The rational Bernstein bases and the multirational blossoms
Computer Aided Geometric Design
Curves and surfaces for CAGD: a practical guide
Curves and surfaces for CAGD: a practical guide
Computer Aided Geometric Design; Proceedings of a Conference Held at the University of Utah, Salt Lake City, Utah, March 18-21, 1974
GMP '00 Proceedings of the Geometric Modeling and Processing 2000
| Hi-index | 7.29 |
A class of new basis functions for curve and triangular patch modeling is constructed by means of Beta functions. Based on these basis functions, a new scheme of generating curves and triangular patches is proposed. First we demonstrate that these basis functions have similar properties as those of the Bernstein-Bezier basis functions, such as non-negativity, partition of unity and others. Thus, these basis functions give rise to curve and triangular patch representations with affine invariance, convex hull, symmetry and endpoint interpolation, as well as an evaluation algorithm, which is similar to the de Casteljau's algorithm for Bezier curves and surfaces. In addition, these basis functions have a shape parameter. The shape of the curve or triangular patch can be modified by changing the value of the shape parameter under the same control polygon or control net. The modeling examples illustrate the validity of the new methods.