Explicit G1 approximation of conic sections using Bezier curves of arbitrary degree

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:292

Article

Hu, Qianqian

关键词: Conic sections;    Geometric continuity;    Bezier curves;    Approximation;    L-2-norm;   

DOI  :  10.1016/j.cam.2015.07.016

来源: Elsevier

【 摘 要 】

In this paper, we propose an explicit and effective method for G(1) approximation of conic sections with arbitrary degree polynomial curves. The geometric constraints can be expressed by two variables. Then we construct an objective function as the alternative approximation error function in the L-2-norm, which is a quadratic function in these two variables. To minimize the objective function is equivalent to solving a system of linear equations with two variables. Since its coefficient matrix is invertible, we can explicitly obtain the unique solution and then derive the explicit G(1) approximation of conic sections by Bezier curves of arbitrary degree. The proposed method has an optimal approximation in the L-2-norm, i.e., the L-2-distance error reaches minimum, and also can process the conic section with center angle larger than pi without subdivision scheme. Finally, numerical examples demonstrate the effectiveness of our method. (C) 2015 Elsevier B.V. All rights reserved.

【 授权许可】

Free