Fast and Memory‐Efficient Voronoi Diagram Construction on Triangle Meshes

• Published in: Computer graphics forum Vol. 36; no. 5; pp. 93 - 104
• Main Authors: Qin, Yipeng, Yu, Hongchuan, Zhang, Jianjun
• Format: Journal Article
• Language: English
• Published: Oxford Blackwell Publishing Ltd 01.08.2017
• Subjects: Categories and Subject Descriptors (according to ACM CCS); Computation; Computer graphics; Computer memory; Geodesy; I.3.5 [Computer Graphics]: Computational Geometry and Object Modeling—Curve, surface, solid, and object representations; Voronoi graphs
• ISSN: 0167-7055; 1467-8659
• DOI: 10.1111/cgf.13248

Geodesic based Voronoi diagrams play an important role in many applications of computer graphics. Constructing such Voronoi diagrams usually resorts to exact geodesics. However, exact geodesic computation always consumes lots of time and memory, which has become the bottleneck of constructing geodesic based Voronoi diagrams. In this paper, we propose the window‐VTP algorithm, which can effectively reduce redundant computation and save memory. As a result, constructing Voronoi diagrams using the proposed window‐VTP algorithm runs 3–8 times faster than Liu et al.'s method [LCT11], 1.2 times faster than its FWP‐MMP variant and more importantly uses 10–70 times less memory than both of them.