| Optimal approximate merging of a pair of Bézier curves with G2-continuity |
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| 基金项目： | Project supported by the National Natural Science Foundation of China （No. 60773179） and the National Basic Research Program （973） of China （No. G2004CB318000） |
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| 摘 要： | We present a novel approach for dealing with optimal approximate merging of two adjacent Bezier eurves with G^2-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 Bezier 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.
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| 关 键 词： | 贝塞尔曲线 连续性 合并 Bezier曲线 配对 逼近误差 矩阵表示 几何信息 |
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