TIP: When you browse the VRML models, you can click on "View source" in Netscape to see the VRML source. In IE, you'll have to download the file using right click and "save target as" and then look at it with a text editor.
Definition of convex polygon. Specifying convexity in VRML. Example.
Recall that we have to specify polygons using counter-clockwise loops. A clockwise loop can be used to represent a hole, as in this example.
Homogeneous representation of points again. Combined 2D rotation/translation using 3x3 matrices. VRML example.
A rigid transformation is one that preserves the distances between all pairs of points in a body. It corresponds to your intuition about a rigid (not deformable) object.
Any 2D rigid transformation can be represented as a rotation/translation pair.
Aside: the center field of the Transform node allows you to specify a rotation center C. A rotation with a specified center is another way to represent 2D rigid transformations. You can compute a single 3x3 matrix representing rotation about the center C in two ways:
General 2D rigid transformations do not commute. VRML example.
Scaling transformations. Matrix representation of X and Y scaling. VRML example.
Because scaling is another 3x3 matrix, we can use any combination of scaling (about any center and along any set of axes), rotation and translation. By multiplying all those transformation matrices together, we get another 3x3 matrix that represents the effects of all of the transformations.