Poisson disk sampling through disk packing

Abstract

Poisson disk sampling is an important problem in computer graphics and has a wide variety of applications in imaging, geometry, rendering, etc. In this paper, we propose a novel Poisson disk sampling algorithm based on disk packing. The key idea uses the observation that a relatively dense disk packing layout naturally satisfies the Poisson disk distribution property that each point is no closer to the others than a specified minimum distance, i.e., the Poisson disk radius. We use this property to propose a relaxation algorithm that achieves a good balance between the random and uniform properties needed for Poisson disk distributions. Our algorithm is easily adapted to image stippling by extending identical disk packing to unequal disks. Experimental results demonstrate the efficacy of our approaches.

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Correspondence to Lin Lu.

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This article is published with open access at Springerlink.com

Guanghui Liang received the BSEE degree in computer science and technology from Shandong University, China, in 2012. Currently, he is studying at Shandong University for a master’s degree. His research interests include computer graphics, computational geometry, and visualization.

Lin Lu is an associate professor of computer science in Shandong University, China. She got her B.Eng. (2002) and M.Eng. (2005) degrees in Shandong University, and Ph.D. (2011) degree in the University of Hong Kong, all in computer science. Her research interests include computer graphics and geometry processing.

Zhonggui Chen received B.S. and Ph.D. degrees in applied mathematics from Zhejiang University, in 2004 and 2009, respectively. Currently, he is working as an associate professor in the Department of Computer Sciences, School of Information Science and Technology, Xiamen University, China. His research interests include computer graphics and computational geometry.

Chenglei Yang is a professor at Shandong University, China. He holds a Ph.D. degree in computer science from Shandong University. His interests include human–computer interaction, virtual reality, computational geometry, and computer graphics. His work involves a variety of research topics such as data modeling and rendering, visibility computing, path planning, collision detection, cooperative design, and interaction in the domains of immersive learning systems.

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Liang, G., Lu, L., Chen, Z. et al. Poisson disk sampling through disk packing. Comp. Visual Media 1, 17–26 (2015). https://doi.org/10.1007/s41095-015-0003-7

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Keywords

  • disk packing
  • image stippling
  • Poisson disk sampling
  • power diagram