Parameterizations of Meshes and Digital Surfaces. An Approach combining Metric and Conformity
I present an algorithm of conformal parameterization of meshes and digital surfaces.
Theoretically, it is a generalization of classical barycentric method (cotan conformal coordinates of Polthier) that leads to a better discretization of the Riemann uniformization theorem, and more natural boudary conditions.
Practically, the method has been implemented using a non linear minimization that allows to preserve more or less angles (conformity) or metric properties (lengths, areas, ...). The method can also be adapted to parameterize digital surfaces (whose faces are voxels). Constraints can be added to map textures with fixed positions.
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