014533 002100014536 002100014534
14410 002100014535 002100014554 000000000000 000000000000 000000000000 000000000000 000000000000 000000000000
14420 000000000000 000000000000 000000000000 000000000000 000000000000 000000000000 202700000000 000000000000
14430 000000000001 000000000001 000000000760 206432737166 000000000000 225125456346 -056051336027 -114665256260
14440 254325236351 312321436025 -052731452525 -113145216060 -200761010561 060660606060 002000014472 000000000000
CELLS 14450 TO 14467 ALL CONTAIN 000000000000
14470 000000000000 000000000000 050000014403 060100014430 050000014403 060100014431 050000014402 060100014432
14500 050000014401 000000000000 053500114430 059999914400 060100114425 007400414404 002000014510 000000014425
14510 050000014430 000000000000 062100013514 007400414405 000000014426 000000014430 000000014406 007400414407
14520 000000014435 000000000000 000000014444 007400414410 000000014431 000000014432 000000014434 000000014433
14530 007400414411 000000000000 002000400001 002000400001 002000400004 002000400005 076100000000 002100000153
* XEQ
C TEST PROGRAM FOR FORTRAN II
DIMENSION X(3)
F TABLE
NR = 1
IR1=1
IR2=496
IR3=0
XR4 = 35.367
X(NR)=3.5
CALL EXAMP1
CALL EXAMP2(X(NR),NR,TABLE)
CALL EXAMP3(17HBRENTON R. GROVES,22HELECTRICAL
X ENGINEERING,8H 7/15/66)
CALL EXAMP4(IR1,IR2,IR3,XR4)
CALL DUMP
END
AC MQ SI KEYS XR1 XR2 XR4
- 075400199274 -206060606060 -000000306200 000000000000 00001 00000 77554
-.33897956-20 -.06095237+02 -77777 -00000 -00224
TRAP DCT IOT OFL SENSE LIGHT 1 2 3 4 SENSE SWITCH 1 2 3 4 5 6
OFF OFF OFF OFF OFF OFF OFF OFF OFF OFF OFF OFF OFF OFF
00000 000000000000 000000000000 000000000000 000000000000 000000000000 000000004470 000000000000 000000003354
00010 002100000275 000000000000 000000000000 000000000000 000000000000 000000000000 000000000000 000000000000
CELLS 00020 TO 00127 ALL CONTAIN 000000000000
00130 000000000000 000000000000 000000000000 000000000000 000000000000 000000000000 000000000000 001101060606
00140 000000000000 000000000103 000000000000 000665077461 002000400001 002000400004 002000400004 002000400005
00150 076100000000 002100000275 002100000150 002100000144 002100000145 002100000146 002100000147 002100000326
00160 050000000002 060100000264 050000000151 060100000010 060000077462 050000000236 060100000266 -053400100266
00170 050000000236 060100500271 050000000237 060100000270 050000000240 060100000267 050000000255 060100000265
00200 050000000256 060100105275 007400400153 075400100275 040200000203 062100000207 007400400154 007400000274
00210 007400000266 007400000152 -053400100266 007400400155 007400000241 007400000245 007400000252 007400400156
00220 007400000271 007400000270 007400000267 007400000265 007400400157 076200001321 054000000232 054400000000
00230 003000000233 002000000001 -100003000000 076000000005 042000700001 002000000234 000001000000 000760000000
00240 000000000000 225125456346 000000000000 -114665256260 -377777777777 254325236351 312321436025 -052731452525
00250 -113145276060 -377777777777 =056051336027 060660606060 -377777777777 206432737166 202700000000 233000000000
00260 000000377777 -000000000000 -200761010561 000000000000 000000000000 206432737166 000001000000 000000000000
00270 000760000000 000001000000 000001000000 000000000000 202700000000 063400400322 053400400000 063400400323
By combining the two core dumps for the respective program statements, we can see the changes required to convert a subroutine:
FORTRAN SCATRAN
CALL EXAMP1 CALL SUBROUTINE()=EXAMP1.()-
ADDRESS CONTENTS ADDRESS CONTENTS
00202 0074 004 00153 14505 0074 004 24404
00153 0021 000 00144 14404 0021 000 14532
00144 0020 004 00001 14532 0020 004 00001
In each case, the CALL statement results in a TSX (0074) tagged by IR4. Control passes through the transfer vector (0021) to the subroutine EXAMP1 (a one line transfer (0020) back to the next statement after the call). Therefore without calling parameters, the two subroutine statements are exactly the same. The next statement requires four locations in succession:
F TABLE CALL EXAMP2 CALL SU8ROUTINE()=EXAMP2. (X(NR),NR,TABLE) (X(NR),NR,TABLE.) ADDRESS CONTENTS ADDRESS CONTENTS 00206 0074 004 00154 14513 0074 004 14405 00207 0074 000 00274 14514 0000 000 14426 00210 0074 000 00266 14515 0000 000 14430 00211 0074 000 00152 14516 0000 000 14406
The first difference is that although the calling parameter addresses follow the TSX tagged by IR4, FORTRAN fills the first four characters with 0074's, while SCATRAN uses zeros. As a general rule, this does not matter because that part of the word is never used, but soma subroutines use the presence of the 0074 as a flag to tell how many calling parameters there are in a call statement. The conversion example will show how to handle this. Let us look at the contents of each of the addresses of the first of the above words:
00154 0021 000 00145 14405 0021 000 14533 00145 0020 004 00004 14533 0020 004 00004
Location 00154 has a transfer (0021) to location 00145. Location 00145 has a transfer (0020) back to the main program. The identical listings can be seen in SCATRAN.
The next address contains
00274 202700000000 14426 202700000000
= 3.5 = X(NR) = 3.5 = X(NR)
This shows that a floating point number declared as a calling parameter is treated in exactly the same way in both programs. Therefore, floating point numbers need no conversion, such as the call to XSCALV. The next address contains
00266 0 00001 0 00000 14430 0 00000 0 00001
= NR = NR
This shows the fundamental difference when the calling parameter is an integer number.
A computer word can be divided up as follows: the highest order integer is the prefix, the next five are the decrement, the next one is the tag, and the last five are the address,
FORTRAN places the integer in the decrement of the word and SCATRAN places it in the address. This is fundamental because many FAP fixed point (integer) operations operate either on the decrement or the address of the word. Since the integers are naturally found in the decrement in FORTRAN, decrement operations are used almost exclusively. When it is desired to have two pieces of information in a word, the integer is brought into the decrement and then shifted into the address. Therefore, a conversion'program has to take in the words representing any integers and then shift the integer into the decrement before calling the subroutine. Without the shift, the subroutine would think that all incoming integers were zero. The last address contains
00152 0021 000 00150 14406 0021 000 14536 00150 0751 000 00000 14536 0761 000 00000
In each case the transfer (0021) is the transfer vector for subroutine TABLE. This shows that subroutine entry points can be called by name in a calling parameter in either system. However, one should note that in SCATRAN the name has to be followed by a period to designate it as a subroutine and not as a variable. In FORTRAN, a letter F in column one followed by a list of names separated by commas starting in column seven has to be used. This is a statement separate from the subroutine calls and it can be placed anywhere in the FORTRAN program.
EXAMP4. is merely a repeat example of the above with both fixed and floating point numbers in the calling parameters. The core dump representation in the two cases are as follows:
SCATRAN - CALL SUBROUTINE()=EXAMP4.(IR1,IR2,IR3,XR4)- ADDRESS CONTENTS ADDRESS CONTENTS 14523 0074 004 14410 14410 0021 000 14535 14524 0000 000 14431 14431 0 00000 0 00001 14525 0000 000 14432 14432 0 00000 0 00760 14526 0000 000 14434 14434 0 00000 0 00000 14527 0000 000 14433 14433 206432737166 FORTRAN - CALL EXAMP4(IR1,IR2,IR3,XR4) ADDRESS CONTENTS ADDRESS CONTENTS 00217 0074 004 00156 00156 0021 000 100147 00220 0074 000 00271 00271 0 00001 0 00000 00221 0074 000 00270 00270 0 00760 0 00000 00222 0074 000 00267 00267 0 00000 0 00000 00223 0074 000 00265 00265 206432737166
Reference to the above text wuill show the differences and similarities between the two compilations.
In addition to data and subroutine names, a calling parameter can refer to a Hollerith field. A Hollerith field is a set of machine words containing BCD coded alphanumeric text. It is variable in length, containing enough words to hold the designated text at six characters to a word. In FORTRAN, a Hollerith field is specified by a number equal to the number of characters followed by the letter H, followed by the text. In SCATRAN, an F 1n column one of a statement will identify the statement as a Hollerith field with the statement name containing the address of the first word in the field. This is not to be confused with the F card in FORTRAN although both have an F in column one.
SCATRAN - CALL SUBROUTINE()=EXAMP3.(NAME,DEPT,DATE)- ADDRESS CONTENTS 14517 0074 004 14407 14520 0000 000 14435 14521 0000 000 14440 14522 0000 000 14444
Looking at the address specified by the calling parameters we find
14407 0021 000 14534 14534 0020 004 00004
14435 22 51 25 45 63 46 14436 -05 60 51 33 60 27
B R E N T D N R . G
14437 -11 46 65 25 62 60
R O V E S
14440 25 43 25 23 63 51 14441 31 23 21 43 60 25
E L E C T R I C A L E
14442 -05 27 31 45 25 25 14443 -11 31 45 27 60 60
N G I N E E R I N G
14444 -20 07 61 01 65 61 14445 06 06 60 60 60 60
7 / 1 5 / 6 6
The above shows how the three Hollerith fields would appear in the core dump. The minus sign on a BCD word means that a four is to be added to the first number to obtain the BCD character.
The FORTRAN statement is
CALL EXAMP3(17HBRENTON R. GROVES,22HELECTRICAL ENGINEERING,
8H 7/15/66)
The equivalent core dump is
ADDRESS CONTENTS 00213 0074 004 00155 00214 0074 000 00241 00215 0074 000 00245 00216 0074 000 00252
If cells 00155, 00241, 00245 and 00252 and the corresponding ones following them are examined, it will be found that they contain exactly the same BCD information as in the SCATRAN call above. Since it is the address of the Hollerith field that is important to the subroutine, the conversion program should handle these in exactly the same manner as the address of the subroutine name.
The other main difference between SCATRAN and FORTRAN is in the way each language stores data words in arrays. SCATRAN stores data in a forward array or one that has the first word in the lowest storage address while FORTRAN uses a backward array in that the first word goes into the highest address.
Fortunately, the SC 4020 subroutines were originally written to accept either a forward or backward array. Generally, one of the calling parameters will have a minus sign attatched to it for the forward array. When a conversion program is written, the proper clear and add, store combination should be used to insure that the minus sign is carried along with the data word.
A sample conversion program follows to convert the SCATRAN statement
CALL SUBROUTINE()EXAMP.(X(NR),NR,TABLE.)-
so that a subroutine that uses the FDRTRAN statement
CALL EXAMP2(X(NR),NR,TABLE)
can be called. The 2 was dropped in the subroutine name because the conversion program has to have its own name. In the SC 4020 programs, the ending V was usually changed to S. Figure 18 will give a sample conversion program.
This sample program shows how to handle three types of calling parameters so that a FORTRAN-FAP subroutine can be called from a SCATRAN main program. The value of X(NR) is brought into the subroutine by indirect addressing and stored in cell A1. The value of NR, which is in the address of the data word, is brought in by indirect addressing through the calling parameter and stored in cell A2 after being shifted into the decrement. This is accomplished by having a ALS 18 (accumulator left shift eighteen bits) between the clear and add which places the whole word into the accumulator and the store which places the word into the proper cell. When a word is printed out in octal notation, it has twelve digits which represent three bits each of the thirty-six bit word in the machine. Therefore, to shift an integer from the address (the right five numbers) to the decrement requires a shift of eighteen bits.
Since it is the address of the subroutine TABLE we are interested in and not the TABLE itself, indirect addressing is not used. The clear and add without the asterisk brings in the third calling parameter word which has the address of the TABLE transfer vector in it. All the other positions are zeros. The address part of this word is placed in cell C3 which simulates a FORTRAN calling parameter for TABLE.
When the four TSX's are assembled and loaded in the computer, they will look like this:
OP CODE TAG ADDRESS 0074 004 Address of Transfer Vector EXAMP2 0074 000 Address of A1 0074 000 Address of A2 (integer in decimal of A2) 0074 000 Address of Transfer Vector to TABLE
It can be seen that these four calls are identical to the FORTRAN compilation for the statement
CALL EXAMP2(X(NR),NR,TABLE)
Since calling parameters are indifferent about whether the called item is a variable or a constant, constants can be used just as easily.
So far, the discussion in this chapter has centered on the use of SCATRAN and FORTRAN II as the programming languages. Should it ever be desired to run these subroutines under a FORTRAN IV operating system that uses FAP as a basic machine language, very few changes would have to be made. A reference is given that lists all of the changes between FAP in FORTRAN II and FORTRAN IV:
IBM 7090 - 7094 IBSYS Operating System Version 13, Macro-Assembly Program (MAP), IBM 1965.
*** FAP
COUNT 20
* CONVERSION PROGRAM FOR EXAMP2 FROM EXAMP
* THE CALL TO THIS PROGRAM IS
* CALL SUBROUTINE()=EXAMP.(X(NR.NR.TABLE.)@
EXAMP SXA (X4).4 ENTRY POINT, SAVE IR4 IN (X4)
CLA* 1.4 BRING IN X(NR)
STO A1 STORE X(NR) IN A1
CLAM 2.4 BRING IN NR
ALS 18 LEFT SHIFT 18 BITS
STO A2 STORE NR IN DECREMENT OF A2
CLA 3.4 BRING IN ADDRESS OF TABLE
STA c3 STORE ADDRESS OF TABLE IN C3
TSX $EXAMP2.4 CALL EXAMP2
TSX A1.0 (X(NR).
TSX A2.0 NR.
C3 TSX **.0 TABLE)
(X4) AXT **.4 RESTORE IR4
TRA 4.4 RETURN TO MAIN PROGRAM
A1 PZE STORAGE FOR X(NR)
A2 PZE STORAGE FOR NR
ENO
This appendix contains the details of the SC 4020 operating system. It is an extension of the SCATRAN operating system in use at the OSU. The system will produce magnetic tape that can be used on any SC 4020 or BL 120 installation and is indifferent to the computing languages used at that location. The appendix can be divided into five sections.
This body of work is complete and there should be no difficulty in producing satisfactory output under the SCATRAN operating system. However, it is useful to have a copy of the SC 4020 Programmer's Manual in support of the subroutine descriptions because where this work would merely repeat the manual, reference was made to the manual rather than giving the complete description.
The performance commands can be represented in a twelve digit octal notation representing a thirty-six bit binary number by a two octal digit code that always appears in the two highest order (left-hand) positions of the command word. These codes are given in Table 4.
The Select Camera commands are used to open the shutter on the selected camera and close the shutter on the other one. Camera 1 corresponds to either the thirty-five millimeter or the sixteen millimeter camera, depending on which is mounted on the SC 4020, and Camera 2 corresponds to the nine by nine hardcopy output,
The use of Advance Film is obvious and will be used most by the programmer when making movies. When this command is used with the earlier SC 4020's or with the BL 120, it should be placed at the end of a record on the magnetic tape to give time for the film to advance. The newer SC 4020's lock out the processing when this command is received and therefore it can be placed anywhere in a record.
The Expand Image and Reduce Image commands will probably not be used in the course of making a movie. The Expand Image is used when it is desired to run one frame into another as when plotting a strip chart. The Reduce Image shrinks the frame area to about one-fourth its normal size. In both cases, normal operation will be restored by calling the opposite command.
.| COMMAND | OCTAL OP CODE |
|---|---|
| Select Camera 1 | 41 |
| Select Camera 2 | 42 |
| Select Both Cameras | 43 |
| Advance Film | 46 |
| Expand Image | 44 |
| Reduce Image | 45 |
The second set of commands are used to draw lines, axes, and vectors. They are given in the table below.
| COMMAND | OCTAL OP CODE |
|---|---|
| Draw Vector | 6X or 7X |
| Generate X=Axis | 30 |
| Generate Y-Axis | 32 |
The third set is used to plot a single character at any desired point on the face of the screen. They are given in the following table.
| COMMAND | OCTAL OP CODE |
|---|---|
| Plot | 00 |
| Expose Heavy | 02 |
| Expose Light | 94 |
The reason for including these two groups of commands in one area is that they use many of the same bits of the thirty-six bit control word. The bits are assigned as follows:
0 - 5 Operation Code 6 - 7 Not Used 8 - 17 X Deflection 18 - 23 Character Code 24 - 25 Not Used 25 - 35 Y Deflection
Each location of the X-Y grid can be specified by a ten bit word representing 1024 different cells in each direction. In the case of vector and axis commands, the specified location is the start of the line to be drawn, and in the case of the plot commands the specified location is the center of the character to be plotted. The cells are numbered in octal notation from zero to 1777 with the zero-zero position being in the upper left-hand corner of the grid. X locations are read across and Y locations down with 1000, 1000 being in the center of the screen.
The other bits of the control word are utilized quite differently depending on the particular operation code at the beginning of the control word. When the first two bits are ones, the SC 4020 will draw a vector from the location specified by the deflection bits. The length of this vector in the X direction is determined by bits two through seven and the Y length by bits twenty through twenty-five. The direction of each of these components is determined by the sign bits in eighteen and nineteen. A one in bit eighteen indicates a plus X component, a zero indicates a minus X component. Likewise, bit nineteen indicates the sign of the Y component.
Because six bits are alotted for each component, the maximum length that a component can cover is sixty-four cells. As there are 1024 cells for full scale, this means that the maximum length of a vector is about 1/16 of full scale. Since the nine-by-nine inch hardcopy examples use about seven and one-half inches for full scale, the longest vector can be approximately one-half inch long. To draw lines longer than this between two arbitrary points requires that vectors be formed end to end. An example is shown by the arrow in the ID Frame. The point of the arrow is a maximum length vector and the lines forming the tail are constructed of three vectors end to end. A subroutine has been written to construct automatically vector control words that will join any two arbitrary points merely by specifying the points to be joined.
When the GENERATE X-AXIS or GENERATE Y-AXIS operation codes are used, bits zero to five specify the operation, eight through seventeen the X deflection, and twenty-six through thirty-five the Y deflection. The remaining ten bits - namely, six, seven, and eighteen through twenty=five - are used to specify a stop point. The X command causes a line to be drawn parallel to the X axis starting at the point designated by the X and Y deflections extending towards the right to the stop point. The Y command causes a line to be drawn parallel to the Y axis upwards to the stop point. The stop point has to be at least sixty-four locations away from the starting point in each case. If the stop point bits all contain zero, the axis will be swept to the far right or upper limit of the picture area. The only difference between the two commands is that the Y-AXIS stop point is expressed directly as a binary number while the X-AXIS stop point is expressed as the ones complement of the location. This means that to calculate the stop point from the X-AXIS command word, it is necessary to subtract the octal number formed from the stop point bits from 1777 in order to determine the true stop point.
The PLOT, EXPOSE HEAVY, and EXPOSE LIGHT commands are identical except for the operation code. Bits six, seven, twenty-four and twenty-five are not used. Bits eighteen through twenty-three are used for a BCD code that corresponds to the desired character that is to be plotted. This format is very easy to interpret when the thirty-six bit word is printed out as a twelve digit octal base word. An example is given below:
0 0 1 4 0 0 5 2 0 4 0 0 OP X CHAR Y CODE DEF DEF
In this case, the 52 is the BCD code for the plotting dot. The X deflection of 1400 would be three-quarters of the way across the screen and the Y deflection of 0400 would be one-quarter of the way down. Of course, these are both octal numbers where the 1024 cells correspond to an octal number of 2000. Therefore, the plot for this command word would look like this:
The EXPOSE HEAVY and EXPOSE LIGHT commands allow for the plotting of two different densities. When either of these calls has been made, all plotting of characters will be in the same density until the opposite mode is called. Usually EXPOSE HEAVY is called at the start of a frame and all plotting is done in this mode. There is no density mode selection when drawing vectors or generating axes, but the intensity can be controlled by repeating the same call several times to increase the shading of a particular line.
The fourth group of command words are concerned with what is referred to as the typing mode. They are as follows:
| COMMAND | OCTAL OP CODE |
|---|---|
| Type Specified Point | 20 |
| Type Current Point | 22 |
| Carriage Return | 52 |
| Stop Type | 12 |
| Reset | 56 |
These commands are used to produce microfilm from text and will generally not be needed when making a movie because the letters (actually the characters on the matrix in the CHARACTRON tube) can be neither rotated nor changed in size. However, these commands are used for the ID Frame that opens and closes each job run on the SC 4020.
The typing mode is initiated by either the TYPE SPECIFIED POINT Or TYPE CURRENT POINT command. The face of the tube can be considered as a page capable of holding sixty-four lines of printing of one hundred and twenty-eight characters each. Any word following the above commands will be translated as BCD text and will be typed in order until the one hundred twenty-eighth position is reached in a line. The logical hardware will then cause the printing to start at X=0 and sixteen cells below the Y deflection specified for the last line.
The TYPE SPECIFIED POINT command uses the deflection bits to give the location of the first character to be typed.
The TYPE CURRENT POINT command uses only the first six bits of the word. The other bits can be used for BCD characters. In this case, typing starts at whatever location was stored in the X and Y deflection registers for the last operation.
The SC 4020 logical hardware does not have any provision for determining whether or not a complete word will fit at the end of a line. Therefore, typed words will be broken whenever the one hundred twenty-eighth location is reached unless the CARRIAGE RETURN command is used. The BCD character 52 will not be printed but will cause the next character to be printed on the line below the present line at X=0.
When the sixty-fourth line has been reached, it is necessary to advance the film or the following characters will be overlayed in the same frame that has already bean plotted.
The typing mode can be halted by calling either a STOP TYPE command (12) or a RESET command (56). The appearance of either a 12 or a 56 in a BCD word returns the SC 4020 to tha plotting mode and all of the rest of the BCD characters in that word are lost. In addition to stopping the typing mode, the RESET command performs two other useful functions. It advances the film and sets the SC 4020 to the plot heavy mode.
One additional command is available to the SC 4020 programmer. This is PROJECT FORM using operation code 50 in the first six bits of the command word. The other bits of this word are not used. This command allows a prepared slide to be projected onto the film along with the data to be displayed.
This completes the number of operations that are available on the SC 4020. I wish to repeat again that these operations are hardware functions (as oppose to software) and are the end result of the computations that are made to produce a movie. For example, to draw a line either a series of touching dots could be plotted or a series of vectors could be drawn end to end. In either case, the one line would consist of many repeated command words on magnetic tape using only two of the eighteen available operation codes. Although the programmer could specify these commands word by word, all of the advantages of computer-generated pictures would be lost. It is the capability of the software in using the eighteen available commands that turn the SC 4020 into a useful tool.
There are two kinds of subroutines, open and closed. An open subroutine is one that is entered at the top in the normal course of events as the computer progresses from command to command. After the subroutine has finished its computations, the program is left at the bottom and takes the next machine instruction. The open subroutine has to be placed where it is to be used and can only be entered once. It must be replaced at each point that it is needed. The main use of an open subroutine is to check out parts of a main program. When each part is running, they can be placed end to end to form the main program. A good example of this is the program used for the first tape of the spheroidal radiator movie.
A closed subroutine is one that is entered by a jump from a location in the main program that is completely independent from the location of the subroutine. The jump can be made to any location in the subroutine. Whan the transfer is made, the original location is stored in an index register so that it is possible to return to the main program from any location in the subroutine. From this it can be seen that a closed subroutine can be stored anywhere in the computer memory, have as many entrances and exits as desired, and be called whenever it is needed. For these reasons, most subroutines used in making an SC 4020 tape are of the closed type.
These subroutines can be divided into seven different categories:
The statement listings for these subroutines were given in this Appendix. Most were written in FAP and have not beeen included here.
This appendix will briefly describe the operation of the various subroutines, the calls that can be made, and any idiosyncrasies that would be of interest to a programmer attempting to use them. The routines that are covered in categories two through five follow very closely the original routines developed by North American Aviation. Except for the SCATRAN conversion subroutines, much additional information can be found in the SC 4020 Programmers' Reference Manual. In addition to the subroutines listed below, there are a number of other programs available in FORTRAN for use on the SC 4020. These programs are covered in the Reference Manual but are not described herein for two reasons.
The first reason is that they form a set of subroutines that are higher in the software hierarchy than the basic subroutines described below. Because of this, they generally use the basic subroutines to perform extremely complex but limited functions for the programmer. GRIDIV is an example of this in that it draws linear and nonlinear graphs and then plots data points and labels them. This subroutine could be considered as the main program to most engineering production on the SC 4020 but it would have almost no use in the making of a movie.
The second reason is that these programs are generally written in FORTRAN and not in FAP, This means that a conversion program cannot be written to utilize them directly under the SCATRAN operating system at OSU. In order to do so, they would have to be rewritten line by line to conform to the SCATRAN language rules. Since SCATRAN is a more flexible language than FORTRAN, this could be done without too much effort except for the time involved, but in view of the limited usefulness of these subroutines, this has not been done. Since a successful FORTRAN operating system extension was developed at OSU prior to the conversion to SCATRAN, if the programmer desired to use these additional capabilities, the program could always be run under the FORTRAN system as outlined in Appendix C.
This category of subroutines was written to produce an SC 4020 tape under the SCATRAN operating system. It has two features that were especially designed with the programmer in mind. As much of the setup routine required as possible was shifted from calls in the main program to calls in the subroutines. This means that the tape non-system file can be opened and the various input parameters read in with only one call. In the same fashion, the file can be closed and the run ended with only one call.
By dividing the job to be done up into a number of different routines instead of one larger package, the programmer can be given the flexibility of having a number of different options with the same call as above. Should any new options be desired, the programmer has to rewrite and debug only one small section instead of the whole package.
The following subroutines must be used for every SC 4020 tape run.
CAMRAV XSCALV (PLOT) ID FRAME JOBNO END FRAME TAPE
This set is self-contained in the sense that for every transfer vector required, there is a matching entry point either in the subroutines themselves or in the SCATRAN system library. The main calls are:
CALL SUBROUTINE()=OUT.(N)-
CALL SUBROUTINE()=CARAV.(N)-
CALL SUBROUTINE()=FRAMEV.(A)-
CALL SUBROUTINE()=CLOSTP.()-
The main program can start with a call to OUT.. The program enters the TAPE. subroutine and sets the variable OUTPUT to the value of N in the calling parameter. N can be any integer from one to four and will have the following effect on the output of the program to be produced.
Each one of these forms has a definite use. 1 is used when it is desired to check the timing of a program to determine time estimates and the output is known or does not matter. 2 is used for checking out programs so that the programmers can analyze the output of a tape without the bother of obtaining a tape dump. It also has the great advantage that the program does not have to be submitted at the Numerical Computation Laboratory but can be run at a remote terminal. A word of caution is necessary when obtaining printed output. The programs to be checked should be very short because in spite of the compact format used to display the output (450 words to a page), it is possible to generate over a hundred pages of output in the course of a one minute program. In the case of a long program, it is better to generate only the tape and then use a special dump routine that was written to check small sections in the middle of a large block of data.
3 and 4 can only be used at the Numerical Computation Laboratory because they result in the physical tape being returned with the program. 3 is the normal operating output parameter. 4 can be used to check the printed output against a test tape that is actually going to be run on the SC 4020.
The next call in the main program should be to CAMRAV..
This call should be made before any attempt to write information on the SC 4020 tape because it opens the non-system file. The following takes place. The call to CAMRAV. immediately calls IDF., part of the TAPE subroutine. The ZCLOCK., a library subroutine, is called to start the clock running. This is done so that a more precise interval will be available to determine the time estimates for longer programs than can be obtained from the bookkeeping routines. Several commands open the non-system file and reserve the necessary space for the buffers. Next, the job number is read off of a data card and stored in JOBNO.. Eight scaling factors are read from a second data card and XSCALV. followed by VSCALV. is called in order to read in the data.
XSCALV. is a very important subroutine that allows the programmer to use his own scale for positioning on the SC 4020 screen rather than the call location numbers the machine uses. In order to scale the programmer's floating point data, it is necessary to know the boundaries of the working field and the width of the margin on the four sides of the field. This information is obtained from a data card that contains the X and Y boundaries and the margin widths.
The next statement in the TAPE subroutine reads in ten six-character alphanumeric words from a third data card. This card contains the title of the program, the programmer's name and department, and the date. This information is stored in the subroutine IDINFO. that is going to write the identification frame as the first frame of the program. The transfer back to the TAPE subroutine ends on a NORMAL EXIT statement which brings the program back to one statemeant after CALL IDFR in CAMRAV.. CAMRAV. then determines the correct command word to be written at the start of the SC 4020 tape to produce either 9 × 9 hardcopy, 35 mm film, or both. This is accomplished by the calling parameter N in the CAMRAV. call statement.
CALL SUBROUTINE()=CAMRAV.(N)
The actual writing of the command word on the tape is done by the CALL (PLOT) statement. This calls the (PLOT) subroutine which in turn calls STORE, a part of TAPE. STORE could be called directly to write on tape except that almost all of the original subroutines called (PLOT) as a subroutine name for their output. The TAPE subroutine is written in SCATRAN which does not allow the use of brackets as part of the name. Therefore, rather than change (PLOT) in the many places where it appeared, the small subroutine (PLOT) was written to make the call (PLOT) equivalent to STORE. The STORE call has two calling parameters associated with it, the word to be written on tape and an integer that is either 0 or 1. When STORE is called through (PLOT), this integer is always zero. The zero tells STORE to place the incoming word into a 170 word buffer. The buffer is then checked to see if it is full. If not, control passes back from STORE to {PLOT) to CAMRAV..
The next statement in CAMARAV is CALL IDFIN in the ID FRAME subroutine. This subroutine calculates the commands, one word at a time, to create the identification frame (Fig. 20) with the programmers name, date, etc., and the job number in big letters. These are stored in the buffer in STORE through (PLOT) but because the total number of words for the identification frame does not reach 170, no tape has been written yet. After calculating approximately sixty words and placing them in the output buffer, IDFIN. returns control to CARAV. which then returns control to the next statement in the main program.
So far, the programmer has made only two statements in his program, namely calls to OUT. and CAMRAV.. The output form is set up, bookkeeping data has been read into the program, a non-system file has been opened, and the command words for the ID frame are in the output buffer.
Incidentally, the ID frame serves another purpose in addition to identifying the job. It combines most of the SC 4020 machine codes in one frame so that the performance of the SC 4020 can be checked merely by looking at the first frame. If it is correct, then it is likely that any difficulties encountered are on the tape and not in the SC 4020 itself.
When the main program is constructed for the generation of a movie, the general procedure is to calculate one frame in a DO loop, using the DO loop limits to change the data at each pass. The patterns generated in the spheroidal radiator example are a good example of this. This DO loop should start with the statement:
CALL SUBROUTINE()FRAMEV.(N)-
The calling parameter N permits the following actions:
N = 0 or missing - the job number and frame count will be displayed in the upper right hand corner of the frame.
N = Anything except zero - the above printing will be suppressed.
N = Negative - when producing hardcopy, the working area is seven by seven inches while the paper is nine inches wide. Four corner marks normally show the smaller working area for each frame.
When N is negative, these marks are suppressed.
The first thing the call to FRAMEV. does is to place operation code for advancing the film in the output buffer. A call to (CLEAN) results in the same call to STORE as (PLOT) except that the second STORE calling parameter is now a one instead of a zero. This causes control to first check to see whether there are more than three words in the buffer and then calls in the SCATRAN library subroutine WRNSFR. (Write non-system file under count control.)
The usual statement for writing tape is the SCATRAN statement WRITE BINARY. The SCATRAN manual in giving the instructions to use this statement neglects to mention that each written record on the tape is preceded by a control word written by the system that contains information as to the number of words in the particular record, This word is used to tell the WRITE BINARY subroutine when the buffer is empty, but unfortunately this word also corresponds to an SC 4020 operation code. The result is that an arbitrary character would be plotted at an arbitrary location on the SC 4020 plot at the start of each record. Since each frame can consist of several hundred records, WRITE BINARY is impossible to use. WRNSFR. is exactly what is needed and is in the SCATRAN library but none of the available manuals or memos covering SCATRAN give instructions for its use or even a hint of its existence. It was discovered by discussing the problem of the control word with one of the senior programmers, Mr Edward Lassiter, at the computer center who knew of its existence.
Since WRNSFR. does not use a leading control word to determine the number of words in the record, the count has to be supplied to it as a calling parameter. This is easily done by counting each word as it is placed in the output buffer. This is the reason for the under count control in the name.
WRNSrR. will not accept a record of fewer than three words because of tape drive limitations. If the program attempts to write a one-word or two-word record, the job will be forced off the computer with a message that the program attempted to write a short record. Since it may be desired to attempt to write with only one word in the buffer, at the end of a frame for instance, the STORE program checks this at the start of each write command. If there are fewer than three words in the buffer, the blanks are filled in with a .0.120000000000 which is equivalent to a no operation for the SC 4020. In the course of placing words into the output buffer, each time 170 is reached WRNSFR. is called to write a new record.
The calling parameter that follows the call to OUT. at the start of the program is checked to see whether output should be printed as well as being written on tape. If not, control exits back to FRAMEV..
The rest of FRAMEV. keeps track of the frame count and determines if the printing and corner marks should be written on the new frame.
The reason for placing the call to FRAMEV. at the beginning of the DO loop and not the end is because it is this command that writes the operation code for film advance and then closes the record. If it were placed at the end of the DO loop, the ID frame would be printed over the first computed frame instead of being separate.
After all the frames have been calculated the call
CALL SUBROUTINE()=CLOSTP.()-
is made as the last statement of the main program. A call to the subroutine CLOSTP. performs the actions necessary to end the run. The LASTFM. call is the same as (CLEAN and it empties any remaining data in the buffer onto the tape before placing an advance frame code on the tape and ending the record. The next few statements in CLOSTP. are used to determine whether or not the SC 4020 tape is to be returned with the job. The calling parameter from OUT. determines if CLOSE REWIND or CLOSE UNLOAD is called. The first merely rewinds the tape while the second prints out a message to the computer operator to save the tape that was just being used and return it with the program. The rewind operation can be given in a program sent in from a remote terminal, but when a tape is to be returned, the program has to be filed at the Numerical Computation Laboratory.
The last operation to be performed before calling ENDJOB. is to read the clock that was zeroed at the start of the program. The time used by the program is printed out as the last piece of output and is expressed in both minutes and seconds to the nearest one-hundredth of a minute. Subroutine ENDJOB. then removes the program from the computer.
One of the major advantages of using a compiler language such as SCATRAN for the TAPE subroutine lies in the handling of data in the form of input and output. Input-output speeds are extremely slow compared with the rate of operation within the computer, and they constitute a bottleneck to the amount of work that can be processed in any unit time. To get around this, either the operating system or the programmer can set up a series of buffers and the internal commands to move data in blocks in and out of the computer. If the programmer desires to do this using FAP, a very lengthy, complicated program will result. This trouble can be avoided by the simple commands PPENFILE and READ or WRITE when the language in the software hierarchy above FAP is used. The compiler reserves space for the buffers, sees that the computed information gets to the right place, and then writes tape while the rest of the computer is still calculating on the remainder of the data. As long as the time used to calculate each piece of information exceeds the time to write that piece of information on tape, which is the usual case in SC 4020 programs, but not so in most programs that require tape storage, the program will be as efficient as possible. However, if the tape writing time is longer than the computation time, than the program has a fixed time to run that cannot be decreased. Since input-output difficulties ere encountered due to hardware differences in the two operating systems, these subroutines were rewritten using the compiler language rather than FAP.
A number of other subroutines have been written that can replace certain sections in this area in order to give the programmer increased flexibility.
TAPE II - This subroutine replaces the TAPE subroutine and is called in exactly the same manner. The first difference is that the open file commands have been rewritten so that instead of writing 170 word records on tape, the number in each record is increased to 1024. This allows much more information to be placed on a single tape, but requires that the microfilm plotter have a 1024 word input buffer.
The other change has been to rewrite the STORE call to allow information already in the output buffer to be changed and to obtain additional calls that are extremely useful when producing a movie. The call is
CALL-SU9ROUTINE()=STORE.(X,N)-
X is a dummy calling parameter that is used only when N is zero. N has the following meanings:
N=0 and N=1 are the same as TAPE. The additional calls can save a large amount of computer time when writing frames of less than 1024 words such as titles. All of the words in a frame are computed once. Then, instead of calling FRAMEV, a call to STORE.(X,4) will add the command to advance the film. Repeated calls to STORE.(X,3) will write as many frames as desired without having to recompute the words in the buffer each time. STORE.(X,2) will remove the advance film command so that additional information can ba placed in the buffer between two frames without losing the information already available in the buffer. The call to OUT is not used with this subroutine because the only output is magnetic tape.
TAPE III - This subroutine was written to permit a quick check by means of printed output. The OUT call, the non-system file statements, and the computation of the ID frame have all been removed. This program should not be used with subroutines ID FRAME or END FRAME because calls to these programs have bean replaced by no ops in the TAPE III program.
CLEAN UP - When a program is run that represents the center section of a movie, the ID frame is not needed and the job number is not required on each frame. This subroutine was written not only to replace the subroutines ID FRAME, CAMRAV, FRAMEV, and JOBNO but it also frees a large amount of room in the computer memory for the main program. The four subroutines above take five hundred octal words of space. The CLEANUP takes twenty-three.
ENO rRAME II - Whan a movie is computed in sections, the end identification frame is not wanted except on the last segment. This subroutine allows the CLOSTP call to be made without writing this frame on the tape.
There are three subroutines that can be used for plotting points and characters. One of the most useful calls in this subroutine library is:
CALL SUBROUTINE()=APLOTV.(~N,X(M),Y(M),IX,IY,NC,CHAR,ERROR)-
Since APLOTV, operates in the manner described in the SC 4020 programmers' manual it will not be described here. An example of the use of the call APLOTV. is given in both the subroutine test description and in the spheroidal radiator example.
The other two subroutines are PLOTS. and POINTS.. The PLOTS. subroutine is used for plotting a single character using the CHARACTRON matrix characters. The call for this subroutine is
CALL SUBROUTINE()=PLOTS.(X,Y,N)-
X and Y represent the locations where the character is to be plotted. N represents the BCD code for the particular character. This call is useful primarily when it is desired to call a character present in the SC 4020 BCD set that is represented by a number not in the IBM BCD code.
The call to POINTS. is identical to that of PLOTS. except for the use of the calling parameter N. In this call, if N is minus, a plotting dot will be called in the center of the character. Also, the values of N do not correspond to the standard BCD code, but to a code that places the most useful plotting characters equivalent to the smaller integers. The table for this code can be found in the Stromberg-Carlson SC 4020 programmers manual.
These subroutines consist of a set that was originally used to produce microfilm from text, but it has proven to be extremely useful in creating desired animation effects with very little effort on the part of the programmer. In this group are the following subroutines:
PRINTS or RITE2S
PRINTV RITE2V
CHSIZV
HOLLV
TABL*V (*=integer)
The typewritten mode of operations was explained in the section on the SC 4020. In order to utilize this mode, one of two calls, PRINTS or PRINT6, can be used. The format is
CALL SUBROUTINE()=PRINT6.(-N,WORD,X, Y,)-
F WORD PLAIN ENGLISH TEXT-
N is the number of letters in the text and X andY are the floating point values specifying the location of where the typing is to start. PRINT6 will automatically supply the carriage return at the end of a line but will not advance the frame at the end of a page. A higher order subroutine, SCOUTV, is available to simulate the action of an output printer but it is not available in SCATRAN.
Notice that although the SCATRAN FORMAT statement is used to insert the text into the subroutine, tha usual brackets and H or Q field indicators are not required. If they are used, the subroutines will treat themselves as part of the text and will drop off the same number of characters at the end of the text.
The call to PRINTS is exactly the same as PRINT6 except that integers equivalent to the raster count on the SC 4020 grid must be used in place of X and Y for the start printing location.
The other block of subroutines is used for variable size letters and to produce animated symbols with only a small amount of programming effort.
The use of these subroutines to produce animated symbols will be explained in the section on special subroutines developed for the spheroidal radiator example. The calls that are used to produce variable sized letters for titles are as follows:
CALL SUBROUTINE()=CHSIZS.(N,M)-
N and M are integers that control the width and height respectively of each character.
CALL SUBROUTINE()=RITSTS.(N,M,TABL*V.)-
N and M are integers that control the spacing between characters and the spacing between lines. The third calling parameter is the name of the table being used for the characters being used. The usual case is to specify TABL1V. as this contains the BCD set common to both SCATRAN and FORTRAN.
CALL SUBROUTINE()=RITE2S.(X,Y,I,J,K,L,-M,WORD,ER)-
All of these calling parameters have the same meaning as for RITE2V in the SC 4020 programming manual except for X and Y. lhen RITE2V is used, X and Y are raster counts, but in the RITE2S. SCATRAN call, they are floating point locations on the programmer grid. The SC 4020 programmers' manual gives a set of instructions for the values of M and N that should be understood and followed when making the above calls. Both the sections on subroutine tests and the spheroidal radiation example give examples of the use of these calls to produce titles in a movie.
Since the SC 4020 hardware commands can only determine that a vector is to be drawn up to sixty-four raster counts in the X and Y increments, it is necessary to have a subroutine that will draw a line between any two specified points by using these vector commands. This is accomplished by using the subroutine LINE. with the call
CALL SUBROUTINE()=LINE.(X1,Y1,X2,Y2)-
The calling parameters are the floating point X's and Y's for the two end points of the line to be drawn. An example of the use of LINE. to draw a desired figure is given in the spheroidal radiator example when the ellipse is drawn. If an accurate curved line is desired, dots can be plotted side by side along the path of the line, but for general work any curved line can be drawn by means of short vectors. Most of the computer-generated pictures to date have used the technique of calculating points and then using subroutine LINE. to fill in the spaces.
Two subroutines are available to draw the axes in the X and Y directions. They are VXAX I and VXAX II. They are mainly used for drawing grids for engineering graphs and their operation is self-evident.
Some of the most useful subroutines for generating computer animation are the ones used for generating variable size letters, The SC 4020 programmer's manual gives instructions for producing titles using the subroutine RITE2V and VCHARV. A slightly different method of writing a TABL*V will be given here.
The name of the table can bs any six alphanumerics. The format TABL1V, TABL2V, etc., is used merely for continuity with the existing programs.
The programmer constructs any desired symbol on an eight-by-eight lattice using straight lines to connect any two points. There is no limit to the number of lines that can be employed. The only restriction is that any one line cannot have a required distance of more than sixty-three raster counts between its ends in either the X or Y direction. The longest line that can be drawn is one that goes from one corner of the lattice to the other where the lattice has sixty-three counts between each point. On the 1024 raster, this would span 441 counts in each direction or approximately forty percent of the distance across the working field.
The GENERATOR SYMBOL (GENSYM) subroutine will be used as an example. It was desired to place a symbol of a generator in the middle of an ellipse. Leads were drawn to the ellipse on both sides and an arrow showed the direction of current flow. The sine symbol was placed in the center of the generator and was tied to the arrow in that it flipped upside down when the arrow changed direction. A drawing was made of the symbol and was broken down into its various parts. This is shown in Figure 21. The reason that the symbol was not generated all at once was that the different parts required different sizes (or counts) between the points of the lattice. A table was then constructed by listing the points to be connected, three lines to a word. The table starts at the bottom and is written upwards. The operation code OCT is used for octal numbers.
*** FAP
COUNT 20
VFD 9/9, 9/10, 9/11, 9/12
ENTR4V VFD 9/0, 9/3, 9/5, 9/7
OCT 026324360000
OCT 020324300000
OCT 222400000000
OCT 000100340000
OCT 560267220000
OCT 012212202500
PZE
OCT 123425435634
PZE
OCT 124325345643
OCT 752052000000
OCT 257757757752
OCT 200200250257
PZE ENTRAV
END
Each of the octal numbers represents the X beginning lattice point followed by the X ending followed by the same for Y expressed as a four digit number. Therefore, each twelve digit number represents three lines. The first three OCT numbers are the eight lines for the octagon figure, the next two lines are for one of the sine symbols, and so on. A symbol ends with four zeros in a row so that when an even multiple of three lines is expressed, they have to ba followed by a PZE (all zeros) in order to shut the symbol generating subroutine off.
The above TABL4V could be used with calls to RITE2S., but because all the pieces formed a single symbol with a preset location, it was decided to continue the subroutine GENSYM which would have the table in it and would make all of the required calls with a single call.
Since the calls were going to be made to CHSIZV and VCHARV rather than to RITE2S, the coordinate positions had to be expressed in raster counts in the decrement of the calling parameter rather than in a floating point number that expressed the location in the programmer's coordinate system. RITE2S is usually called to perform this conversion through XSCALV, but in this case the design has a fixed location and the calls to the basic subroutines were easier. Also, RITE2S and RITE2V are not needed which leaves more room for the main program.
A large figure of the design was drawn (Figure 22) to determine the number of counts required between the points of the eight by eight lattice and the location to center each part of the design properly. It should be kept in mind that a call to VCHARV requires that the location of the lower left-hand corner of the eight by eight lattice be given whereas when calling RITE2S or RITE2V, the center of the design should be given.
Details of the calls to draw the octagon will be given. Referring to the subroutine GENSYM one finds the following calls about two-thirds of the way down the page. A section of this page is written out after Figure 22.
TSX $CHSIZV,4 TSX =05000000,0 TSX =05000000,0 TSX $VCHARV,4 TSX =0132000000,0 TSX =01000000,0 TSX =0757000000,0 TSX =0757000000,0 TSX =0,0 TSX TABLE,0
This is the FAP language notation for
CALL SUBROUTINE()=CHSIZV.(5,5)-
CALL SUBROUTINE()=VCHARV.(90,1,495,495,0,TABLE.)-
in SCATRAN. The calling parameters for CHSIZV indicate that the eight by eight lattice will have five cells between each point. The call to VCHARV will have the following specifications:
132 = figure will be upright
1 = figure will be plotted once
757,757 = lower left-hand corner of figure will be
at raster counts 757 in X, 757 in Y
0 = figure should be constructed from first item in the table
TABLE = the table used is part of this subroutine
All of these numbers are in octal notation due to the basic subroutine called. Each integer calling parameter should be followed by six zeros so that the subroutine is assembled with the integer in the decrement and not in the address. This is a reflection of the fact that the subroutines were originally written for the FORTRAN compiled programs which have integers in the decrement.
The SC 4020 coordinate system has zero,zero at the lower left-hand corner of the grid and uses the octal notation in the calling parameters. Therefore, the drawing of designs using these subroutines is facilitated by using this coordinate system and eight by eight per inch graph paper rather than ten by ten.
Although most of the GENSYM subroutine is made up of the above described table and the calls to VCHARV and CHSIZV, the rest is used to invert the sine symbol in the center of the octagon and to draw an arrow whose size and direction is related to current magnitude. The actual call to this subroutine from the main program is
CALL SUBROUTINE()=GENSYM.(M, N)-
M=1 Current arrow points up. First sine symbol used
M=2 Current arrow points down. Second sine symbol used
N- The length of the array in integer raster counts
Subroutine RULE is almost identical in its construction with GENSYM. It was used to illustrate the concept of resonance in the spheroidal radiator example. Two rulers placed on the radiating pattern indicated that the interfocal distance of the ellipse was the same as the distance of one-half cycle of the radiating field. Figure 23 shows the computer generated output of the RULE subroutine.
Subroutine TABL5V was written to show the words THE END in block letters for use in closing a movie. A three by five section of the eight by eight matrix was used to form the letters.
The definition of H is given as:
0000 0000 0000 2122 1120 0100 3350 3200 2202 1233 2235 2355 0005 0155 1153
Reading backwards, H consists of 0,0 to 0,5 to 1,5 to 1,3 to 2,3 and so on. Each set of four octal digits gives the start and end of X followed by the start and end of Y for each line.
The use of this table gives an example of how any table constructed by the programmer can be used. The first call
CALL SUBROUTINE()=CHIZS.(IXS,IYS)-
gives the number of raster counts between the eight by eight lattice of each letter. The call
CALL SUBROUTINE()=RITSTS.(IX,IY,TABL5V.)-
gives the spacing between each letter, between the rows, and identifies which table is to be used.
F WORD 0125234-
CALL SUBROUTINE()=RITE2S.(X,Y,750,90,1,7,-1,WORD,IR)-
is the call that actually calculates the required vectors and writes them on the output tape. The use of these calling parameters can be determined from the programmer's manual except for the use of the variable WORD. It will be noticed that WORD is the address of a SCATRAN format statement consisting of a series of integers. The format statement compiles these numbers into BCD words as follows:
000102050203 046060606060
Since T equals item zero in the table, H equals item one, blank equals item five and so on, it can be seen that each BCD character starting at the address WORD is interpreted as an equivalent item in the specified TAB*L. This is fine as long as the table has ten or less items that are labled with the number zero through nine in the format statement. But if you called for item ten at "10", this would be interpreted as an item one followed by an item zero. This difficulty can be avoided by the use of an octal literal instead of the format statement. An example is given below.
WORD = .0.00102050203-
WORD(1) = .0.046060606060-
is equivalent to the format statement provided WORD has been dimensioned properly.
If only six items are to be called at a time, any place in the table can be reached, including the illegal BCD characters, by replacing the variable WORD in the call to RITE2S with an octal literal representing the desired six items.
It is now apparent why TABL1V can be used with straight text. The construction for A is at the seventeenth place in the table, B is at the eighteenth, and so on through the alphabet. Text in the format statement is converted to BCD words which automatically draw the correct letters if TABL1V is used.
Table TABL2V and TABL3V cover the lower and upper case Greek letters. Figure 24 gives the characters generated by these three tables along with the decimal location for each character. All of the characters can be generated by use of the octal literal as described above.
The 4-QUAD(PLOT) subroutine was designed to replace the regular subroutine (PLOT) to perform a special function when making the spheroidal radiator movie. It cut the IBM 7094 computer time required to a quarter when the antenna patterns were calculated. These patterns were constructed mainly of dots plotted one after the other and were identical in all four quadrants. The first step was to calculate the X and Y points required in one quadrant. Then, instead of calculating the other X's and Y's required for the other three quadrants, the SC 4020 command word was manipulated to give the three other commands to plot in the other three quadrants. Mixed in with the plot commands were other operation codas, such as frame advance. Repeating these would have been very undesirable so a test was made on the six highest order bits of each word. Since the plot command has six zeros for the high order bits, these words were repeated three more times through the proper logic. All other words were sent to STORE, unaltered, one time only.
4-QUAD(PLOT) Version II is an extension of the above which not only plots the four quadrants but also decides whether or not to plot each dot at all. The output gives an appearance of moving segments in the lines constructed for the plotted dots. This subroutine requires a number of key words that interlock it with the main program with which it is used and the subroutine operation can best be explained in the section of the spheroidal radiator example covering the implementation of the D electric field.
During the course of this work, a number of small programs were written to check out the subroutine. These test programs are included here for two reasons. The first is that they give an idea of the output to be expected from the different subroutines so that when these subroutines are used with a main program, the programmer will know what to expect. The second reason is that they give the programmer an example to follow. It is far easier to show how software works than to try to explain it in words.
The first test is a program that was written not only to check out all the subroutines, but also to check out the entire operating system including the microfilm plotter that will be used to run the job. The output consists of a series of asterisks plotted on concentric circles following an identification frame. The entire pattern rotates between each frame. The number of frames, the number of circles, the number of asterisks on each circle, and the degree of rotation between each picture can be specified by the input parameters. An example of the output of one of these frames along with the corner and cut marks is shown in Figure 25.
After calling OUT. and CAMRAV. to set up the output and open the non-system file, the input variables which are called in with the read input statement are :
RL = Radius of inner circle RI = Increment of radius between each circle THETA = Angle of rotation of first frame in radians SD = Distance between each asterisk along the circle TP = Increment of rotation between each frame VP = Number of frames NC = Number of circles
The circumference of each circle is divided by SD, the average distance between each asterisk, to give the number on each circle. SD is then adjusted to space the asterisks evenly around each circle. The various DO loops utilize the input data to generate tha right amount of data. Of course, for more than 350 asterisks the DIMENSION statement would have to be changed. This test shows the use of
CALL SUBROUTINE():APLOTV.(NR,X(L),Y(L),1,1,1,44,ERRDR)-
to plot out only part of an array. L is preset at the start of the FRAMEV DO loop by setting it equal to JL and this supplies the starting address of the array through X(L) and Y(L). The number of asterisks in each frame is summed up through the statement NR = NR - N - after NR has been set equal to zero at the start of the frame. NR gives APLOTV. the number of points to be plotted from the array and the minus sign indicates the forward storage common to SCATRAN.
A number of tests were run to check out the subroutines LINE, AXIS, PRINTS, RITE2S, GENSYM, RULE, and TABL5V. The resulting output drawn from the printed output is shown in Figure 26. The results of these tests were deliberately drawn by hand rather than run on an SC 4020. This was to indicate how a subroutine might be debugged if the plotter was not available to run a tape. The command words to a small run are printed out. Each word is broken down into its component parts of operation code, location, etc., and the result plotted on an eight by eight to the inch graph paper. This will seem like very tedious work at first, but with a little practice the words can be interpreted almost by eye and a plot made in a reasonable time. Very often only key words have to be plotted, like the beginning and end letters of a line of print, to give a clear picture of what the finished product is going to look like or whether the subroutine is working.
A spacial tape dump has bean written to selectively dump tape in order to check the output of a long SC 4020 tape for correct data without obtaining an excessive amount of printed data. Normally, the IBM 1410 computer is used to dump tape because it is far cheaper to operate than the IBM 7094. However, if it was desired to check out each frame in a complete tape, the printed output could amount to several hundred pages, most of which would be completely useless. If the output can be checked with only a small fraction of the data printed out, as is often the case, the IBM 7094 can be used to great advantage. The subroutine SC 4020 TAPE DUMP was written to search every record on the tape for those that end in command word 460000000000. When this word is found, the next ten records are printed out. Since this is the advance film command, the final result is that only the first ten records of every frame are printed out. Since this many records usually have enough data to tell what is in each frame and since each frame can easily have over a hundred records, the advantage can be seen over printing out all the data on the tape and throwing most of it away.
Several additional subroutines have bean checked out in SCATRAN. They are CUTIV, mARKV, BRITEV, XPANDV, and ST0PTV. They are given in the statement listings but they are not described here because they are only used during the production of 9 × 9 hardcopy. Calls to these subroutines are listed' in the SC 4020 Programmer's Manual.
A brief review of the steps necessary to run an SC 4020 tape program is helpful to the programmer to avoid having a run forced off the machine. It is a good idea to use a check list of both the necessary control cards and the subroutines needed for any call in the main program. This is particularly true if an SC 4020 run is attempted after an interval of time because some of the many details can easily be forgotten.
The first item after the usual ID cards and before any three-star control cards is the file control card. This card is green and has the information needed to determine the tape unit to be used and the writing density on it. The SCATRAN programmer's manual gives information as to how these cards are to be punched. To run an SC 4020 tape, the card should be filled out as follows:
Column No. Punch 2-3 ** 7-10 FILE 17 * 19-21 801 (zero, not letter o) 27 N 28 P 30 L 31 B 55-60 SC 4020
If the tape dump subroutine is to be used, the N and P in columns 27 and 28 should be replaced with an I in column 28 and the SC 4020 beginning at column 55 with the word REEL NUMBER followed by the number of the reel to be dumped.
This card is followed by the usual three-star SCATRAN control cards depending on the wishes of the programmer.
The next deck of cards is the main program. This can be either an original SCATAAN statement listing or it can be a symbolic binary deck headed by a READ SYMBOLIC BINARY card (a SCATRAN statement, not a three-star card) and any changes or modifications to the main program.
The next task is to assemble the subroutine decks that are necessary to run the program. The first block is needed for every job. They are
CAMRAV (PLOT) JOBNO TAPE XSCALV(MOD) ID FRAME END FRAME
Each one of these decks has to have a three-star LOAD card preceding it but the decks themselves can be put in any order. This is the basic package for running tape.
There are several options available in this set of subroutines. They are listed below:
NORMAL NO ID FRAME NO EFRAME PRINTED OUTPUT ONLY
Same as Substitute Substitute Substitute
above CLEAN UP ERAME II TAPE III
for for for
CAMRAV EFRAME TAPE
JOBNO ID FRAME
ID FRAME END FRAME
In the PRINTED OUTPUT ONLY section, CAMRAV can be removed if the main program has a direct call to subroutine IDFM.
To plot characters or dots - APLOTV
To plot lines - LINE and LINEV
To plot standard CHARACTRON printing - PRINTS and PRINTV
To plot variable sized letters and symbols such as titles, etc. - RITE2S, CHSIZV, RITE2V, HOLLV, TABL*V (any necessary table)
The following two subroutines'wera developed for the spheroidal radiator example and require some of the above routines even if they are not called directly:
GENSYM RULE requires requires CHSIZV CHSIZV RITE2V HOLLV
The last deck is followed by a three-star ***DATA card. The data cards themselves will depend on the main program but each program will have three additional data cards required by the call to CAMRAV. The first card contains the job number in the first six columns of the card. The rest of the card is blank. If no number at all is desired, a blank card can be used but the card, blank or not, must appear in the data deck. Because of the way the subroutine ID rRAME handles this information, only the number zero through nine, or a blank, can be used. Letters and symbols are not permitted.
The second card contains the information for the scaling ratios used in XSCALV. The entire card uses a (8F9.6) format to fill columns 1 - 72. The floating point field for each number covers nine columns for seven figure accuracy.
The other two columns are used for the decimal point and the sign, if necessary. The eight "nine column" fields have the following representation:
FIELD COLUMNS USE 1 1 - 9 Value of X at left boundary 2 10 - 18 Value of X at right boundary 3 19 - 27 Size of left margin 4 28 - 36 Size of right margin 5 37 - 45 Value of Y at bottom boundary 6 46 - 54 Value of Y at top boundary 7 55 - 63 Size of bottom margin 8 64 - 72 Size of top margin
The numbers for the margin sizes have to be floating point integers between zero and 1024 followed by a decimal point. They are never negative and are usually "0." when producing movies.
The third data card contains the information to be printed on the ID frame. It has four alphanumeric fields, each of which is separated by a zero punch on the card. The format is as follows:
FIELD COLUMNS USE
1 1 - 17 Name of program
18 Punch zero
2 19 - 35 Programmer's name
36 Punch zero
3 37 - 47 Programmer's department
48 Punch zero
4 49 - 56 Date in form MO/DAY/YEAR
57 Punch zero
The zero in columns 18, 36, 48, and 57 are required even if the rest of the card is blank. They serve as flags in the ID FRAME subroutine to reset the SC 4020 from the typing mode after reading in each of the above data items. (this card is omitted when using subroutine TAPE III.)
With regard to the data deck, the CAMRAV statement should be treated as a READ INPUT statement. In other words, these three data cards are placed in relation to the other data cards in the same relationship that the CAMRAV call has to any READ INPUT statement in the main program.
SCATRAN programs can be run in two different modes, time share and non-time share; When referring to core space, it is better to calculate in octal notation than decimal because both subroutine lengths and the core dump addresses are in octal notation. In this case time share addresses run from 00000 to 37777 and non-time share from 00000 to 77777.
Five items have to be allowed for to determine the size of a program. The SCATRAN monitor (input-output controls, etc.) always occupies all addresses up to 14400. The main program size is determined by the programmer and is therefore unknown. However, experience will give the programmer a feel for the size of any particular program. The SC 4020 subroutines follow the main program. As an aid, the space required for each subroutine listed is given in Appendix B. Subroutines from the SCATRAN library can use quite a bit of room. Their length can be determined either from the memory map, if the program has been run once, or from the SCATRAN programmer's manual. Finally, a small amount of room has to be allowed for a literals table that uses one word for each literal number in the main program.
Ona of the most difficult decisions the programmer has to make is the time estimate to be used for each run. As long as check out work is being done, a time estimate of one minute is completely adequate and almost no job will run over this estimate.
However, it is when the programmer is running the final tapes for a movie that a dilemma has to be faced. Each run can be up to a half hour long. If the run takes longer than the time estimate, the job will automatically be forced off the computer and all the tape made up to that time will be lost. This is because the tape is rewound without a DISMOUNT message being given to the computer operator. The answer to this problem is to make certain how long a problem will run and then put down some excess time- to cover unforseen contingencies.
The other horn of the dilemma is that if an excessive amount of time is put down and the program has a loop in it, all the time will again be lost due to the loop. Therefore, the time should be as short as possible in case a loop is encountered. This problem troubled the spheroidal radiator example run because the inherent loop in the way the successive points were calculated would not show up in some of the runs but would in others when the same problem was run with slightly different input data.
The only way around this is to make many different runs at different times, each covering some part of the input data spectrum, and each taking less than a minute. Ten minutes of computer time spent here could save much more when the longer runs are attempted because the timing can be more exact based on the times of the short runs and the programmer can be assured that looping will not occur.
There are two means of dividing up the data that is placed on a reel: a minor division called a record, and a major division called a file.
A record consists of the amount of information that is written or read at one time. It can be of any length but in this case the size depends on the size of the input buffer of the particular SC 4020 that is going to be used. If the record is too long for the size of the buffer, it will be read until the buffer is full and the tape will then be moved to the start of the next record. All successive words in the record will be lost. Buffer lengths in the SC 4020 have three different sizes: 170 words, 1024 words, and 4096 words. Before a tape is produced, it is necessary to determine the buffer size of the SC 4020 that will be used to run the job. If this size cannot be determined, the 170 word length should be used. The longer buffers will accept the short records but at the cost of very poor efficiency both when writing the tape and when reading it with the SC 4020.
The beginning and ending of each record can be identified by a record gap. This is a 3/4 inch gap in which no recording appears. Its purpose is to allow time for the tape drive to accelerate and reduce speed when reading a record. The tape can only stop at a record gap which is why only complete records can be read. When more words are to be computed than the length of the buffers, by far the usual case, the write subroutine will automatically close the record at the right count, write a record gap, and then open a new record as the information continues to be computed.
The major division of a tape is the file. A file mark consists of a one word record that is used to tell the computer uhen a section of the tape is computed. It is used when it is desired to repeat a scene over several times. The SC 4020 will halt on a record gap only long enough to perform operations contained in that record, but when a file mark is reached, the machine stops and returns to operator control. The operator can than either go on to the next file or backspace and repeat the file already recorded. In this way, a small amount of tape can result in a great number of frames to increase the running time of a scene in a movie.
The tape density determines the capacity of the tape. At the present time, there are three densities in standard use, 200 characters per inch, 556 characters per inch, and 800 characters per inch. So little work is being done with 200 characters per inch that it can almost be considered to be obsolete. However, it is necessary to know that this density exists when defining low and high density tape. As an example, at OSU low and high density refer to 556 BPI (bits per inch) and 800 BPI respectively. At North American Aviation, low and high density refer to 200 BPI and 556 BPI. Therefore, a low density tape at OSU is a high density tape at North Amarican. At the present time, the SC 4020 will accept only 556 BPI tapes.
The formula given by IBM for a density of 556 BPI for the number of inches per record is:
Inches per record = 0.75 + 0.0108N
where N is the number of words per record and the 0.75 is the 3/4 of an inch allowed for the record gap. Since a reel of tape is 2500 feet long or 30,000 inches, we can calculate the number of words that can be placed on one reel of tape, assuming either 170 words par record or 4096 words per record.
At 170 words per record:
I = 0.75 + .0108 × 170 = 2.586 inches
Records = 30,000/2.586 = 11600
Words = 11600 × 170 = 1,972,000
At 4096 words per record:
I = 0.75 + .0108 × 4096 = 44.987 inches
Records = 30,000/44.987 = 667
Words = 667 × 4096 = 2,732,000
In the case of 4096 words per record, the number of words that can be placed on a reel of tape is approximately forty per cent greater than that which can be placed on the reel at 170 words par record. Therefore, tape should be written using the largest size records possible allowing for the SC 4020 input buffer size. In general, the output buffer size of the IBM 7094 computer will not be a problem.
One difficulty was encountered when producing tape at OSU for running elsewhere. The original tape computed by the IBM 7094 seemed to be noisy in that non-repeatable errors were encountered when these tapes were run. The symptoms were that the SC 4020 would occassionally fail to recognize a valid command word on the tape and would give an error signal while advancing the tape to the end of the record. Naturally, all command words from that point to the and of the record were lost. This meant that the picture was spotty or if one of the missing words happened to be an advance film command, the following frame would be overlaid on the one already recorded. The SC 4020 does not have as high a degree of error checking as the IBM 7094 which is why the difficulty showed up only when the tapes were being actually run. After some investigation, it was found that the problem could be avoided entirely if the IBM 7094 tapes were copied on a small computer (IBM 1410) designed for this purpose. A perfect copy is made without any noise that might have been present in the original. The tape is only being copied rather than being computed so the costs of the copying operation are negligible compared to that of the original program.
A word of warning is necessary when copying tape with the IBM 1410. There are two copy routines available, CP 1 and CP 2. It is essential that CP 2 be used for this purpose and that this information be given to the computer operator before the tape is to be copied.
If CP 1 is used to copy a tape, the input buffer is hardware limited to accepting one hundred and five words per record. After the first one hundred and five words are copied, the tape is moved to the end of the record and all the succeeding words are lost. This means that if a tape has been written with 170 word records, about forty per cent of the information is lost in making the copy. When copying tape that is written with 1024 word records, the result is disastrous.
This section contains the operating subroutines used with the SC 4020 and BL 120 computer plotters. They are listed alphabetically below with the amount of octal core space required for each subroutine. The subroutines are not filed alphabetically but by groups according to their interlocking requirements and frequency of use. Also included are two tests for checking the subroutines and a tape dump for checking magnetic tape output.
A number of these subroutines will run under either a FORTRAN or SCATRAN operating system. They have asterisks in front of the name. They are of two types, ones that are not called from a main program, such as TABL-V, and ones that have an associated conversion program so that they can be called in SCATRAN. RITE2V and CHSIZV are of the second type and need RITE2S to be convected to the SCATRAN operating system. The preceding section on program running operations gives the data on which particular subroutines must be run together. Should it be desired to modify any of these subroutines, the section on the differences between FORTRAN and SCATRAN should be thoroughly understood before any changes are attempted.
The table below gives the core space requirements for these subroutines.
| NAME | OCTAL SPACE REQUIREMENTS |
|---|---|
| APLOTV | 224 |
| CAMRAV | 211 |
| CHSIZV* | 251 |
| CLEANUP | 023 |
| CUT MARKS | 046 |
| EFRAME I | 122 |
| EFRAME II | 011 |
| GENSYM | 222 |
| HOLLV* | 037 |
| ID FRAME | 252 |
| JOB NO | 012 |
| LINE | 043 |
| LINEV* | 133 |
| MARKV* | 042 |
| (PLOT) | 030 |
| PLOTV* | 026 |
| POINTV* | 133 |
| PRINTS | 050 |
| PRINTV* | 133 |
| 4 QUAD(PLOT)I | 126 |
| 4 QUAD(PLOT)II | 226 |
| RITE2S | 113 |
| RITE2V* | 242 |
| RULE | 174 |
| TABL1V* | 321 |
| TABL2V* | 115 |
| TABL3V* | 110 |
| TABL5V* | 031 |
| TAPE I | 2377 |
| TAPE II | 7777 |
| TAPE III | 2155 |
| VXAX | 063 |
| VXAXV I* | 053 |
| VXAXV II* | 024 |
| XSCALV | 213 |
The PDF Version of this thesis gives the listings of these SCATRAN subroutines on the next 40 pages.
A dump of the SC4020 instructions generated for the Dot Test Program and the test for LINE, VXAX,VYAX,PRINT and RITE2S follows.
The SC 4020 instructions that start with 00 define the asterisk positions shown in Figure 25.
777633011612 777633211576 777534011616 777534211572 300000000000 460000000000 001177540777 001077540621 000700540621 000600541000 000700541156 001077541156 001277540777 001222540604 001041540503 000640540531 000513540676 000513541101 000640541246 001041541274 001222541173 001377540777 001335540600 001177540442 000777540400 000600540442 000442540600 000400541000 000442541177 000600541335 001000541377 001177541335 001335541177 001477540777 001444540575 001325540422 001142540317 000736540302 000540540353 000375540504 000307540675 000307541102 000375541273 000540541424 000736541475 001142541460 001325541355 001444541202 001577540777 001550540574 001445540411 001277540263 001102540206 000675540206 000500540263 000332540411 000227540574 000200541000 000227541203 000332541366 000500541514 000675541571 001102541571 001277541514 001445541366 001550541203 001677540777 001653540574 001561540403 001427540242 001243540137 001041540101 000634540113 000440540174 000267540317 000154540475 000105540675 000105541102 000154541302 000267541460 000440541603 000634541664 001041541676 001243541640 001427541535 001561541374 001653541203 460000000000 000777540600 000621540700 000621541077 001000541177 001156541077 001156540700 000777540500 000604540555 000503540736 000531541137 000676541264 001101541264 001246541137 001274540736 001173540555 000777540400 000600540442 000442540600 000400541000 000442541177 000600541335 001000541377 001177541335 001335541177 001377540777 001335540600 001177540442 000777540300 000575540333 000422540452 000317540635 000302541041 000353541237 000504541402 000675541470 001102541470 001273541402 001424541231 001475541041 001440540635 001355540452 001202540333 000777540200 000574540227 000411540332 000263540500 000206540675 000206541102 000263541277 000411541445 000574541550 001000541577 001203541550 001366541445 001514541277 001571541102 001571540675 001514540500 001366540332 001203540227 000777540100 000574540124 000403540216 000242540350 000137540534 000101540736 000113541143 000174541337 000317541510 000475541623 000675541672 001102541672 001302541623 001460541510 001603541337 001664541143 001676540736 001640540534 001535540350 001374540216 001203540124 460000000000 000600541000 000700541156 001077541156 001177540777 001077540621 000700540621 000500541000 000555541173 000736541274 001137541246 001264541101 001264540676 001137540531 000736540503 000555540604 000400541000 000442541177 000600541335 001000541377 001177541335 001335541177 001377540771 001335540600 001177540442 000777540400 000600540442 000442540600 000300541000 000333541202 000452541355 000635541460 001041541475 001237541424 001402541273 001470541102 001470540675 001402540504 001237540353 001041540302 000635540317 000452540422 000333540575 000200541000 000227541203 000332541366 000500541514 000675541571 001102541571 001277541514 001445541366 001550541203 001577540777 001550540574 001445540411 001277540263 001102540206 000675540206 000500540263 000332540411 000227540574 000100541000 000124541203 000216541374 000350541535 000534541640 000736541676 001143541664 001337541603 001510541460 001623541302 001672541102 001672540675 001623540475 001510540317 001337540174 001143540113 000736540101 000534540137 000350540242 000216540403 000124540574 460000000000 001000541177 001156541077 001156540700 000777540600 000621540700 000621541077 001000541277 001173541222 001274541041 001244540440 001101540513 000676540513 000531540640 000503541041 000604541222 001000541377 001177541335 001335541177 001377540777 001335540600 001177540442 000777540400 000600540442 000442540600 000400541000 000442541177 000600541335 001000541477 001202541444 001355541325 001460541142 001475540736 001424540540 001273540375 001102540307 000675540307 000504540375 000353540540 000302540736 000317541142 000422541325 000575541444 001000541577 001203541550 001366541445 001514541277 001571541102 001571540675 001514540500 001366540332 001203540227 000777540200 000574540227 000411540332 000263540500 000206540675 000206541102 000263541277 000411541445 000574541550 001000541671 001203541653 001374541561 001535541427 001640541243 001676541041 001664540634 001603540440 001460540267 001302540154 001102540105 000675540105 000475540154 000317540267 000174540440 000113540634 000101541041 000137541243 000242541427 000403541561 000574541653 460000000000
The main SC 4020 output in this case for Figure 26 draws the lines that make up the letters in the message. The small text at the bottom of the frame is defined by the SC4020 hardware text drawing routines.
636000000000 600000236000 636000001777 600000037777 637777400000 601777236000 637777401777 601777037777 201642600000 040002004000 051200000000 201610600014 606060000102 606060000000 120000000000 776074777703 776173777604 776272777505 776371777406 776470777307 776567777210 776666777111 776765777012 777064776713 777163776614 777262776515 777361776416 777460776317 777557776220 653656652121 320777075741 320777075741 777454100551 777355076611 777256100650 777157100710 743060060750 302400000400 302400000400 302400000400 460000000000 636000000000 600000236000 636000001777 600000037777 637777400000 601777236000 637777401777 601777037777 200170451703 120000000000 224666603162 606330256063 314425602646 516021434360 274646246044 254560634660 234644256063 466063302560 213124604626 606330253151 602346644563 517012000000 460000000000 636000000000 600000236000 636000001777 600000037777 637777400000 601777236000 637777401777 601777037777 600132754127 770132554041 600226754127 600250710116 636250622052 674267600041 636325422041 600344510052 636344022116 674325200127 636267222127 674344044041 636366554041 636405710127 636424510063 636443754127 674641600127 600660754127 674641600041 637034222052 675015200041 636757022041 600740422052 636740422063 674757600074 637015422074 601034422105 637034022116 675015200127 636757222127 601232750127 771174600041 601312754127 771312600074 601406754127 771524200127 601430754127 771436600041 733430600074 600170754233 770132600145 674267600233 600306754233 674267600145 600366754233 674366466145 674424666200 600462554l45 770600200233 600504754233 770504600145 732504600200 600740754233 770740600145 732740600200 601056710222 637056622156 675075600145 637133422145 601152510156 637152022222 675133200233 637075222233 675152044145 601174754233 733174600145 637251422145 601270422156 637270022167 733251200200 675232466200 675430754233 675466554145 675447600200 601546754233 771546600233 600132754337 770132600337 636462222262 674443200251 636405022251 600366510262 636366422326 674405600337 636443622337 600462644326 674462200304 600504710326 636504622262 67452360025I 636561422251 600600510262 636600022326 674561200337 636523222337 674600044251 600622710326 636622622262 67464160025I 636677422251 600716510262 636716022326 674677200337 636641222337 674716044251 600740754337 732740600251 637015422251 60l034510262 637034022326 733015200337 601174754337 675174466251 675232666304 601270554251 771406200337 601312754337 771312600251 733312600304 601430754337 771430554251 601524754337 600170754443 770132600355 600250710432 636250622366 674267600355 636325422355 600344510366 636344022432 674325200443 636267222443 674344044355 636600222366 674561200355 636523022355 600504510366 636504422432 674523600443 636561622443 600622710432 636622622366 674641600355 636677422355 600716510366 636716022432 674677200443 636641222443 674716044355 600740754443 674740446355 674776666410 601034554355 771152200443 601056754443 771056600355 733056600410 601350754443 771312600355 601430710432 637430622366 675447600355 637505422355 601524510366 637524022432 675505200443 637447222443 675524044355 600170754547 77013260046I 600250754547 770250600514 600344754547 770462200547 600366754547 770366600461 732366600514 674622754547 674660554461 674641600514 674757600547 600776754547 674757600461 601056754547 733056600461 637133422461 601152510472 637152022536 733133200547 601312710536 637312622472 675331600461 637367422461 601406510472 637406022536 675367200547 637331222547 675406044461 601430754547 771430600461 733430600514 600170754653 770132600565 600250754653 770250600620 600344754653 770462200653 600366754653 770366600565 732366600620 674523600653 600542754653 674523600565 600622754653 732622600565 636677422565 600716422576 636716022607 732677200620 674660466620 637152222576 675133200565 637075022565 601056510576 637056422642 675075600653 637133622653 601174710642 637174622576 675213600565 637251422565 601270510576 637270022642 675251200653 637213222653 675270044565 601312532565 637312422642 675331600653 637367622653 601406732642 601930754453 771430554565 601524754653 601604754653 771546600565 600132754757 732132600671 636207422671 600226422702 636226022713 732207200724 674170466724 674250466671 600306666757 674306666724
The SC 4020 subroutines that were used as a guide for this work were originally written for a FORTRAN II operating system. Since the subroutines had run in FORTRAN elsewhere, they were debugged at OSU and made operational in that language. Since the SC 4020 FORTRAN extension exists and unlike the original subroutines, is self-contained, the details will be given here. Having operating FORTRAN subroutines could prove very useful in the event that a program was to be written and debugged at OSU, but the main runs ware to be done elsewhere due to the computer time involved.
The FORTRAN subroutines are given in this appendix in the PDF version of the thesis but not in this inline version. In order to run a program, the following subroutines are needed:
CAMIR AV - FORTRAN (PLOT) - FORTRAN CUTIV - FORTRAN MARK V CONVRT - FORTRAN
This forms the basic package to produce SC 4020 tapes under the FORTRAN operating system.
CAMRAV - FORTRAN is almost identical to CAMRAV except that a call is made to MARKV through CUTIV to place out marks on hardcopy. In SCATRAN, the subroutines CUTIV and MARKV have been separated and require their own calls.
(PLOT) - FORTRAN is an extremely complex subroutine that replaces the SCATRAN (PLOT)-TAPE-ID FRAME combination. One reason for its complexity is that it is two different subroutines written on top of each other. The first time (PLOT) is called, the non-system file is opened and the ID frame is written. The information used for the ID frame fills the space allocated for the output buffers (two 170 word buffers in this case). An entry is made to what will be a data word the next time (PLOT) is called, but when the subroutine is loaded it represents an operation to call in the ID information. The logic for filling in the blanks in the ID frame takes place within the space that is going to be used for the output buffers. The buffer area is left and a write command empties the buffer onto the non-system file tape creating the ID frame. The next time (PLOT) is called the space that was occupied by the ID frame is overlaid with the SC 4020 command words, word by word. When 170 words are reached or (CLEAN is called, the stored information is transferred to tape.
This subroutine also keeps track of the number of frames produced and controls whether or not a cut mark should be written by CUTIV and MARKV.
CONVRT is a small subroutine that serves to simulate the North American Aviation operating system as far as the SC 4020 subroutines are concerned. The ten entry points match the transfer vectors in the FORTRAN subroutines themselves. This subroutine also has provision for reading in the information required by the ID frame and CUTIV. It uses the following calls:
READ INPUT,TAPE 5,1,N1,N2,N3,N4,N5,N6,N7,N8,N9
1 FORMAT (9A6)
CALL IDINFO(N1,N2,N3,N4,N5,N6,N7,NB,N9)
These calls should be made before CAMRAV is called. CAMRAV can be called without the above information calls and will merely result in an ID frame with blanks in the spaces for the programmer's name, etc. When these calls are used, the following data card is needed:
COLUMN
1 Blank
2-24 Programmer's name
25-27 Dept.
28-30 Group
31-33 Blank
34-36 Box No.
31-41 Blank
42 Cut mark Flag
0 = no cut mark
1 = normal cut mark
2 = cut mark for expanded operation
Anything else or blank = same as zero
43-48 JOBNO (a dash will be placed between the numbers
in 46 and 47, Use 0 through 9 only here)
49-54 DATE (the date should be written as six figures
without separation. For example, 7/15/66 b71566)
55-80 Blank
The call to FRAME empties the buffer of any remaining information, writes a record gap, and then adds the frame advance command followed by the corner marks and cut mark of the new frame. The placement of the advance frame command would have to be moved to the other side of the record gap if tapes made with these subroutines were to run on a plotter such as the BL 120 that requires a record gap after this command.
XSCALV and YSCALV have to be called explicitly so that the scaling factors can be set up. The programmer's manual covers these calls.
A call to CLEAN will empty the buffer of the last frame and call in EFRAME to close the program. The main program ends with the statements
CALL TAPE,9
CALL EXIT or CALL DUMP
END
The CALL TAPE statement rewinds the non-system file tape and prints out a dismount message for the computer operator to return the tape with the program.
There are a few subroutines that have-the same name in both SCATRAN and FORTRAN but are different in the two systems. They are
APLOTV FRAME CAMRAV (PLOT) CUTIV
Outside of these exceptions, any subroutine that ends in V will run under both systems without changes. Subroutines that end in anything but a V will run only under the SCATRAN system.
A few subroutines are written in FORTRAN for the purpose of creating a grid with titles and labels for graphs. Since they were useful mainly for engineering purposes and not for making movies, they are available in the SC 4020 library but they will operate only under the FORTRAN operating system and have not been checked out at OSU. Refer to the SC 4020 Programmers Manual for the following subroutines: BNCV, GRID1V, LABLV, NONLNV, and DXDYV.
This appendix originally contained the statement listings for three programs:
The @ symbol at the end of each line in the listing represents the SCATRAN end symbol on the particular printer used for these printouts.
Pages 354-366 of the Thesis is the SCATRAN Listing of the three main programs.
An SVG animation of the first and third programs has been constructed to replace the SCATRAN code.
The font definitions which were coded in FAP data statements are shown below:
The main part of this animated film consists of various animations of the spheroidal radiator. Unfortunately, the thesis contains no details of the scenes actually constructed. The spheroidal radiator shows:
Given that the program is written in SCATRAN for which there is unlikely to be a compiler and the only known manual for SCATRAN appears to be a paper version in the OSU Library the only hope was to convert the SCATRAN Code to FORTRAN II by guesswork and then attempt to run the Fortran code to generate some graphical output.
The major problem was the size of the number of points generated. They had to be close together to appear as lines on the SC 4020 but no more than necessary. Much of the code is aimed at keeping the number of points to a minimum as the streamlines are drawn. Two flow diagrams are the original SCATRAN code redefined in pidgin Fortran. The first flow diagram shows the generation of the central ellipse and the second shows the more complex code that generated the cycles of streamlines.
The central ellipse has a fringe of lines that indicate the size of the current and the centre of the lellipse contains a number of symbols indicating the state of the animation. A small font is used to describe the central features together with a vertical line. The character set is shown below.
A typical example of the central ellipse is shown below. The blue lines are drawn as SC 4020 lines while the ellipse itself are SC 4020 point output, shown here in red. A possible central diagram is shown in green.
A typical frame from the animated film is shown below. This was generated from the Furtran rewrite of the original SCATRAN program. The SC 4020 points have been deliberately placed further apart so that the output can be seen to be points. The frame shows 4 cycles of 8 streamlines. This is about 10,000 points so the time to draw on the SC 4020 would have been significant but less than attempting to do the same using SC 4020 short lines. The blue border indicates where the SC 4020 display boundary was reached. Points outside that boundary would not have been drawn.
[1] Selected Films on Instrumentation (Pittsburgh Instrument Society of America, 1956).
[2] The National Observer, September 11, 1965, p. 15.
[3] J G Brainerd et al, Summary Report, Conference an Motion Pictures for Instruction in Electrical Engineering, University of Illinois, September 23-25, 1962, pg. A-5.
[4] H H Skilling, Electrical Transmission Lines (New York, McGraw-Hi11, Inc., 1951),
[5] V Bush, Operational Circuit Analysis (New York. John Wiley and Sons, Inc., 1937).
[6] H Skilling, Fundamentals of Electrical Waves (New York: John Wiley and Sons, Inc., 1948), pg 124.
[7] T Morano, Microwave Transmission Data (New Yorks Dover Publications, Inc, 1958) pp 113-119.
[8] H Skilling, Fundamentals of Electrical Waves (New York: John Wiley and Sons, Inc., 1948).
[9] FORTRAN II Assembly Programming Manual, IBM 7090-21, 1963
[10] H E Kosters et al, Automatic Data Processing Glossary U S Goverment Printing Office, 1962.
[11} M V Wilkes, Automatic Digital Computers, John Wiley, 1958, p 273.
[12] Bernard A Galler, The Language of Computers, McGraw-Hill, 1962.
[13] Ivan Flores, Computer Software, Prentice Hall, 1965).
[14] David M Shupe, Streamline Representation of Radiating Electromagnetic Fields (unpublished Master's thesis, Dept. of Electrical Engineering, OSU, 1966)
[15] Ivan L. Finkle, "Recording Lissajous Figures," Science, Vol 148, No 3577, June 1965, pp 1541-1542.
[16] G A McCue and J D 0'Keefe, Computer Stereography, Science, Vol 151, No 3712, Feb 1966, pp. 839-840.
[17} W H Huggins, Symposium on the Human Side of Computing Machines, Bell Telephone Laboratories, Murray Hill, June 20, 21, 1966.
[18] L J Chu, J A Stratton, Forced Oscillations of a Prolate Spheroid, Journal of Applied Physics, Vol 12, March, 1941, p 242,
[19] Ryder pp328-329.
[20] K C Knowlton, A Computer Technique for Producing Animated movies, SJCC, 1964, Spartan.
[21] I E Sutherland, Sketchpad: A Man-Machine Graphical Communication System, AFIPS, Spring, 1963.
A motion picture of the electromagnetic field pattern of a prolate spheroid antenna was completely produced by an IBM 7094 computer and an SC 4020 microfilm plotter. The technique of illustrating complex mathematical subjects by means of computer pictures should lead to better understanding in electrical engineering.
I am reporting on a computergenerated movie that I produced using an IBM 7094 and an SC 4020 CRT plotter at the Ohio State University department of electrical engineering. My purpose was to determine if computer-generated movies would be of value in the understanding of electrical engineering phenomena.
A number of topics have been reported based on the use of computer pictures [1]. Electromagnetics are an ideal subject for this technique because the mathematical abstractions obscure the real events taking place. This is particularly true with time-varying fields where even a still picture cannot give a true representation of the motion taking place.
The subject selected was the resonant spheroidal radiator. The distribution of current on the spheroid was chosen to be rotationally symmetric so that the radiated field could be pictured with a two-dimensional representation of a plane section containing the interfocal axis. Figure 1 and Figure 2 show scenes from the movie. The field in the second picture is approximately 90 degrees out of phase with the first. The lines represent streamlines of constant potential, which are actually a plane sectional view of toroidal-shaped tubes. The stream surfaces in the three-dimensional case represent surfaces over which no displacement current flows. The mathermatical basis for these surfaces can be derived from Ampere's law. If H is independent of φ and the path of integration is a circle normal to the interfocalm axis, then
where H is the magnetic field vector; dI is the vector differential along the path of integration; Hφ is the single component of a rotationally symmetric magnetic field; IC, are the conduction currents enclosed by path of integration; ID are the displacement currents enclosed by path of integration; and ρ is the radius from z-axis in x-y plane. If the currents are set equal to a constant, a surface of revolution is generated.
Since 2πρ Hφ is equal to a constant, the integral around a closed path in one of these surfaces must be equal to zero. Therefore, if the only conduction currents are on the spheroid, the flow of displacement current across any surface must be zero. The movement of the field can be pictured as follows: each group of lines represents a nest of toroids. A constant displacement current flows between each surface, with each set reversing in direction as the current on the antenna changes. The density of this current is greatest closest to the x-axis, and this is shown by the greater density of lines there.
An equation for ρHφ was obtained from Ryder [2]:
where η and ψ are the radial and angular coordinates, respectively, ω is the angular velocity, and ρ is an integer for each harmonic. The real part of this equation was used with ρ set equal to 1:
This equation was made equal to a constant, and a different value was used for each streamline in a nest.
where the outermost streamline of each half cycle is determined by the smallest constant. The spheroid coordinates ξ and η are related to the 2-D cartesian coordinates ρ and χ by
These equations hold for a resonant spheroidal antenna whose interfocal distance (2f) is λ/2. The points along a streamline are computed at approximately equal spacing through an iterative process. First, is incremented, then η is computed, followed by ρ, χ and the distance from the preceding point. If the distance between points is within set limits, the new point is stored; otherwise, the increment in ξ is changed by the ratio of the desired distance to the calculated distance, and the above procedure is repeated. When all the points for one streamline have been calculated, they are transformed into SC 4020 control words and placed on magnetic tape.
Both the time increment between each frame and the distance for each half-cycle can be calculated by adding the proper value to η before transforming to the ρ,χ coordinate system used by the plotter.
My investigation shows that, for many curves, it may be better to plot curved lines by means of touching dots rather than by line segments. The pictures have a smoother appearance, and the machine time for calculating these does not seem to be excessive. In the examples shown, the dots are two raster counts apart. About 20 seconds on the 7094 computer was used to produce the tape for each picture.
The IBM 7094 computed this pattern at 96 different positions in the cycle. The tape represented one cycle over 4 seconds of movie at 24 frames per second. This tape was processed eight times by the SC 4020 to create 30 seconds of 16-mm film.
The movie started with the title, credits, and one scene of text. This was followed by displaying the focal points, drawing an ellipse, and rotating it to show that three dimensions were present. A generator symbol in the center and the dark fringe on the surface, proportional to charge, were added. This was followed by three main scenes. First, the radiated field was shown (Figure 1 and Figure 2). Then the field was frozen, and two rulers were used to show that the distance between the focal points of the ellipse was equal to one-half wavelength. Finally, segments were added to the streamlines. These segments moved around the streamlines to indicate the direction of motion of the displacement field. This was followed by the end in block letters. All scenes including the lettering were generated by the computer. The method of using streamlines to show the magnetic field and moving segments to show the displacement current could be applied to a number of field configurations in electromagnetics.
One of the main purposes behind the film was to explain a rather complex subject to the viewer regardless of his mathematical background. For example, the increased phase velocity of the near field can be seen very clearly. In conclusion, the technique should serve as an accessory in promoting understanding in both classrooms and laboratories.
(1) I. L. Finkle. Science 148, 1541; K. C. Knowlton, ibid. 150, 1116; G. A. McCue and J. D. O'Keefe, ibid. 151, 839 (1966); A, C. Wahl, ibid., p. 961.
(2) These equations are explained in detail by R. M. Ryder, J. Appl. Phys. 13, 327 (1942).
(3) I thank Prof. J. D. Cowan, Jr., Prof. E. Kennaugh, and D. Shupe of the electrical engineering department of Ohio State University, the Numerical Computation Laboratory of Ohio State University, the National Committee for Electrical Engineering Films, and Educational Services, Inc., for help in this work. 1 December 1966