Name
Abstract | ||
|---|---|---|
The manipulation of surface homeomorphisms is an important aspect in three-dimensional modeling and surface processing. Every homeomorphic surface map can be considered as a quasi-conformal map, with its local nonconformal distortion given by its Beltrami differential. As a generalization of conformal maps, quasi-conformal maps are of great interest in mathematical study and real applications. Efficient and accurate computational construction of desirable quasi-conformal maps between general surfaces is crucial. However, in the literature we have reviewed, all existing computational works on construction of quasi-conformal maps to or from a compact domain require global parametrization onto the plane and are difficult to directly apply to maps between arbitrary surfaces. This work fills the gap by proposing to compute quasi-conformal homeomorphisms between arbitrary Riemann surfaces using discrete Beltrami flow, which is a vector field corresponding to the adjustment to the intrinsic Beltrami differential of the map. The vector field is defined by a partial differential equation in a local conformal coordinate. Based on this formulation and a composition formula, we can compute the Beltrami flow of any homeomorphism adjustment as a vector field on the target domain defined from the source domain, with appropriate boundary conditions and correspondences. Numerical tests show that our method provides a robust and efficient way of adjusting surface homeomorphisms. It is also insensitive to surface representation and has no limitation to the classes of surfaces that can be processed. Extensive numerical examples will be shown. |
Year | DOI | Venue |
|---|---|---|
2014 | 10.1137/14097104X | SIAM JOURNAL ON IMAGING SCIENCES |
Keywords | Field | DocType |
quasi-conformal maps,Beltrami differential,homeomorphism adjustments,least squares | Mathematical optimization,Parametrization,Riemann surface,Vector field,Mathematical analysis,Beltrami equation,Quasi-open map,Surface map,Conformal map,Mathematics,Homeomorphism | Journal |
Volume | Issue | ISSN |
7 | 4 | 1936-4954 |
Citations | PageRank | References |
2 | 0.38 | 0 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Tsz Wai Wong | 1 | 80 | 4.82 |
| Hongkai Zhao | 2 | 797 | 74.83 |