Anisotropic diffusion of surfaces and functions on surfaces
Anisotropic diffusion of surfaces and functions on surfaces
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DOI：
10.1145/588272.588276
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发表时间：
2003-01-01
影响因子：
6.2
通讯作者：
Xu, GL
中科院分区：
文献类型：
--
作者：
Bajaj, CL;Xu, GL
我们提出了一个统一的各向异性几何扩散 PDE 模型，用于平滑（消除）IR3 中的三角双流形表面网格和这些表面网格上定义的函数中的噪声，同时通过仔细选择各向异性扩散张量来增强两者的曲线特征。我们将三角形表面网格的 Loop 细分的 C-1 极限表示和表面网格上的矢量函数与已建立的扩散模型相结合，得到空间方向上扩散问题的离散化版本。时间方向离散化会产生稀疏线性方程组。迭代求解稀疏线性系统会产生一系列公平（平滑）网格以及公平函数。
We present a unified anisotropic geometric diffusion PDE model for smoothing (fairing) out noise both in triangulated two-manifold surface meshes in IR3 and functions defined on these surface meshes, while enhancing curve features on both by careful choice of an anisotropic diffusion tensor. We combine the C-1 limit representation of Loop's subdivision for triangular surface meshes and vector functions on the surface mesh with the established diffusion model to arrive at a discretized version of the diffusion problem in the spatial direction. The time direction discretization then leads to a sparse linear system of equations. Iteratively solving the sparse linear system yields a sequence of faired (smoothed) meshes as well as faired functions.