Exact Sphere Representations over Platonic Solids Based on Rational Multisided Bézier Patches
This Demonstration shows representations of Platonic solids by patches inscribed into a sphere. Depending on the Platonic solid, we use 3, 4 or 5-sided rational S-patches. Hover over the control points and associated weights to see numerical values.[more]
You can also see coverage of the whole sphere with S-patches in all five cases.[less]
Snapshot 1: S-patch defined over a face of an icosahedron that represents one-twentieth of the sphere
Snapshot 2: S-patch defined over a face of a dodecahedron that represents one-twelfth of the sphere
Snapshot 3: whole sphere covered with 12 five-sided S-patches
This Demonstration will be adapted to a research paper to be published .
 A. Š. Praprotnik, "Exact Sphere Representations over Platonic Solids Based on Rational Multisided Bézier Patches," forthcoming.
 C. T. Loop, T. D. DeRose, "A Multisided Generalization of Bézier Surfaces," ACM Transactions on Graphics, 8(3), 1989 pp. 204–234. doi:10.1145/77055.77059.