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The Visual Computer

, Volume 28, Issue 11, pp 1115–1125 | Cite as

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

  • Xiaoqiang Zhu
  • Xiaogang JinEmail author
  • Shengjun Liu
  • Hanli Zhao
Original Article

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.

Keywords

Convolution surface Closed-form solution Planar polygon skeleton Sketch-based modeling CUDA 

Notes

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).

Supplementary material

(MP4 13.3 MB)

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Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  • Xiaoqiang Zhu
    • 1
  • Xiaogang Jin
    • 1
    Email author
  • Shengjun Liu
    • 2
  • Hanli Zhao
    • 3
  1. 1.State Key Lab of CAD&CGZhejiang UniversityHangzhouP.R. China
  2. 2.School of Mathematical Science and Computing TechnologyCentral South UniversityChangshaP.R. China
  3. 3.College of Physics & Electronic Information EngineeringWenzhou UniversityWenzhouP.R. China

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