Minimal Polyhedron
Minimal Polyhedron is a discrete surface, of zero mean curvature, given by a parametrisation, immersed.
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aperiodic def-parametric discrete immersed implemented minimal
Properties
- Family
- discrete
- Given by
- a parametrisation
- Curvature
- zero mean curvature
- Periodicity
- not periodic
- Ends
- 0
- Embedding
- immersed
- Fidelity
- exact
Definition
No chart is stored: faces are pierced and Laplacian-relaxed into membranes over the edge frame; the surface exists only as the relaxed mesh. The shipped implementation is authoritative; an unverified transcription would silently define a different surface.
Sources
Derived from the Math Art generator registries and cross-referenced to the literature; not transcribed from any gallery's compilation.
- Minimal surfaces / Plateau's problem: the pierced membrane approximates a soap film spanning the held edge frame.
- Discrete membrane relaxation: U. Pinkall and K. Polthier, "Computing Discrete Minimal Surfaces and Their Conjugates", Experimental Mathematics 2(1), 1993, pp. 15-36.
- Laplacian mesh smoothing: M. Desbrun, M. Meyer, P. Schroder, A. Barr, "Implicit Fairing of Irregular Meshes using Diffusion and Curvature Flow", SIGGRAPH 1999.
- Quad-split topology: E. Catmull and J. Clark, "Recursively generated B-spline surfaces on arbitrary topological meshes", Computer-Aided Design 10(6), 1978.