Efficient and Robust Discrete Conformal Equivalence with Boundary
Autor(en): | Campen, Marcel Capouellez, Ryan Shen, Hanxiao Zhu, Leyi Panozzo, Daniele Zorin, Denis |
Stichwörter: | ALGORITHM; Computer Science; Computer Science, Software Engineering; cone metric; conformal map; conformal parametrization; edge flip; intrinsic Delaunay; intrinsic triangulation; SURFACES; UNIFORMIZATION THEOREM | Erscheinungsdatum: | 2021 | Herausgeber: | ASSOC COMPUTING MACHINERY | Journal: | ACM TRANSACTIONS ON GRAPHICS | Volumen: | 40 | Ausgabe: | 6 | Zusammenfassung: | We describe an efficient algorithm to compute a discrete metric with prescribed Gaussian curvature at all interior vertices and prescribed geodesic curvature along the boundary of a mesh. The metric is (discretely) conformally equivalent to the input metric. Its construction is based on theory developed in [Gu et al. 2018b] and [Springborn 2020], relying on results on hyperbolic ideal Delaunay triangulations. Generality is achieved by considering the surface's intrinsic triangulation as a degree of freedom, and particular attention is paid to the proper treatment of surface boundaries. While via a double cover approach the case with boundary can be reduced to the case without boundary quite naturally, the implied symmetry of the setting causes additional challenges related to stable Delaunay-critical configurations that we address explicitly. We furthermore explore the numerical limits of the approach and derive continuous maps from the discrete metrics. |
ISSN: | 0730-0301 | DOI: | 10.1145/3478513.3480557 |
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geprüft am 10.05.2024