计算点的离散Voronoi、Johnson-Mehl或Laguerre图的一种简单快速算法
A simple and fast algorithm for computing discrete Voronoi, Johnson-Mehl or Laguerre diagrams of points
摘要：
本文提出了一种算法来计算数字图像的Voronoi，约翰逊-梅尔或Laguerre图的一组点的网站，在一个域的欧几里德空间的任何维。该算法的原理是，在第一步骤中，调查以位点为中心的球中的体素，并且在第二步骤中，处理球外部剩余的体素。球半径的最佳选择可以通过分析或数字来确定，这允许执行$O(N_v \ln N_s$）中的算法，其中$N_v$是域的体素的总数，而$N_s$是棋盘形布置的位点的数量。周期和非周期的边界条件被认为是。该算法的一个主要优点是它的简单性，这使得它很容易实现。这使得该算法适用于创建包含大量细胞的微结构的高分辨率图像，特别是当使用基于FFT的均化方法的计算然后应用于模拟材料时。
英文摘要：
This article presents an algorithm to compute digital images of Voronoi, Johnson-Mehl or Laguerre diagrams of a set of punctual sites, in a domain of a Euclidean space of any dimension. The principle of the algorithm is, in a first step, to investigate the voxels in balls centred around the sites, and, in a second step, to process the voxels remaining outside the balls. The optimal choice of ball radii can be determined analytically or numerically, which allows a performance of the algorithm in $O(N_v \ln N_s$), where $N_v$ is the total number of voxels of the domain and $N_s$ the number of sites of the tessellation. Periodic and non-periodic boundary conditions are considered. A major advantage of the algorithm is its simplicity which makes it very easy to implement. This makes the algorithm suitable for creating high resolution images of microstructures containing a large number of cells, in particular when calculations using FFT-based homogenisation methods are then to be applied to the simulated materials.
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