A new bivariate basis representation for Bzier-based triangular patches with quadratic complexity
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Author list: Dejdumrong N.
Publisher: Elsevier
Publication year: 2011
Journal: Computers & Mathematics with Applications (0898-1221)
Volume number: 61
Issue number: 8
Start page: 2292
End page: 2295
Number of pages: 4
ISSN: 0898-1221
Languages: English-Great Britain (EN-GB)
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Abstract
A new class of bivariate bases for the triangular surface construction, based on quadratic and cubic bivariate Bernstein polynomials, is proposed, by extending a model for the univariate basis with linear complexity. This new basis is recursively expressed by its recurrence formulae which are provided, and its important geometric properties are also described. In addition, a recursive algorithm for calculating a point on this triangular surface is recursively defined in the same manner as in the well known de Casteljau algorithm. The main advantage of this model is its recursive algorithm that is proven to construct a triangular surface of degree n in quadratic computational complexity, O(n2). ฉ 2010 Elsevier Ltd. All rights reserved.
Keywords
Bzier triangular patches
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