Inverting Laguerre Tessellations
Inverting Laguerre Tessellations
复制标题
反转拉盖尔镶嵌
DOI：
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发表时间：
2014
期刊：
影响因子：
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通讯作者：
V. Schmidt
中科院分区：
文献类型：
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作者：
Q. Duan;Dirk P. Kroese;T. Brereton;A. Spettl;V. Schmidt
拉盖尔曲面细分是Voronoi曲面细分的推广，其中点之间的接近度通过幂距离而不是欧几里得距离来测量。拉盖尔镶嵌在材料科学中有着重要的应用，它提供了（多）晶体微观结构和晶粒生长的改进模型。存在有效的算法来从给定的加权生成点集合构造拉盖尔曲面细分，类似于用于Voronoi曲面细分的方法。本文的目的是提供理论和方法的逆构造，即恢复加权生成点从一个给定的拉盖尔曲面细分。我们表明，与Voronoi的情况下，逆问题是在一般非唯一的：不同的加权生成点可以创建相同的镶嵌。为了恢复相关的发电机点，我们制定的反演问题作为一个多峰优化问题，并应用交叉熵方法来解决它。
A Laguerre tessellation is a generalization of a Voronoi tessellation where the proximity between points is measured via a power distance rather than the Euclidean distance. Laguerre tessellations have found significant applications in materials science, providing improved modeling of (poly)crystalline microstructures and grain growth. There exist efficient algorithms to construct Laguerre tessellations from given sets of weighted generator points, similar to methods used for Voronoi tessellations. The purpose of this paper is to provide theory and methodology for the inverse construction; that is, to recover the weighted generator points from a given Laguerre tessellation. We show that, unlike the Voronoi case, the inverse problem is in general non-unique: different weighted generator points can create the same tessellation. To recover pertinent generator points, we formulate the inversion problem as a multimodal optimization problem and apply the cross-entropy method to solve it.
多晶微结构中 3D 晶粒系综的参数化表示
影响因子：
1.6
作者：
A Spettl;T Werz;C E Krill III;V Schmidt
通讯作者：
V Schmidt