Chapter 10. Visualizing Interpolation Methods
In this chapter we complete our set of fundamental visualization methods by studying interpolation in the context of spheres, and eventually in the context of quaternion points. The interpolation from one quaternion to another has profound analogies with standard polynomial interpolation methods in Euclidean space. We will see that geodesic curves on spheres provide the starting point for a rich family of interpolation methods and their graphical depiction.
Basics of Interpolation
We will begin with the most fundamental object—the interpolation that creates a great circle on a sphere of any dimension. This interpolation is in fact slightly nontrivial to derive even for S1. The derivation we present is ...
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