Conformal Structures and Period Matrices of Polyhedral Surfaces
arXiv:0909.13054 citations
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Provides a computational tool for discrete differential geometry, enabling period matrix calculations for polyhedral surfaces.
The paper develops a method to compute period matrices of polyhedral surfaces using linear discrete Riemann surfaces, recovering known results and computing the previously unknown period matrix of the Lawson genus-2 surface.
We recall the theory of linear discrete Riemann surfaces and show how to use it in order to interpret a surface embedded in R^3 as a discrete Riemann surface and compute its basis of holomorphic forms on it. We present numerical examples, recovering known results to test the numerics and giving the yet unknown period matrix of the Lawson genus-2 surface.