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Chapter 7

# Convexity and Interpolation

It’s time now to get some of the geometric concepts underlying 3D modeling and lighting in place before we reach those particular chapters. We’ve seen programs where colors, defined at the vertices of a primitive, are mixed and spread throughout the primitive’s interior. This is done by means of interpolation. In this chapter we’ll study the exact mechanics of the interpolation process.

Section 7.1 motivates the process of interpolation with simple examples. Section 7.2 gets to the heart of the matter by showing first that line segment and triangle primitives are particularly suited for interpolation because of the property they share that any point of such a primitive can be uniquely represented as a so-called ...

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