A new intrinsic numerical method for PDE on surfaces
A new intrinsic numerical method for PDE on surfaces
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DOI：
10.1080/00207160.2011.627435
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发表时间：
2009-07
影响因子：
1.8
通讯作者：
Jyh-Yang Wu;Mei-Hsiu Chi;Sheng-Gwo Chen
中科院分区：
文献类型：
--
作者：
Jyh-Yang Wu;Mei-Hsiu Chi;Sheng-Gwo Chen
在这篇文章中，我们介绍了一个简单，有效的数值方法，局部切向提升方法，用于解决偏微分方程的标量和矢量值的数据定义在表面上。虽然我们遵循传统的方法来近似所考虑的三角形网格的规则曲面，我们的算法的核心思想是开发一个内在的和统一的方法来直接计算三角形网格上定义的函数的偏导数。我们目前的例子在计算机图形学和图像处理应用。
In this note, we introduce a simple, effective numerical method, the local tangential lifting method, for solving partial differential equations for scalar- and vector-valued data defined on surfaces. Even though we follow the traditional way to approximate the regular surfaces under consideration by triangular meshes, the key idea of our algorithm is to develop an intrinsic and unified way to compute directly the partial derivatives of functions defined on triangular meshes. We present examples in computer graphics and image processing applications.