Convolution Surfaces for Line Skeletons with Polynomial Weight Distributions

Xiaogang Jin, Jieqing Feng, and Qunsheng Peng
State Key Lab of CAD & CG, Zheijang University

Chiew-Lan Tai
Hong Kong University of Science and Technology

This paper appears in issue Volume 6, Number 3.
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Abstract

Convolution surfaces generalize point-based implicit surfaces to incorporate higher-dimensional skeletal elements; line segments can be considered the most fundamental skeletal elements since they can approximate curve skeletons. Existing analytical models for line-segment skeletons assume uniform weight distributions, and thus they can produce only constant-radius convolution surfaces. This paper presents an analytical solution for convolving line-segment skeletons with a variable kernel modulated by a polynomial function, allowing generalized cylindrical convolution surfaces to be modeled conveniently. Its computational requirement is competitive with that of uniform weight distribution. The source code of the field computation is available online.

Author Information

Xiaogang Jin, State Key Lab of CAD & CG, Zheijang University310027 Hangzhou, China jin@cad.zju.edu.cn

Chiew-Lan Tai, Hong Kong University of Science and Technology, Dept of Computer Science, Clear Water Bay Kowloon, Hong Kong taicl@cs.ust.hk

Jieqing Feng, State Key Lab of CAD & CG, Zheijang University310027 Hangzhou, China jqfeng@cad.zju.edu.cn

Qunsheng Peng, State Key Lab of CAD & CG, Zheijang University310027 Hangzhou, China peng@cad.zju.edu.cn

Source Code

Click here for the C source code of the author’s routine to calculate the field of a point generated by a skeleton line with polynomial weight distributions, using the Cauchy kernel.

Figures

[Thumbnail of Figure 2(b)]

Figure 2b. Convolution surface modeling for a deer horn.

[Thumbnail of Figure 5]

Figure 5. Convolution surface modeling for a maple tree.

[Thumbnail of Figure 6]

Figure 6. Convolution surface modeling for a potted plant.

BibTeX Entry

@article{JinEtAl01,
  author = "Xiaogang Jin and Chiew-Lan Tai and Jieqing Feng and Qunsheng Peng",
  title = "Convolution Surfaces for Line Skeletons with Polynomial Weight Distributions",
  journal = "journal of graphics, gpu, and game tools",
  volume = "6",
  number = "3",
  pages = "17-28",
  year = "2001",
}