使用拟蒙特卡罗方法计算点模型的体积

基于体积加细的方法构造点模型的八叉树，在点模型的包围盒内采用Niederreiter低差异数序列产生拟随机点．点模型的体积可以估算为：位于点模型内的随机点个数与全体随机点个数的比值乘以包围盒的体积．实验结果表明，该算法简单、高效，可以快速地计算任意拓扑结构的封闭模型的体积，其与平滑运算结合实现了保体积平滑．

Using Quasi-Monte Carlo Method to Compute Volume of Point Set

Not having to reconstruct any surface, the algorithm first constructs an octree for a point set using a new volume-based refinement method. Then uniformly distributed quasi-random points are generated inside a box enclosing the point set using Niederreiter's low discrepancy sequences. The volume of the point set can be estimated as the ratio of number of random points that are contained within the point set to the total number of random points generated, multiplied by the volume of the box. By testing on a number of point sets, experiments suggest that the new algorithm is simple, efficient and can work well for closed point sets with arbitrary topology. In addition, by combining the algorithm with smoothing operation, a volume-preserving smoothing is obtained.