ABSTRACT
The presentation of each subdivision schema in this chapter is identical. Each presentation starts with orienting one of the polyhedron’s faces in a way that makes calculations easier. This face is called the principal polyhedral triangle (PPT), and it serves as our subdivision workbench. Points are located on the PPT’s edges, and great circle arcs span from one edge point to another. Subdivision grid points are defined where these arcs intersect over the face of the PPT or at some point near their intersection. We will illustrate each of these steps, noting the mathematical principles. We will also present the key formulas and algorithms in Appendix C.
