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Modifying the shape of NURBS surfaces with geometric constraints

Shi-Min Hu Tsinghua University Youfu Li City University og Hong Kong Tao JU Tsinghua University Xiang Zhu Tsinghua University

Geometric Modeling and Processing mathscidoc:1608.16078

Computer Aided Design, 33, (12), 903-912, 2001
NURBS surfaces are among the most commonly used parametric surfaces in CAGD and Computer Graphics. This paper investigates shape modification of NURBS surfaces with geometric constraints, such as point, normal vector, and curve constraints. Two new methods are presented by constrained optimization and energy minimization. The former is based on minimizing changes in control net of surfaces, whereas the latter is based on strain energy minimization. By these two methods, we change control points and weights of an original surface, such that the modified surface satisfies the given constraints. Comparison results and practical examples are also given.
NURBS surfaces, geometric constraints
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@inproceedings{shi-min2001modifying,
  title={Modifying the shape of NURBS surfaces with geometric constraints},
  author={Shi-Min Hu, Youfu Li, Tao JU, and Xiang Zhu},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160826222652664235461},
  booktitle={Computer Aided Design},
  volume={33},
  number={12},
  pages={903-912},
  year={2001},
}
Shi-Min Hu, Youfu Li, Tao JU, and Xiang Zhu. Modifying the shape of NURBS surfaces with geometric constraints. 2001. Vol. 33. In Computer Aided Design. pp.903-912. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160826222652664235461.
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