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Optimal Cone Singularities for Conformal Flattening by Yousuf Soliman; Dejan Slepčev; Keenan Crane is a Computer Science article available to read on EtoBox.

What is Optimal Cone Singularities for Conformal Flattening about?

Angle-preserving or conformal surface parameterization has proven to be a powerful tool across applications ranging from geometry processing, to digital manufacturing, to machine learning, yet conformal maps can still suffer from severe area distortion. Cone singularities provide a way to mitigate this distortion, but finding the best configuration of cones is notoriously difficult. This paper develops a strategy that is globally optimal in the sense that it minimizes total area distortion among all possible cone configurations (number, placement, and size) that have no more than a fixed total cone angle. A key insight is that, for the purpose of optimization, one should not work directly with curvature measures (which naturally represent cone configurations), but can instead apply Fenchel-Rockafellar duality to obtain a formulation involving only ordinary functions. The result is a convex optimization problem, which can be solved via a sequence of sparse linear systems easily built from the usual cotangent Laplacian. The method supports user-defined notions of importance, constraints on cone angles ( e.g. , positive, or within a given range), and sophisticated boundary conditions

Who reads Optimal Cone Singularities for Conformal Flattening?

Author

Yousuf Soliman; Dejan Slepčev; Keenan Crane

Publisher

Association for Computing Machinery (ACM)

Published

2018

Language

EN

Field

Computer Science (Physical Sciences)