Practical spherical embedding of manifold triangle meshes
Practical spherical embedding of manifold triangle meshes
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DOI：
10.1109/smi.2005.32
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发表时间：
2005-06
期刊：
影响因子：
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通讯作者：
S. Saba;I. Yavneh;C. Gotsman;A. Sheffer
中科院分区：
文献类型：
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作者：
S. Saba;I. Yavneh;C. Gotsman;A. Sheffer
Gotsman等人（SIGGRAPH 2003）提出了第一种方法来生成一个可证明的双射参数化的封闭亏格0流形网格的单位球。这涉及到一个大的非线性方程组的解决方案。然而，他们没有展示如何有效地求解这些方程，因此，虽然理论上合理，但该方法至今仍不实用。我们说明了为什么简单的迭代方法来解决方程一定会失败，并提供了一个有效的数值方案，成功。我们的方法使用了一些优化方法与代数多重网格技术相结合。有了这些，我们能够在几分钟内对包含多达10万个顶点的球形参数化网格进行参数化。
Gotsman et al. (SIGGRAPH 2003) presented the first method to generate a provably bijective parameterization of a closed genus-0 manifold mesh to the unit sphere. This involves the solution of a large system of non-linear equations. However, they did not show how to solve these equations efficiently, so, while theoretically sound, the method has remained impractical till now. We show why simple iterative methods to solve the equations are bound to fail, and provide an efficient numerical scheme that succeeds. Our method uses a number of optimization methods combined with an algebraic multigrid technique. With these, we are able to spherically parameterize meshes containing up to a hundred thousand vertices in a matter of minutes.