Conformal Equivalence of Triangle Meshes
Ulrich Pinkall, Peter Schröder, Boris Springborn
Description
A new algorithm for conformal mesh parameterization is presented here. It is based on a precise notion of discrete conformal equivalence for triangle meshes which mimics the notion of conformal equivalence for smooth surfaces. The problem of finding a flat mesh that is discretely conformally equivalent to a given mesh can be solved efficiently by minimizing a convex energy function, whose Hessian turns out to be the well known $cot$-Laplace operator. This method can also be used to map a surface mesh to a parameter domain which is flat except for isolated cone singularities.
Examples are shown of how these can be placed automatically in order to reduce the distortion of the parameterization.
References
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B. Springborn, P. Schröder, and U. Pinkall.
Conformal equivalence of triangle meshes.
ACM Transactions on Graphics, 2008.
URL: http://www.multires.caltech.edu/pubs/ConfEquiv.pdf, doi:10.1145/1360612.1360676.
