Abstract In this paper, a set of quasi-Bernstein polynomials of degree n with one parameter is presented, which is an extension of the Bernstein polynomials over the triangular domain. Using the presented polynomials as basis functions, we construct a class of shape adjusting surfaces defined over the triangular domain with a shape parameter, namely, quasi-B-B parametric surfaces. These surfaces share many properties with the B-B parametric surfaces. In particular, when shape parameters equal 1, they degenerate to be the B-B parametric surfaces. By changing the value of the shape parameter, we can get different surfaces under the fixed control net. ** Supported by National Natural Science Foundation of China (Grant N0. 60473130) and National Program on Key Basic Research Project (Grant No. 2004CB318000)
[1]
Gerald Farin,et al.
Triangular Bernstein-Bézier patches
,
1986,
Comput. Aided Geom. Des..
[2]
Gerald E. Farin.
Curvature continuity and offsets for piecewise conics
,
1989,
TOGS.
[3]
Juan Manuel Peña,et al.
Shape preserving alternatives to the rational Bézier model
,
2001,
Comput. Aided Geom. Des..
[4]
Guozhao Wang,et al.
A class of Bézier-like curves
,
2003,
Comput. Aided Geom. Des..
[5]
Guozhao Wang,et al.
Trigonometric polynomial B-spline with shape parameter
,
2004
.
[6]
Wang Wen-tao,et al.
Bézier curves with shape parameter
,
2005
.
[7]
Wen-Tao Wang,et al.
Hyperbolic Polynomial Uniform B-Spline with Shape Parameter
,
2005
.