Ellipsoidal Density-Equalizing Map for Genus-0 Closed Surfaces
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866915940887691264 |
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| author | Lyu, Zhiyuan Lui, Lok Ming Choi, Gary P. T. |
| author_facet | Lyu, Zhiyuan Lui, Lok Ming Choi, Gary P. T. |
| contents | Surface parameterization is a fundamental task in geometry processing and plays an important role in many science and engineering applications. In recent years, the density-equalizing map, a shape deformation technique based on the physical principle of density diffusion, has been utilized for the parameterization of simply connected and multiply connected open surfaces. More recently, a spherical density-equalizing mapping method has been developed for the parameterization of genus-0 closed surfaces. However, for genus-0 closed surfaces with extreme geometry, using a spherical domain for the parameterization may induce large geometric distortion. In this work, we develop a novel method for computing density-equalizing maps of genus-0 closed surfaces onto an ellipsoidal domain. This allows us to achieve ellipsoidal area-preserving parameterizations and ellipsoidal parameterizations with controlled area change. We further propose an energy minimization approach that combines density-equalizing maps and quasi-conformal maps, which allows us to produce ellipsoidal density-equalizing quasi-conformal maps for achieving a balance between density-equalization and quasi-conformality. Using our proposed methods, we can significantly improve the performance of surface remeshing for genus-0 closed surfaces. Experimental results on a large variety of genus-0 closed surfaces are presented to demonstrate the effectiveness of our proposed methods. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_12331 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Ellipsoidal Density-Equalizing Map for Genus-0 Closed Surfaces Lyu, Zhiyuan Lui, Lok Ming Choi, Gary P. T. Graphics Computational Geometry Numerical Analysis Differential Geometry Surface parameterization is a fundamental task in geometry processing and plays an important role in many science and engineering applications. In recent years, the density-equalizing map, a shape deformation technique based on the physical principle of density diffusion, has been utilized for the parameterization of simply connected and multiply connected open surfaces. More recently, a spherical density-equalizing mapping method has been developed for the parameterization of genus-0 closed surfaces. However, for genus-0 closed surfaces with extreme geometry, using a spherical domain for the parameterization may induce large geometric distortion. In this work, we develop a novel method for computing density-equalizing maps of genus-0 closed surfaces onto an ellipsoidal domain. This allows us to achieve ellipsoidal area-preserving parameterizations and ellipsoidal parameterizations with controlled area change. We further propose an energy minimization approach that combines density-equalizing maps and quasi-conformal maps, which allows us to produce ellipsoidal density-equalizing quasi-conformal maps for achieving a balance between density-equalization and quasi-conformality. Using our proposed methods, we can significantly improve the performance of surface remeshing for genus-0 closed surfaces. Experimental results on a large variety of genus-0 closed surfaces are presented to demonstrate the effectiveness of our proposed methods. |
| title | Ellipsoidal Density-Equalizing Map for Genus-0 Closed Surfaces |
| topic | Graphics Computational Geometry Numerical Analysis Differential Geometry |
| url | https://arxiv.org/abs/2410.12331 |