A class of algebraic-trigonometric blended splines

作者：Yan Lanlan^*; Liang Jiongfeng

来源：Journal of Computational and Applied Mathematics, 2011, 235(6): 1713-1729.

DOI：10.1016/j.cam.2010.09.016

• Trigonometric basis
• Spline curve
• Shape parameter
• Tangent polygon
• Curve interpolation

This paper presents a new kind of algebraic-trigonometric blended spline curve, called xyB curves, generated over the space {1, t, sin t, cos t, sin(2) t, sin(3) t, cos(3) t}. The new curves not only inherit most properties of usual cubic B-spline curves in polynomial space, but also enjoy some other advantageous properties for modeling. For given control points, the shape of the new curves can be adjusted by using the parameters x and y. When the control points and the parameters are chosen appropriately, the new curves can represent some conics and transcendental curves. In addition, we present methods of constructing an interpolation xyB-spline curve and an xyB-spline curve which is tangent to the given control polygon. The generation of tensor product surfaces by these new spline curves is straightforward. Many properties of the curves can be easily extended to the surfaces. The new surfaces can exactly represent the rotation surfaces as well as the surfaces with elliptical or circular sections.

• 出版日期2011-1-15
• 单位东华理工大学