Form from Function: Analysis of Shapes

Some examples of functions and their graphs were given in chapter 4. In this chapter we develop this theme further, looking at ways that some important 2D shapes can be represented as the loci of functions, and further how these may be extended as the bases of standard forms in 3D. The subject of calculus is introduced as a way of analyzing graph structure. We start with the mathematical properties of the straight line. Bresenham’s algorithm, the standard method for drawing straight lines on a raster computer display, is explained in most computer graphics texts, such as those listed in the section on further reading.