Christopher J. Kimmer, Ph.D.

IU Southeast Informatics

Next: The Voronoi Construction Up: Quasiperiodic Minimal Surfaces Previous: The Critical Surface

Discrete Structure of the Surface

Discrete approximations to minimal surfaces are quite useful and often necessary since analytic representations of most minimal surfaces are too cumbersome for computational use. Simple discrete approximations merely share the same topology and provide a framework for visualizing the structure of the labryinths in the case of periodic minimal surfaces. Detailed triangulated surfaces, which attempt to also approximate the geometry of the surface, will be treated in Chapter 4.

• The Voronoi Construction
• The Voronoi Construction at t = 1
• The t → 0 Voronoi Construction
• The Critical Surface Obtained from the t → 0 Voronoi Construction

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