Fast ellipsoidal conformal and quasi-conformal parameterization of genus-0 closed surfaces
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866907843012067328 |
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| author | Choi, Gary P. T. |
| author_facet | Choi, Gary P. T. |
| contents | Surface parameterization plays a fundamental role in many science and engineering problems. In particular, as genus-0 closed surfaces are topologically equivalent to a sphere, many spherical parameterization methods have been developed over the past few decades. However, in practice, mapping a genus-0 closed surface onto a sphere may result in a large distortion due to their geometric difference. In this work, we propose a new framework for computing ellipsoidal conformal and quasi-conformal parameterizations of genus-0 closed surfaces, in which the target parameter domain is an ellipsoid instead of a sphere. By combining simple conformal transformations with different types of quasi-conformal mappings, we can easily achieve a large variety of ellipsoidal parameterizations with their bijectivity guaranteed by quasi-conformal theory. Numerical experiments are presented to demonstrate the effectiveness of the proposed framework. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_01788 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Fast ellipsoidal conformal and quasi-conformal parameterization of genus-0 closed surfaces Choi, Gary P. T. Computational Geometry Graphics Complex Variables Differential Geometry Surface parameterization plays a fundamental role in many science and engineering problems. In particular, as genus-0 closed surfaces are topologically equivalent to a sphere, many spherical parameterization methods have been developed over the past few decades. However, in practice, mapping a genus-0 closed surface onto a sphere may result in a large distortion due to their geometric difference. In this work, we propose a new framework for computing ellipsoidal conformal and quasi-conformal parameterizations of genus-0 closed surfaces, in which the target parameter domain is an ellipsoid instead of a sphere. By combining simple conformal transformations with different types of quasi-conformal mappings, we can easily achieve a large variety of ellipsoidal parameterizations with their bijectivity guaranteed by quasi-conformal theory. Numerical experiments are presented to demonstrate the effectiveness of the proposed framework. |
| title | Fast ellipsoidal conformal and quasi-conformal parameterization of genus-0 closed surfaces |
| topic | Computational Geometry Graphics Complex Variables Differential Geometry |
| url | https://arxiv.org/abs/2311.01788 |