Curves and Patches
In this chapter we investigate the foundations of curves and surface patches. This is a very large and complex subject and it will be impossible for us to delve too deeply. However, we can explore many of the ideas that are essential to understanding the mathematics behind 2D and 3D curves and how they are developed to produce surface patches. Once you have understood these ideas you will be able to read more advanced texts and develop a wider knowledge of the subject.
In the previous chapter we saw how polynomials are used as interpolants and blending functions. We will now see how these can form the basis of parametric curves and patches. To begin with, let’s start with the humble circle.