| G3 continuous curve modeling with rational cubic Bézier spline? |
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| 作者姓名： | CHEN Jinhui ZHANG Sanyuan BAO Hujun PENG Qunsheng |
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| 作者单位： | State Key Laboratory of CAD & CG, Zhejiang University, Hangzhou 310027, China,State Key Laboratory of CAD & CG, Zhejiang University, Hangzhou 310027, China；Department of Computer Science and Engineering, Zhejiang University, Hangzhou 310027, China,State Key Laboratory of CAD & CG, Zhejiang University, Hangzhou 310027, China,State Key Laboratory of CAD & CG, Zhejiang University, Hangzhou 310027, China |
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| 基金项目： | 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) and Zhejiang Provincial Natural Science Foundation (Grant No. 600015) |
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| 摘 要： | 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.
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| 关 键 词： | rational cubic Bézier curve G3 continuity torsion closed curve modeling shape parameters |
G3 continuous curve modeling with rational cubic Bézier spline |
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| CHEN Jinhui,ZHANG Sanyuan,BAO Hujun,PENG Qunsheng.G3 continuous curve modeling with rational cubic Bézier spline[J].Progress in Natural Science,2002,12(3):217-221. |
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| Authors: | CHEN Jinhui ZHANG Sanyuan BAO Hujun Peng Qunsheng |
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| Abstract: | 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. |
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| Keywords: | rational cubic Bézier curve G3 continuity torsion closed curve modeling shape parameters |
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