A simple algorithm for homeomorphic surface reconstruction
A simple algorithm for homeomorphic surface reconstruction
复制标题
DOI：
10.1142/s0218195902000773
复制
发表时间：
2002-02-01
影响因子：
--
通讯作者：
Leekha, N
中科院分区：
文献类型：
--
作者：
Amenta, N;Choi, S;Leekha, N
从一组采样点计算曲面的分段线性逼近问题在实体造型、计算机图形学和计算机视觉中具有重要意义。使用样本点的Voronoi图的最新算法（1）在假设样本足够密集的情况下给出了输出表面与原始采样表面的距离的保证。我们给出了一个类似的算法，简化了计算和几何保证的证明。此外，我们保证我们的输出表面是同胚的原始表面;据我们所知，这是第一个这样的拓扑保证这个问题。
The problem of computing a piecewise linear approximation to a surface from a set of sample points is important in solid modeling, computer graphics and computer vision. A recent algorithm(1) using the Voronoi diagram of the sample points gave a guarantee on the distance of the output surface from the original sampled surface assuming that the sample was sufficiently dense. We give a similar algorithm, simplifying the computation and the proof of the geometric guarantee. In addition, we guarantee that our output surface is homeomorphic to the original surface; to our knowledge this is the first such topological guarantee for this problem.