| 刘华勇,徐虎,李亚男,王曾珍.G2 连续条件下圆域 B 样条曲线的延拓与拼接[J].安徽建筑大学学报,2023,31(3):77-83 |
| G2 连续条件下圆域 B 样条曲线的延拓与拼接 |
| Extension and Splicing of Disk B-Spline Curve with G2 Constraint |
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| DOI： |
| 中文关键词: 圆域曲线 延拓 G2 连续 能量函数 拼接 |
| 英文关键词: disk curve curve extension G2 continuity energy function curve splicing |
| 基金项目:安徽省高等学校自然科学研究资助项目（KJ2021A0630、KJ2021A0633） |
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| 中文摘要: |
| 为克服圆域 B 样条曲线在 C2 连续条件下延拓到目标圆盘时的形状不可调整性，提出利用圆域 Bézier曲线在 G2 连续条件下延拓圆域 B 样条曲线的算法。首先通过极小化能量目标函数确定延拓部分自由度，使延拓后的圆域曲线形状达到最优状态。然后将节点向量重新参数化，令得到的混合圆域曲线转化为圆域 B 样条曲线，重复利用该算法可以把圆域 B 样条曲线延拓至多个目标圆盘。此外提出利用六次圆域 Bézier 曲线作为过渡曲线拼接任意两条圆域 B 样条曲线的算法，最后给定数值实例验证算法的普适性和有效性。 |
| 英文摘要: |
| An algorithm is proposed to handle the non-adjustable shape of disk B-spline curve when it is extended to the target disk under the condition of C2 continuity. The energy objective function is minimized to determine the parameters and obtain the curve with optimal shape. Then，the knot vectors are re-parameterized to transform the combined disk curve after extension into disk B-spline curve. Repeating this algorithm to extend the disk B-spline curve to multiple target disks. In addition，an algorithm for splicing any two disk B-spline curves using the six-degree disk Bézier curve is proposed. Finally，the numerical example is given to verify the universality and effectiveness of the algorithm. |
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