Abstract
We present different linear parametrization techniques for the purpose of surface remeshing: the energy minimizing harmonic map, the convex map, and the least square conformal map. The implementation of those mappings as well as the associated boundary conditions is presented in a unified manner and the issues of triangle flipping and folding that may arise with discrete linear mappings are discussed. We explore the optimality of these parametrizations for surface remeshing by applying several classical 2D meshing algorithms in the parametric space and by comparing the quality of the generated elements. We present various examples that permit to draw guidelines that a user can follow in choosing the best parametrization scheme for a specific topology, geometry, and characteristics of the target output mesh.
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