Chapter 17. Advanced Sphere Visualization
This chapter presents additional methods that can be used to study spheres. We will start from the basic observations of Chapter 8 and explore a selection of other mathematical methods that can be used in specific applications for representing, manipulating, and visualizing spheres. As usual, we introduce the methods beginning with the circle, S1, and work our way up to the ordinary sphere S2 and the unit hypersphere S3 needed to describe quaternions.
Projective Method
An alternative to the Northern–Southern hemisphere method introduced in Chapter 8 is to construct a projection that removes one point of the sphere to infinity and maps the rest to a flat Euclidean space. The advantage of this approach is ...
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