Please wait a minute...
ZJUS-A
Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering)  2006, Vol. 7 Issue (Supplement 2): 174-180    DOI: 10.1631/jzus.2006.AS0180
Original Paper     
Optimal multi-degree reduction of Bézier curves with G 1-continuity
Lu Li-Zheng, Wang Guo-Zhao
Institute of Computer Graphics and Image Processing, Department of Mathematics, Zhejiang University, Hangzhou 310027, China
Download:     PDF (0 KB)     
Export: BibTeX | EndNote (RIS)      

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.

Key words： Bézier curve      Optimal approximation      Degree reduction      Degree raising      G1-continuity     
CLC:  TP391.72  
Service
E-mail this article
Add to my bookshelf
Add to citation manager
E-mail Alert
RSS
Articles by authors
Lu Li-Zheng
Wang Guo-Zhao
Cite this article:

Lu Li-Zheng, Wang Guo-Zhao. Optimal multi-degree reduction of Bézier curves with G 1-continuity. Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering), 2006, 7(Supplement 2): 174-180.

URL:

http://www.zjujournals.com/xueshu/zjus-a/10.1631/jzus.2006.AS0180     OR     http://www.zjujournals.com/xueshu/zjus-a/Y2006/V7/ISupplement 2/174

[1] Lian ZHOU, Guo-jin WANG. Optimal constrained multi-degree reduction of Bézier curves with explicit expressions based on divide and conquer[J]. Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering), 2009, 10(4): 577-582.
[2] Hua-hui CAI, Guo-jin WANG. A new method in highway route design: joining circular arcs by a single C-Bézier curve with shape parameter[J]. Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering), 2009, 10(4): 562-569.
[3] 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.
[4] 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.
[5] 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.
[6] CHENG Min, WANG Guo-jin. Rational offset approximation of rational Bézier curves[J]. Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering), 2006, 7( 9): 14-.
[7] SHEN Wan-qiang, WANG Guo-zhao. A class of quasi Bézier curves based on hyperbolic polynomials[J]. Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering), 2005, 6(Supplement 1): 116-123.
[8] WU Qing-biao, XIA Fei-hai. Shape modification of Bézier curves by constrained optimization[J]. Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering), 2005, 6(Supplement 1): 124-127.
[9] LI Ya-juan, WANG Guo-zhao. Two kinds of B-basis of the algebraic hyperbolic space*[J]. Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering), 2005, 6( 7): 24-.
[10] WANG Wen-tao, WANG Guo-zhao. B¨|zier curves with shape parameter[J]. Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering), 2005, 6( 6): 4-.
[11] ZHENG Zhi-hao, WANG Guo-zhao. PH-spline approximation for Bézier curve and rendering offset[J]. Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering), 2004, 5(3): 343-349.