二维广义平衡功率图的分析表示法

IF 0.4 4区 计算机科学 Q4 MATHEMATICS
Christian Jung, Claudia Redenbach
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引用次数: 0

摘要

棋盘格是模拟蜂窝和多晶材料微观结构的重要工具。经典的网格模型包括 Voronoi 图和 Laguerre 网格,其单元是多面体。由于其单元的凸性,这些模型在描述包括可能具有弯曲边界的各向异性晶粒的数据时可能过于局限。目前存在几种通用模型。广义平衡幂图的单元是由椭圆距离引起的,从而产生更多样化的结构。迄今为止,计算广义平衡幂图的方法仅限于标签图像形式的离散版本。在这项工作中,我们推导出了广义平衡幂图顶点和边的二维解析表示。在此基础上,我们提出了一种计算整个图的新算法。
本文章由计算机程序翻译,如有差异,请以英文原文为准。

An analytical representation of the 2d generalized balanced power diagram

An analytical representation of the 2d generalized balanced power diagram

Tessellations are an important tool to model the microstructure of cellular and polycrystalline materials. Classical tessellation models include the Voronoi diagram and the Laguerre tessellation whose cells are polyhedra. Due to the convexity of their cells, those models may be too restrictive to describe data that includes possibly anisotropic grains with curved boundaries. Several generalizations exist. The cells of the generalized balanced power diagram are induced by elliptic distances leading to more diverse structures. So far, methods for computing the generalized balanced power diagram are restricted to discretized versions in the form of label images. In this work, we derive an analytic representation of the vertices and edges of the generalized balanced power diagram in 2d. Based on that, we propose a novel algorithm to compute the whole diagram.

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来源期刊
CiteScore
1.60
自引率
16.70%
发文量
43
审稿时长
>12 weeks
期刊介绍: Computational Geometry is a forum for research in theoretical and applied aspects of computational geometry. The journal publishes fundamental research in all areas of the subject, as well as disseminating information on the applications, techniques, and use of computational geometry. Computational Geometry publishes articles on the design and analysis of geometric algorithms. All aspects of computational geometry are covered, including the numerical, graph theoretical and combinatorial aspects. Also welcomed are computational geometry solutions to fundamental problems arising in computer graphics, pattern recognition, robotics, image processing, CAD-CAM, VLSI design and geographical information systems. Computational Geometry features a special section containing open problems and concise reports on implementations of computational geometry tools.
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