Four new trigonometric Bernstein-like basis functions with two exponential shape pa- rameters are constructed, based on which a class of trigonometric Bézier-like curves, anal- ogous to the cubic Bézier curv...Four new trigonometric Bernstein-like basis functions with two exponential shape pa- rameters are constructed, based on which a class of trigonometric Bézier-like curves, anal- ogous to the cubic Bézier curves, is proposed. The corner cutting algorithm for computing the trigonometric Bézier-like curves is given. Any arc of an eliipse or a parabola can be represented exactly by using the trigonometric Bézier-like curves. The corresponding trigonometric Bernstein-like operator is presented and the spectral analysis shows that the trigonometric Bézier-like curves are closer to the given control polygon than the cu- bic Bézier 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 pa- rameters 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 C2 N FC3 continuous for a non-uniform knot vector, and C3 or C5 continuous for a uniform knot vector. A new class of trigonometric Bézier-like basis functions over triangular domain is also constructed. A de Casteljau-type algorithm for computing the associated trigonometric Bézier-like patch is developed. The conditions for G1 continuous joining two trigonometric Bézier-like patches over triangular domain arededuced．展开更多
基金We, wish to express our gratitude to the referees for their valuable re- marks for improvements. The research is supported by the National Natural Science Foun-dation of China （No. 60970097, No. 11271376）, Postdoctoral Science Foundation of China （2015M571931）, and Graduate Students Scientific Research Innovation Project of Hunan Province （No. CX2012Blll）.
文摘Four new trigonometric Bernstein-like basis functions with two exponential shape pa- rameters are constructed, based on which a class of trigonometric Bézier-like curves, anal- ogous to the cubic Bézier curves, is proposed. The corner cutting algorithm for computing the trigonometric Bézier-like curves is given. Any arc of an eliipse or a parabola can be represented exactly by using the trigonometric Bézier-like curves. The corresponding trigonometric Bernstein-like operator is presented and the spectral analysis shows that the trigonometric Bézier-like curves are closer to the given control polygon than the cu- bic Bézier 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 pa- rameters 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 C2 N FC3 continuous for a non-uniform knot vector, and C3 or C5 continuous for a uniform knot vector. A new class of trigonometric Bézier-like basis functions over triangular domain is also constructed. A de Casteljau-type algorithm for computing the associated trigonometric Bézier-like patch is developed. The conditions for G1 continuous joining two trigonometric Bézier-like patches over triangular domain arededuced．
