Conversion between triangular and rectangular Bezier patches

Shi-Min Hu Tsinghua University

Geometric Modeling and Processing mathscidoc:1608.16079

Computer Aided Geometric Design, 18, (7), 667-671, 2001
In this paper, two explicit conversion formulae between triangular and rectangular Bézier patches are derived. Using the formulae, one triangular Bézier patch of degree n can be converted into one rectangular Bézier patch of degree $n \times n$. And one rectangular Bézier patch of degree m × n can be converted into two triangular Bézier patches of degree $m + n$ . Besides, two stable recursive algorithms corresponding to the two conversion formulae are given. Using the algorithms, when converting triangular Bézier patches to rectangular Bézier patches, we can computer the relations between the control points of the two types of patches for any $n\ge2$ based on the relationships for $n=1$. When converting rectangular Bézier patches to triangular Bézier patches, we can computer the relations between the control points of the two types of patches for any $m\ge 2, n \subset N^+ $ and $n \ge 2, m \subset N^+$ based on the relationships for $m=n=1$.
Triangular Bezier patches, rectangular Bezier patches, Conversion
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@inproceedings{shi-min2001conversion,
  title={Conversion between triangular and rectangular Bezier patches},
  author={Shi-Min Hu},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160826223151754265462},
  booktitle={Computer Aided Geometric Design},
  volume={18},
  number={7},
  pages={667-671},
  year={2001},
}
Shi-Min Hu. Conversion between triangular and rectangular Bezier patches. 2001. Vol. 18. In Computer Aided Geometric Design. pp.667-671. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160826223151754265462.
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