Hyperbolic Delaunay Complexes and Voronoi Diagrams Made Practical

机译：双曲Delaunay复数和Voronoi图变得实用

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We study Delaunay complexes and Voronoi diagrams in the Poincare ball, a conformal model of the hyperbolic space, in any dimension. We elaborate on our earlier work on the space of spheres, giving a detailed description of algorithms. We also study algebraic and arithmetic issues, observing that only rational computations are needed. All proofs are based on geometric reasoning, they do not resort to any use of the analytic formula of the hyperbolic distance. This allows for an exact and efficient implementation in 2D. All degenerate cases are handled. The implementation will be submitted to the CGAL editorial board for future integration into the CGAL library.

机译：我们研究Poincare球（一个双曲空间的共形模型）在任何维度上的Delaunay配合物和Voronoi图。我们详细介绍了我们在球体空间上的早期工作，对算法进行了详细描述。我们还研究代数和算术问题，观察到只需要理性计算。所有证明均基于几何推理，它们不求助于双曲线距离的解析公式。这允许在2D中进行精确而有效的实施。所有退化的案件都得到处理。该实现将提交给CGAL编辑委员会，以供将来集成到CGAL库中。

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来源
《Annual symposium on computational geometry》|2013年|67-76|共10页
会议地点 Rio de Janeiro(BR)
作者
Mikhail Bogdanov; Olivier Devillers; Monique Teillaud;
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作者单位

INRIA Sophia Antipolis - Mediterranee;

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原文格式 PDF
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关键词
Triangulation; Hyperbolic geometry; Poincare ball; Space of spheres;

机译：三角剖分；双曲几何；庞加莱球；球体空间;

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1. A unified approach towards computing Voronoi diagram, medial axis, Delaunay graph and a-hull of planar closed curves using touching discs [J] . Sundar Bharath Ram, Mukundan Manoj Kumar, Muthuganapathy Ramanathan Computers & Graphics . 2020,第Juna期

机译：使用触摸盘计算Voronoi图，内侧轴，DELAUNAIG图和平面闭曲线的A-HULL的统一方法
2. Constructing Intrinsic Delaunay Triangulations from the Dual of Geodesic Voronoi Diagrams [J] . YONG-JIN LIU, DIAN FAN, CHUN-XU XU, ACM Transactions on Graphics . 2017,第2期

机译：从测地Voronoi图对偶构造本征Delaunay三角剖分
3. Localised sensor direction adjustments with geometric structures of Voronoi diagram and Delaunay triangulation for directional sensor networks [J] . Sung Tien-Wen, Yang Chu-Sing International journal of ad hoc and ubiquitous computing . 2015,第2期

机译：用于定向传感器网络的具有Voronoi图和Delaunay三角剖分的几何结构的局部传感器方向调整
4. Hyperbolic Delaunay Complexes and Voronoi Diagrams Made Practical [C] . Mikhail Bogdanov, Olivier Devillers, Monique Teillaud Annual symposium on computational geometry . 2013

机译：双曲线德拉尼亚复合体和voronoi图实用
5. Efficient/practical algorithms for geometric structures: Convex hulls, Delaunay triangulations and Voronoi diagrams. [D] . Kao, Chiung-Tung Thomas. 1992

机译：几何结构的高效/实用算法：凸包，Delaunay三角剖分和Voronoi图。
6. Using Delaunay triangulation and Voronoi tessellation to predict the toxicities of binary mixtures containing hormetic compound [O] . Rui Qu, Shu-Shen Liu, Qiao-Feng Zheng, -1

机译：使用Delaunay三角剖分和Voronoi细分来预测包含钟形化合物的二元混合物的毒性
7. Hyperbolic Delaunay Complexes and Voronoi Diagrams Made Practical [O] . Bogdanov, Mikhail, Devillers, Olivier, Teillaud, Monique 2014

机译：双曲Delaunay复数和Voronoi图变得实用

Hyperbolic Delaunay Complexes and Voronoi Diagrams Made Practical

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