A generalized Ball curve and its recursive algorithm
ACM Transactions on Graphics (TOG) - Special issue on computer-aided design
Curves and surfaces for CAGD: a practical guide
Curves and surfaces for CAGD: a practical guide
A shape preserving representation with an evaluation algorithm of linear complexity
Computer Aided Geometric Design
Efficient Algorithms for Non-Rational and Rational Bézier Curves
CGIV '08 Proceedings of the 2008 Fifth International Conference on Computer Graphics, Imaging and Visualisation
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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).