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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You can also see coverage of the whole sphere with S-patches in all five cases.

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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.



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