Name
Abstract | ||
|---|---|---|
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 (e.g., convex, or polygonal). We compare our approach to previous techniques on a variety of challenging models, often achieving dramatically lower distortion, and demonstrating that global optimality leads to extreme robustness in the presence of noise or poor discretization.
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Year | DOI | Venue |
|---|---|---|
2018 | 10.1145/3197517.3201367 | ACM Trans. Graph. |
Keywords | Field | DocType |
conformal mapping, discrete differential geometry, geometry processing, mesh parameterization | Discrete differential geometry,Flattening,Mesh parameterization,Parametrization,Computer graphics (images),Computer science,Geometry processing,Conformal map,Gravitational singularity,Geometry,Distortion | Journal |
Volume | Issue | ISSN |
37 | 4 | 0730-0301 |
Citations | PageRank | References |
2 | 0.36 | 21 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Yousuf Soliman | 1 | 5 | 1.06 |
| Dejan Slepčev | 2 | 95 | 11.01 |
| Keenan Crane | 3 | 586 | 29.28 |