凸多面体上切割轨迹的实现

IF 0.4 4区计算机科学 Q4 MATHEMATICS

Computational Geometry-Theory and Applications Pub Date : 2023-10-01 DOI:10.1016/j.comgeo.2023.102010

Joseph O'Rourke , Costin Vîlcu

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引用次数: 3

摘要

我们证明了每一个正加权树T都可以实现为凸多面体P上点x的切割轨迹C（x），其中T的边权重与C（x）的边长度相匹配。如果T有n个叶子，则P（通常）有n+1个顶点。我们证明了事实上存在一个多面体P的连续体，每个多面体P对一些x∈P实现T。证明中的三个主要工具是P的星展开性质、Alexandrov的粘合定理和一个新的割轨迹配分引理。从T构造P的过程非常简单。

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Cut locus realizations on convex polyhedra

We prove that every positively weighted tree T can be realized as the cut locus $C (x)$ of a point x on a convex polyhedron P, with T edge weights matching $C (x)$ edge lengths. If T has n leaves, P has (in general) $n + 1$ vertices. We show there is in fact a continuum of polyhedra P each realizing T for some $x \in P$ . Three main tools in the proof are properties of the star unfolding of P, Alexandrov's gluing theorem, and a new cut-locus partition lemma. The construction of P from T is surprisingly simple.

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来源期刊

Computational Geometry-Theory and Applications 数学-数学

CiteScore

1.60

自引率

16.70%

发文量

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.