均匀点云的简洁表示
Succinct Representation of Well-Spaced Point Clouds
摘要：
一组低维的n个点需要Theta（n w）位存储在w位机器上。曲面重建和网格细化对它们处理的点的分布提出了要求。我展示了如何使用这个假设来有损地将一组n个输入点压缩成一个只需要O（n）位的表示，与单词大小无关。该损耗可以将点间距离保持在10%的相对误差内，同时仍然实现三倍的空间节省。该表示允许标准的四叉树操作，以及计算一个点的受限Voronoi单元，时间为O（w^2 + log n），如果w在Theta（log n）内，则可以改进为O（log n）。因此，人们可以使用这种压缩表示来执行网格细化或表面重建在O（n）位，只有一个对数减速。
英文摘要：
A set of n points in low dimensions takes Theta(n w) bits to store on a w-bit machine. Surface reconstruction and mesh refinement impose a requirement on the distribution of the points they process. I show how to use this assumption to lossily compress a set of n input points into a representation that takes only O(n) bits, independent of the word size. The loss can keep inter-point distances to within 10% relative error while still achieving a factor of three space savings. The representation allows standard quadtree operations, along with computing the restricted Voronoi cell of a point, in time O(w^2 + log n), which can be improved to time O(log n) if w is in Theta(log n). Thus one can use this compressed representation to perform mesh refinement or surface reconstruction in O(n) bits with only a logarithmic slowdown.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
