A Varifold Approach to Surface Approximation
A Varifold Approach to Surface Approximation
复制标题
曲面逼近的多种方法
DOI：
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发表时间：
2016
期刊：
影响因子：
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通讯作者：
S. Masnou
中科院分区：
文献类型：
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作者：
Blanche Buet;G. P. Leonardi;S. Masnou
我们表明，varifolds理论可以适当地丰富，开辟了道路，在离散和计算几何领域的应用。使用适当的正则化的质量和第一变化的varifold，我们引入的概念近似平均曲率，并显示各种收敛的结果，特别是，与点云或像素/体素型离散的d-曲面在欧几里得n-空间的离散varifold序列，没有限制的尺寸和余维。该方法的变分性质还允许我们考虑具有奇点的曲面，在这种情况下，近似平均曲率与极限曲面的广义平均曲率一致。一系列的数值试验，以说明该方法的有效性和通用性。
We show that the theory of varifolds can be suitably enriched to open the way to applications in the field of discrete and computational geometry. Using appropriate regularizations of the mass and of the first variation of a varifold we introduce the notion of approximate mean curvature and show various convergence results that hold, in particular, for sequences of discrete varifolds associated with point clouds or pixel/voxel-type discretizations of d-surfaces in the Euclidean n-space, without restrictions on dimension and codimension. The variational nature of the approach also allows us to consider surfaces with singularities, and in that case the approximate mean curvature is consistent with the generalized mean curvature of the limit surface. A series of numerical tests are provided in order to illustrate the effectiveness and generality of the method.