Discrete multiscale vector field decomposition
Discrete multiscale vector field decomposition
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DOI：
10.1145/882262.882290
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发表时间：
2003-07-01
影响因子：
6.2
通讯作者：
Desbrun, M
中科院分区：
文献类型：
--
作者：
Tong, YY;Lombeyda, S;Desbrun, M
虽然2D和3D矢量场在计算科学中无处不在，但它们在图形中的使用通常仅限于规则网格，在规则网格中，计算很容易通过有限差分方法处理。在这篇论文中。我们提出了一套简单而准确的工具来分析任意四面体上的三维离散矢量场，RIDS。我们引入了向量场的变分多尺度分解为三个直观分量：无散度部分，无旋度部分。还有一个和声部分。我们展示了我们的离散方法如何匹配其著名的光滑模拟，称为Helmotz-Hodge分解，以及由此产生的计算工具具有非常直观的几何解释。我们在一系列应用中演示了这些工具的多功能性，从数据可视化到流体和可变形对象模拟。
While 2D and 3D vector fields are ubiquitous in computational sciences, their use in graphics is often limited to regular grids, where computations are easily handled through finite-difference methods. In this paper. we propose a set of simple and accurate tools for the analysis of 3D discrete vector fields on arbitrary tetrahedral,rids. We introduce a variational, multiscale decomposition of vector fields into three intuitive components: a divergence-free part, a curl-free part. and a harmonic part. We show how our discrete approach matches its well-known smooth analog, called the Helmotz-Hodge decomposition, and that the resulting computational tools have very intuitive geometric interpretation. We demonstrate the versatility of these tools in a series of applications, ranging from data visualization to fluid and deformable object simulation.