G^3 continuous curve modeling with rational cubic Bézier spline  

作　　者：CHEN Jinhui, ZHANG Sanyuan, BAO Hujun and PENG Qunsheng( State Key Laboratory of CAD & CG, Zhejiang University, Hangzhou 310027, China Department of Computer Science and Engineering, Zhejiang University, Hangzhou 310027, China) 

出　　处：《Progress in Natural Science:Materials International》2002年第3期217-221,共5页自然科学进展·国际材料（英文版）

基　　金：Supported by the National Natural Science Foundation for Excellent Young Scholar of China (Grant No. 69925204); the National Natural Science Foundation of China (Grant No. 60073026) ;Zhejiang Provincial Natural Science Foundation (Grant No. 600015)

摘　　要：Based on the study of some intrinsic properties of the weights of rational Bezier curve, it has been found that the shape of a curve can be changed by adjusting the weights without moving its control points. An approach for improving the geometric continuity order between two adjacent curves by modifying the weights is presented. The G3 continuity conditions for two adjacent curves are first derived, which reveals that the geometric meaning of G continuity is torsion continuity. A constructive method is then presented to blend two rational Bezier curves with G3 continuity. Finally, the proposed method is used to construct closed G2 curves, or G3 curves by changing or inserting one control point.Based on the study of some intrinsic properties of the weights of rational Bézier curve, it has been found that the shape of a curve can be changed by adjusting the weights without moving its control points. An approach for improving the geometric continuity order between two adjacent curves by modifying the weights is presented. The G3 continuity conditions for two adjacent curves are first derived, which reveals that the geometric meaning of G3 continuity is torsion continuity. A constructive method is then presented to blend two rational Bézier curves with G3 continuity. Finally, the proposed method is used to construct closed G2 curves, or G3 curves by changing or inserting one control point.

关 键 词：rational cubic Bezier curve G3 continuity torsion closed curve modeling shape parameters. 

分 类 号：O29[理学—应用数学]