Morse–Smale complexes on convex polyhedra

IF 0.6 3区 数学 Q3 MATHEMATICS Periodica Mathematica Hungarica Pub Date : 2024-06-05 DOI:10.1007/s10998-024-00583-4
Balázs Ludmány, Zsolt Lángi, Gábor Domokos
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Abstract

Motivated by applications in geomorphology, the aim of this paper is to extend Morse–Smale theory from smooth functions to the radial distance function (measured from an internal point), defining a convex polyhedron in 3-dimensional Euclidean space. The resulting polyhedral Morse–Smale complex may be regarded, on one hand, as a generalization of the Morse–Smale complex of the smooth radial distance function defining a smooth, convex body, on the other hand, it could be also regarded as a generalization of the Morse–Smale complex of the piecewise linear parallel distance function (measured from a plane), defining a polyhedral surface. Beyond similarities, our paper also highlights the marked differences between these three problems and it also relates our theory to other methods. Our work includes the design, implementation and testing of an explicit algorithm computing the Morse–Smale complex on a convex polyhedron.

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凸多面体上的莫尔斯-斯马尔复合体
受地貌学应用的启发,本文旨在将莫尔斯-斯马尔理论从光滑函数扩展到径向距离函数(从内部点测量),定义三维欧几里得空间中的凸多面体。由此产生的多面体莫尔斯-斯马尔复合体一方面可以看作是定义光滑凸体的光滑径向距离函数的莫尔斯-斯马尔复合体的一般化,另一方面也可以看作是定义多面体表面的分段线性平行距离函数(从平面测量)的莫尔斯-斯马尔复合体的一般化。除了相似性,我们的论文还强调了这三个问题之间的显著差异,并将我们的理论与其他方法联系起来。我们的工作包括设计、实现和测试计算凸多面体上莫尔斯-斯马尔复数的显式算法。
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来源期刊
CiteScore
1.40
自引率
0.00%
发文量
67
审稿时长
>12 weeks
期刊介绍: Periodica Mathematica Hungarica is devoted to publishing research articles in all areas of pure and applied mathematics as well as theoretical computer science. To be published in the Periodica, a paper must be correct, new, and significant. Very strong submissions (upon the consent of the author) will be redirected to Acta Mathematica Hungarica. Periodica Mathematica Hungarica is the journal of the Hungarian Mathematical Society (János Bolyai Mathematical Society). The main profile of the journal is in pure mathematics, being open to applied mathematical papers with significant mathematical content.
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