| Computer & Information Science |
|
|
|
|
| Optimal multi-degree reduction of Bézier curves with G1-continuity |
| Lu Li-Zheng, Wang Guo-Zhao |
| Institute of Computer Graphics and Image Processing, Department of Mathematics, Zhejiang University, Hangzhou 310027, China |
|
|
|
Abstract This paper presents a novel approach to consider optimal multi-degree reduction of Bézier curve with G1-continuity. By minimizing the distances between corresponding control points of the two curves through degree raising, optimal approximation is achieved. In contrast to traditional methods, which typically consider the components of the curve separately, we use geometric information on the curve to generate the degree reduction. So positions and tangents are preserved at the two endpoints. For satisfying the solvability condition, we propose another improved algorithm based on regularization terms. Finally, numerical examples demonstrate the effectiveness of our algorithms.
|
|
Received: 29 December 2005
|
|
|
|
|
| [1] |
Ahn, Y.J., 2003. Degree reduction of Bézier curves with Ck-continuity using Jacobi polynomials. Computer Aided Geometric Design, 20(7):423-434.
doi: 10.1016/S0167-8396(03)00082-7
|
|
|
| [2] |
Ahn, Y.J., Lee, B.G., Park, Y., Yoo, J., 2004. Constrained polynomial degree reduction in the L2-norm equals best weighted Euclidean approximation of Bézier coefficients. Computer Aided Geometric Design, 21(2):181-191.
doi: 10.1016/j.cagd.2003.10.001
|
|
|
| [3] |
Chen, G.D., Wang, G.J., 2002. Optimal multi-degree reduction of Bézier curves with constraints of endpoints continuity. Computer Aided Geometric Design, 19(6):365-377.
doi: 10.1016/S0167-8396(02)00093-6
|
|
|
| [4] |
de Boor, C., Höllig, K., Sabin, M., 1987. High accuracy geometric Hermite interpolation. Computer Aided Geometric Design, 4(4):269-278.
doi: 10.1016/0167-8396(87)90002-1
|
|
|
| [5] |
Degen, W.L.F., 2005. Geometric Hermite Interpolation—In memoriam Josef Hoschek. Computer Aided Geometric Design, 22(7):573-592.
doi: 10.1016/j.cagd.2005.06.008
|
|
|
| [6] |
Eck, M., 1995. Least squares degree reduction of Bézier curves. Computer-Aided Design, 27(11):845-851.
doi: 10.1016/0010-4485(95)00008-9
|
|
|
| [7] |
Farin, G., 1983. Algorithms for rational Bézier curves. Computer-Aided Design, 15(2):73-79.
doi: 10.1016/0010-4485(83)90171-9
|
|
|
| [8] |
Farin, G., 2001. Curves and Surfaces for CAGD (5th Ed.). Morgan Kaufmann, San Francisco, p.81-93.
|
|
|
| [9] |
Fleishman, S., Drori, I., Cohen-Or, D., 2003. Bilateral mesh denoising. ACM Trans. on Graphics, 22(3):950-953.
doi: 10.1145/882262.882368
|
|
|
| [10] |
Forrest, A.R., 1972. Interactive interpolation and approximation by Bézier curve. The Computer Journal, 15(1):71-79.
|
|
|
| [11] |
Hu, S.M., Sun, J.G., Jin, T.G., Wang, G.Z., 1998. Approximate degree reduction of Bézier curves. Tsinghua Science and Technology, 3(2):997-1000.
|
|
|
| [12] |
Hu, S.M., Tong, R.F., Ju, T., Sun, J.G., 2001. Approximate merging of a pair of Bézier curves. Computer-Aided Design, 33(2):125-136.
doi: 10.1016/S0010-4485(00)00083-X
|
|
|
| [13] |
Szegö, G., 1975. Orthogonal Polynomials (4th Ed.). American Mathematical Society, Providence, RI, p.22-106.
|
|
|
|
Viewed |
|
|
|
Full text
|
|
|
|
|
Abstract
|
|
|
|
|
Cited |
|
|
|
|
| |
Shared |
|
|
|
|
| |
Discussed |
|
|
|
|
