Chapter 19. Two-Dimensional Curves
Our purpose in this chapter is to introduce the idea of orientation frames in two dimensions, and in particular to study the technology of moving orientation frames. We choose two dimensions as our logical starting point because it is the simplest framework available, and there are many basic concepts that generalize to three dimensions and provide insight into quaternion methods.
Orientation Frames for 2D Space Curves
Suppose we have a 2D object (a simple box, for example), as shown in Figure 19.1. The orientation frame consists of two orthogonal vectors, denoted by the tangent T (the direction corresponding to the slope of the “hillside” the box is sitting on) and the normal N, which is the direction perpendicular ...
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