Conversion between triangular Bézier patches and rectangular Bézier patches

Lanlan Yan, Xuli Han and Jiongfeng Liang

Applied Mathematics and Computation, 2014, vol. 232, issue C, 469-478

Abstract: 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×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⩾2 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⩾2, n∈N+ and n⩾2, m∈N+ based on the relationships for m=n=1.

Keywords: Triangular Bézier surface; Rectangular Bézier surface; Conversion algorithm (search for similar items in EconPapers)
Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:232:y:2014:i:c:p:469-478

DOI: 10.1016/j.amc.2014.01.030

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