Explicit G2-constrained degree reduction of Bezier curves by quadratic optimization

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:253

Article

Lu, Lizheng

关键词: Bezier curve;    Degree reduction;    G(2)-continuity;    Quadratic optimization;   

DOI  :  10.1016/j.cam.2013.04.008

来源: Elsevier

【 摘 要 】

In this paper, we revisit G(2)-constrained degree reduction of Bezier curves which has been solved in our previous work by using iterative methods. We propose an explicit and effective method for G(1)-constrained degree reduction and C(1)G(2)-constrained degree reduction. Our main idea is to express the distance function defined in the L-2-norm as a strictly convex quadratic function of two variables, which becomes a quadratic optimization problem. We can explicitly obtain the unique solution by solving two linear equations such that the distance function is minimized. The existence of the unique solution is also proved. (C) 2013 Elsevier B.V. All rights reserved.

【 授权许可】

Free