Paths can also be defined as curves (quadratic and cubic bezier, and elliptical arcs). Probably the most useful is the cubic bezier. This has the initial letter C and has three coordinates as its parameters. A curved path is defined from the current position (either established by a Move command or a previous line or curve command) to the third point defined in the cubic bezier. The first two points define the bezier control points that give the shape of the curve. The positioning of the control points change the shape of the curve under the user's control as can be seen if the circle is clicked.
A real world example is the creation of a duck as shown below. In the top left the duck has been defined by a set of points and the path is a sequence of straight lines between those points (the points are marked by circles):
<path d="M 0 112 L 20 124 L 40 129 L 60 126 L 80 120 L 100 111 L 120 104 L 140 101 L 164 106 L 170 103 L 173 80 L 178 60 L 185 39 L 200 30 L 220 30 L 240 40 L 260 61 L 280 69 L 290 68 L 288 77 L 272 85 L 250 85 L 230 85 L 215 88 L 211 95 L 215 110 L 228 120 L 241 130 L 251 149 L 252 164 L 242 181 L 221 189 L 200 191 L 180 193 L 160 192 L 140 190 L 120 190 L 100 188 L 80 182 L 61 179 L 42 171 L 30 159 L 13 140 Z"/>
The duck without point markers is shown in the top right. In the bottom left the duck has been defined by a set of cubic bezier curves (the control points are marked by aqua circles and the end points by yellow circles) and the duck without the point markers is shown bottom right. The duck defined by bezier curves is:
<path d="M 0 312 C 40 360 120 280 160 306 C 160 306 165 310 170 303 C 180 200 220 220 260 261 C 260 261 280 273 290 268 C 288 280 272 285 250 285 C 195 283 210 310 230 320 C 260 340 265 385 200 391 C 150 395 30 395 0 312 Z"/>
The number of points in the path defined by lines is 43 while the bezier definition uses 25. The path could also be defined using relative coordinates and commas as separators in which case it would be:
<path d="M 0 312c40,48,120,-32,160,-6c0,0,5,4,10,-3c10,-103,50,-83,90,-42 c0,0,20,12,30,7c-2,12,-18,17,-40,17c-55,-2,-40,25,-20,35c30,20,35,65,-30,71 c-50,4,-170,4,-200,-79 z"/>
Note that it does not really make any difference whether you complete the closed curve with upper or lowercase Z as the effect is identical. Removing unnecessary spaces reduces the path definition to 160 characters compared with the 443 characters in the initial line path representation:
<path d="M 0 312c40 48 120-32 160-6c0 0 5 4 10-3c10-103 50-83 90-42c0 0 20 12 30 7c-2 12-18 17-40 17
c-55-2-40 25-20 35c30 20 35 65-30 71c-50 4-170 4-200-79 z"/>