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Analytical solutions for sketch-based convolution surface modeling on the GPU

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Abstract

Convolution surfaces are attractive for modeling objects of complex evolving topology. This paper presents some novel analytical convolution solutions for planar polygon skeletons with both finite-support and infinite-support kernel functions. We convert the double integral over a planar polygon into a simple integral along the contour of the polygon based on Green’s theorem, which reduces the computational cost and allows for efficient parallel computation on the GPU. For finite support kernel functions, a skeleton clipping algorithm is presented to compute the valid skeletons. The analytical solutions are integrated into a prototype modeling system on the GPU (Graphics Processing Unit). Our modeling system supports point, polyline and planar polygon skeletons. Complex objects with arbitrary genus can be modeled easily in an interactive way. Resulting convolution surfaces with high quality are rendered with interactive ray casting.

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Acknowledgements

Xiaogang Jin was supported by the National Key Basic Research Foundation of China (Grant No. 2009CB320801), the NSFC-MSRA Joint Funding (Grant No. 60970159), the National Natural Science Foundation of China (Grant No. 60933007), and the Zhejiang Provincial Natural Science Foundation of China (Grant No. Z1110154). Shengjun Liu was supported by the National Natural Science Foundation of China (Grant No. 61173119).

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Authors and Affiliations

  1. State Key Lab of CAD&CG, Zhejiang University, Hangzhou, 310027, P.R. China

    Xiaoqiang Zhu & Xiaogang Jin

  2. School of Mathematical Science and Computing Technology, Central South University, Changsha, 410083, P.R. China

    Shengjun Liu

  3. College of Physics & Electronic Information Engineering, Wenzhou University, Wenzhou, 325035, P.R. China

    Hanli Zhao

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  1. Xiaoqiang Zhu
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  2. Xiaogang Jin
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Correspondence to Xiaogang Jin.

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Zhu, X., Jin, X., Liu, S. et al. Analytical solutions for sketch-based convolution surface modeling on the GPU. Vis Comput 28, 1115–1125 (2012). https://doi.org/10.1007/s00371-011-0662-z

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