NEW TRIGONOMETRIC BASIS POSSESSING EXPONENTIAL SHAPE PARAMETERS

Four new trigonometric Bernstein-like basis functions with two exponential shape parameters are constructed, based on which a class of trigonometric Bezier-like curves, analogous to the cubic Bezier curves, is proposed. The corner cutting algorithm for computing the trigonometric Bezier-like curves is given. Any arc of an ellipse or a parabola can be represented exactly by using the trigonometric Bezier-like curves. The corresponding trigonometric Bernstein-like operator is presented and the spectral analysis shows that the trigonometric Bezier-like curves are closer to the given control polygon than the cubic Bezier curves. Based on the new proposed trigonometric Bernstein-like basis, a new class of trigonometric B-spline-like basis functions with two local exponential shape parameters is constructed. The totally positive property of the trigonometric B-spline-like basis is proved. For different values of the shape parameters, the associated trigonometric B-spline-like curves can be C-2 boolean AND FC3 continuous for a non-uniform knot vector, and C-3 or C-5 continuous for a uniform knot vector. A new class of trigonometric Bezier-like basis functions over triangular domain is also constructed. A de Casteljau-type algorithm for computing the associated trigonometric Bezier-like patch is developed. The conditions for G(1) continuous joining two trigonometric Bezier-like patches over triangular domain are deduced.