A new bivariate basis representation for Bezier-based triangular patches with quadratic complexity

作者：Dejdumrong Natasha^*

来源：Computers & Mathematics with Applications, 2011, 61(8): 2292-2295.

DOI：10.1016/j.camwa.2010.09.051

• Bezier triangular patches
• Recurrence formulae
• Recursive algorithm
• Quadratic complexity

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(n(2)).

• 出版日期2011-4