Please wait a minute...
ZJUS-A
Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering)  2009, Vol. 10 Issue (4): 554-561    DOI: 10.1631/jzus.A0820301
Computer-aided Geometric Design     
Optimal approximate merging of a pair of Bézier curves with G2-continuity
Ping ZHU, Guo-zhao WANG
Institute of Computer Graphics and Image Processing; State Key Lab of CAD & CG, Zhejiang University, Hangzhou 310027, China
Download:     PDF (0 KB)     
Export: BibTeX | EndNote (RIS)      

Abstract  We present a novel approach for dealing with optimal approximate merging of two adjacent Bézier curves with G2-continuity. Instead of moving the control points, we minimize the distance between the original curves and the merged curve by taking advantage of matrix representation of Bézier curve’s discrete structure, where the approximation error is measured by L2-norm. We use geometric information about the curves to generate the merged curve, and the approximation error is smaller. We can obtain control points of the merged curve regardless of the degrees of the two original curves. We also discuss the merged curve with point constraints. Numerical examples are provided to demonstrate the effectiveness of our algorithms.

Key words： Approximate merging      G1-continuity      G2-continuity      Discrete subdivision      Point constraints     
Received: 21 April 2008     
CLC:  TP391.72  
Service
E-mail this article
Add to my bookshelf
Add to citation manager
E-mail Alert
RSS
Articles by authors
Ping ZHU
Guo-zhao WANG
Cite this article:

Ping ZHU, Guo-zhao WANG. Optimal approximate merging of a pair of Bézier curves with G2-continuity. Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering), 2009, 10(4): 554-561.

URL:

http://www.zjujournals.com/xueshu/zjus-a/10.1631/jzus.A0820301     OR     http://www.zjujournals.com/xueshu/zjus-a/Y2009/V10/I4/554

[1] Zhen-fei Zhan, Jie Hu, Yan Fu, Ren-Jye Yang, Ying-hong Peng, Jin Qi. Multivariate error assessment of response time histories method for dynamic systems[J]. Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering), 2012, 13(2): 121-131.
[2] Nur Saaidah Abu Bakar, Mohd Rizal Alkahari, Hambali Boejang. Analysis on fused deposition modelling performance[J]. Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering), 2010, 11(12): 972-977.
[3] Zhi-long LI, Jun-jie CAO, Xiu-ping LIU, Zhi-xun SU. A code-based approach for labeling in complex irregular regions[J]. Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering), 2009, 10(10): 1450-1460.
[4] Jorge CARAVANTES, Laureano GONZALEZ-VEGA. Computing the topology of an arrangement of implicitly defined real algebraic plane curves[J]. Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering), 2008, 9(12): 1685-1693.
[5] Ya-juan LI, Li-zheng LU, Guo-zhao WANG. Paths of algebraic hyperbolic curves[J]. Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering), 2008, 9(6): 816-821.
[6] WANG Jin, LU Guo-dong, LI Ji-tuo, CHEN Long, ZHANG Dong-liang. Pattern design on 3D triangular garment surfaces[J]. Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering), 2007, 8(10): 1642-1649.
[7] CAI Hong-jie, WANG Guo-jin. Constrained multi-degree reduction of rational Bézier curves using reparameterization[J]. Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering), 2007, 8(10): 1650-1656.
[8] LU Li-zheng, WANG Guo-zhao. A quadratic programming method for optimal degree reduction of Bézier curves with G1-continuity[J]. Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering), 2007, 8(10): 1657-1662.
[9] CAO Juan, WANG Guo-zhao. Relation among C-curve characterization diagrams[J]. Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering), 2007, 8(10): 1663-1670.
[10] ZOU Wan-hong, DING Zhan, YE Xiu-zi, CHEN Zhi-yang. Interactive point cloud blending by drag-and-drop[J]. Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering), 2007, 8(10): 1633-1641.
[11] JUHÁSZ Imre. Vanishing torsion of parametric curves[J]. Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering), 2007, 8(4): 593-595.
[12] MO Guo-liang, ZHAO Ya-nan. A new extension algorithm for cubic B-splines based on minimal strain energy[J]. Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering), 2006, 7(12): 13-.
[13] ZHANG Xing-wang, WANG Guo-jin. A new algorithm for designing developable Bézier surfaces[J]. Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering), 2006, 7(12): 14-.
[14] CAO Yan-long, LIU Yu-sheng, MAO Jian, YANG Jiang-xin. 3DTS: A 3D tolerancing system based on mathematical definition[J]. Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering), 2006, 7(11): 4-.
[15] LI Ya-juan, WANG Guo-zhao. Symmetric alteration of four knots of B-spline and NURBS surfaces[J]. Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering), 2006, 7(6 ): 23-.