4.7 Article

Discrete Conformal Equivalence of Polyhedral Surfaces

期刊

ACM TRANSACTIONS ON GRAPHICS
卷 40, 期 4, 页码 -

出版社

ASSOC COMPUTING MACHINERY
DOI: 10.1145/3450626.3459763

关键词

conformal parameterization; injective mapping; discrete differential geometry

资金

  1. Packard Fellowship
  2. NSF [1717320]
  3. DFG [TRR 109]
  4. NSF Graduate Research Fellowship
  5. Division of Computing and Communication Foundations
  6. Direct For Computer & Info Scie & Enginr [1717320] Funding Source: National Science Foundation

向作者/读者索取更多资源

This paper introduces a numerical method for surface parameterization that produces locally injective and discretely conformal maps on any manifold triangle mesh. The method is extremely robust in practice and provides high-quality interpolation even on meshes with poor elements.
This paper describes a numerical method for surface parameterization, yielding maps that are locally injective and discretely conformal in an exact sense. Unlike previous methods for discrete conformal parameterization, the method is guaranteed to work for any manifold triangle mesh, with no restrictions on triangulatiothat each task can be formulated as a convex problem where the triangulation is allowed to change-we complete the picture by introducing the machinery needed to actually construct a discrete conformal map. In particular, we introduce a new scheme for tracking correspondence between triangulations based on normal coordinates, and a new interpolation procedure based on layout in the light cone. Stress tests involving difficult cone configurations and near-degenerate triangulations indicate that the method is extremely robust in practice, and provides high-quality interpolation even on meshes with poor elements.

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