Name
Abstract | ||
|---|---|---|
AbstractWe 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. |
Year | DOI | Venue |
|---|---|---|
2021 | 10.1145/3478513.3480557 | ACM Transactions on Graphics |
Keywords | DocType | Volume |
intrinsic Delaunay, intrinsic triangulation, edge flip, conformal parametrization, conformal map, cone metric | Journal | 40 |
Issue | ISSN | Citations |
6 | 0730-0301 | 0 |
PageRank | References | Authors |
0.34 | 0 | 6 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Marcel Campen | 1 | 407 | 23.47 |
| Ryan Capouellez | 2 | 0 | 0.34 |
| Hanxiao Shen | 3 | 6 | 2.09 |
| Leyi Zhu | 4 | 0 | 0.34 |
| Daniele Panozzo | 5 | 0 | 0.34 |
| Denis Zorin | 6 | 2248 | 151.26 |