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SurfaceVoronoi: Efficiently Computing Voronoi Diagrams Over Mesh Surfaces with Arbitrary Distance Solvers

文献类型：期刊论文

作者Xin, Shiqing5; Wang, Pengfei5; Xu, Rui5; Yan, Dongming3,4; Chen, Shuangmin2; Wang, Wenping1; Zhang, Caiming5; Tu, Changhe5
刊名ACM TRANSACTIONS ON GRAPHICS
出版日期2022-12-01
卷号41期号:6页码:12
关键词digital geometry processing geodesic distance geodesic Voronoi diagram restricted Voronoi diagram
ISSN号0730-0301
DOI10.1145/3550454.3555453
通讯作者Chen, Shuangmin(csmqq@163.com)
英文摘要In this paper, we propose to compute Voronoi diagrams over mesh surfaces driven by an arbitrary geodesic distance solver, assuming that the input is a triangle mesh as well as a collection of sites P = {p(i)}(i=1)(m) In on the surface. We propose two key techniques to solve this problem. First, as the partition is determined by minimizing the m distance fields, each of which rooted at a source site, we suggest keeping one or more distance triples, for each triangle, that may help determine the Voronoi bisectors when one uses a mark-and-sweep geodesic algorithm to predict the multi-source distance field. Second, rather than keep the distance itself at a mesh vertex, we use the squared distance to characterize the linear change of distance field restricted in a triangle, which is proved to induce an exact VD when the base surface reduces to a planar triangle mesh. Specially, our algorithm also supports the Euclidean distance, which can handle thin-sheet models (e.g. leaf) and runs faster than the traditional restricted Voronoi diagram (RVD) algorithm. It is very extensible to deal with various variants of surface-based Voronoi diagrams including (1) surface-based power diagram, (2) constrained Voronoi diagram with curve-type breaklines, and (3) curve-type generators. We conduct extensive experimental results to validate the ability to approximate the exact VD in different distance-driven scenarios.
WOS关键词COMPUTATION
资助项目National Key RD Program of China[2021YFB1715900] ; National Natural Science Foundation of China[62272277] ; National Natural Science Foundation of China[62002190] ; National Natural Science Foundation of China[62172415] ; National Natural Science Foundation of China[62072284] ; NSF of Shandong Province[ZR2020MF036]
WOS研究方向Computer Science
语种英语
WOS记录号WOS:000891651900005
出版者ASSOC COMPUTING MACHINERY
资助机构National Key RD Program of China ; National Natural Science Foundation of China ; NSF of Shandong Province
源URL[http://ir.ia.ac.cn/handle/173211/51305]  
专题模式识别国家重点实验室_三维可视计算
通讯作者Chen, Shuangmin
作者单位1.Texas A&M Univ, College Stn, TX 77843 USA
2.Qingdao Univ Sci & Technol, Qingdao, Peoples R China
3.Univ Chinese Acad Sci, Sch AI, Beijing, Peoples R China
4.Chinese Acad Sci, Inst Automat, NLPR, Beijing, Peoples R China
5.Shandong Univ, Jinan, Peoples R China
推荐引用方式
GB/T 7714		 Xin, Shiqing,Wang, Pengfei,Xu, Rui,et al. SurfaceVoronoi: Efficiently Computing Voronoi Diagrams Over Mesh Surfaces with Arbitrary Distance Solvers[J]. ACM TRANSACTIONS ON GRAPHICS,2022,41(6):12.
APA Xin, Shiqing.,Wang, Pengfei.,Xu, Rui.,Yan, Dongming.,Chen, Shuangmin.,...&Tu, Changhe.(2022).SurfaceVoronoi: Efficiently Computing Voronoi Diagrams Over Mesh Surfaces with Arbitrary Distance Solvers.ACM TRANSACTIONS ON GRAPHICS,41(6),12.
MLA Xin, Shiqing,et al."SurfaceVoronoi: Efficiently Computing Voronoi Diagrams Over Mesh Surfaces with Arbitrary Distance Solvers".ACM TRANSACTIONS ON GRAPHICS 41.6(2022):12.

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