Exact Sphere Representations over Platonic Solids Based on Rational Multisided Bézier Patches
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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.
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Contributed by: Ada Šadl Praprotnik (August 2022)
Open content licensed under CC BY-NC-SA
Snapshots
Details
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 [1].
References
[1] A. Š. Praprotnik, "Exact Sphere Representations over Platonic Solids Based on Rational Multisided Bézier Patches," forthcoming.
[2] 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.
Permanent Citation