A Signal Processing Approach To Fair Surface Design
A Signal Processing Approach To Fair Surface Design
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DOI：
10.1145/3596711.3596724
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发表时间：
2023-08
期刊：
影响因子：
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通讯作者：
G. Taubin
中科院分区：
文献类型：
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作者：
G. Taubin
在本文中，我们描述了一个新的工具，交互式自由形式的公平曲面设计。通过将经典的离散傅立叶分析推广到二维离散表面信号-定义在任意拓扑结构的多面体表面上的函数-，我们将表面平滑或光顺的问题减少到低通滤波。我们描述了一个非常简单的表面信号低通滤波算法，适用于任意拓扑结构的表面。相对于其他现有的基于优化的光顺方法，这是计算上更昂贵的，这是一个线性的时间和空间复杂度的算法。有了这个算法，光顺非常大的表面，如那些从体积医学数据，变得负担得起。将该算法与曲面细分方法相结合，得到了一种非常有效的光顺曲面设计技术。然后，我们扩展分析，并相应地修改算法，以适应不同类型的约束。一些约束可以在不对算法进行任何修改的情况下施加，而另一些约束则需要求解一个小的相关线性方程组。特别是，顶点位置约束，顶点法线约束，和表面法线不连续性跨嵌入在表面中的曲线，可以施加这种技术。
In this paper we describe a new tool for interactive free-form fair surface design. By generalizing classical discrete Fourier analysis to two-dimensional discrete surface signals - functions defined on polyhedral surfaces of arbitrary topology -, we reduce the problem of surface smoothing, or fairing, to low-pass filtering. We describe a very simple surface signal low-pass filter algorithm that applies to surfaces of arbitrary topology. As opposed to other existing optimization-based fairing methods,which are computationally more expensive, this is a linear time and space complexity algorithm. With this algorithm, fairing very large surfaces, such as those obtained from volumetric medical data, becomes affordable. By combining this algorithm with surface subdivision methods we obtain a very effective fair surface design technique. We then extend the analysis, and modify the algorithm accordingly, to accommodate different types of constraints. Some constraints can be imposed without any modification of the algorithm, while others require the solution of a small associated linear system of equations. In particular, vertex location constraints, vertex normal constraints, and surface normal discontinuities across curves embedded in the surface, can be imposed with this technique.