Signed distance computation using the angle weighted pseudonormal
Signed distance computation using the angle weighted pseudonormal
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DOI：
10.1109/tvcg.2005.49
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发表时间：
2005-05-01
影响因子：
5.2
通讯作者：
Aanæs, H
中科院分区：
文献类型：
--
作者：
Bærentzen, JA;Aanæs, H
闭合、光滑表面的法线长期以来一直被用来确定一个点是在该表面的内部还是外部。对于表示为三角形网格的多面体也可以使用此方法。不幸的是，这是不可能的，因为在三角形网格的顶点和边处，表面不是 C-1 连续的，因此，法线在这些轨迹处未定义。在本文中，我们承诺证明角度加权伪法线（最初由 Thurmer 和 Wuthrich 提出，由 Sequin 独立提出）具有重要的属性，即它允许我们区分网格内部的点和外部的点，无论网格顶点、边或面是否是最接近的特征。这种内外信息通常表示为到网格的有符号距离中的符号。实际上，我们的结果表明该符号可以作为距离计算的一个组成部分来计算。此外，它还提供了一个额外的论据，支持角度加权伪法线是面法线的自然延伸。除了理论结果之外，我们还提出了一种简单有效的算法来计算到闭合 C-0 网格的符号距离。实验表明，运行该算法时的符号计算开销几乎可以忽略不计。
The normals of closed, smooth surfaces have long been used to determine whether a point is inside or outside such a surface. It is tempting to also use this method for polyhedra represented as triangle meshes. Unfortunately, this is not possible since, at the vertices and edges of a triangle mesh, the surface is not C-1 continuous, hence, the normal is undefined at these loci. In this paper, we undertake to show that the angle weighted pseudonormal (originally proposed by Thurmer and Wuthrich and independently by Sequin) has the important property that it allows us to discriminate between points that are inside and points that are outside a mesh, regardless of whether a mesh vertex, edge, or face is the closest feature. This inside-outside information is usually represented as the sign in the signed distance to the mesh. In effect, our result shows that this sign can be computed as an integral part of the distance computation. Moreover, it provides an additional argument in favor of the angle weighted pseudonormals being the natural extension of the face normals. Apart from the theoretical results, we also propose a simple and efficient algorithm for computing the signed distance to a closed C-0 mesh. Experiments indicate that the sign computation overhead when running this algorithm is almost negligible.