Harmonic functions for quadrilateral remeshing of arbitrary manifolds
Harmonic functions for quadrilateral remeshing of arbitrary manifolds
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DOI：
10.1016/j.cagd.2005.04.004
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发表时间：
2005-07-01
影响因子：
1.5
通讯作者：
Garland, M
中科院分区：
文献类型：
--
作者：
Dong, S;Kircher, S;Garland, M
在本文中，我们提出了一种新的用于任意属流形的四边形重新网格划分方法，该方法通用、灵活且高效。我们的技术基于使用在网格上定义的平滑谐波标量场。给定这样一个场，我们计算它的梯度场和第二个向量场，该向量场处处与梯度正交。然后，我们通过这些矢量场追踪积分线以对网格进行采样。两个积分线网络一起用于形成输出网格的多边形。曲率敏感的线间距提供了适应局部形状的各向异性网格。我们的标量场构造允许用户对最终网格的结构进行广泛的控制。整个过程的执行无需计算表面的显式参数化，因此适用于任何属的流形，无需将表面切割成面片。 (C) 2005 Elsevier B.V. 保留所有权利。
In this paper, we propose a new quadrilateral remeshing method for manifolds of arbitrary genus that is at once general, flexible, and efficient. Our technique is based on the use of smooth harmonic scalar fields defined over the mesh. Given such a field, we compute its gradient field and a second vector field that is everywhere orthogonal to the gradient. We then trace integral lines through these vector fields to sample the mesh. The two nets of integral lines together are used to form the polygons of the output mesh. Curvature-sensitive spacing of the lines provides for anisotropic meshes that adapt to the local shape. Our scalar field construction allows users to exercise extensive control over the structure of the final mesh. The entire process is performed without computing an explicit parameterization of the surface, and is thus applicable to manifolds of any genus without the need for cutting the surface into patches. (C) 2005 Elsevier B.V. All rights reserved.