Conversion between triangular Bézier patches and rectangular Bézier patches

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...

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Bibliographic Details
Published in:Applied mathematics and computation Vol. 232; pp. 469 - 478
Main Authors: Yan, Lanlan, Han, Xuli, Liang, Jiongfeng
Format: Journal Article
Language:English
Published: Elsevier Inc 01.04.2014
Subjects:
Algorithms
Bezier patches
Computation
Conversion
Conversion algorithm
Converting
Mathematical models
Rectangular Bézier surface
Recursive
Triangular Bézier surface
Rectangular Bézier surface
Conversion algorithm
Triangular Bézier surface
ISSN:0096-3003, 1873-5649
Online Access:Get full text
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Summary: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.
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ISSN:0096-3003
1873-5649
DOI:10.1016/j.amc.2014.01.030