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• 计算机辅助几何设计 • 上一篇    下一篇

用细分螺线插值容许G2Hermite 数据

  

  • 出版日期:2012-04-27 发布日期:2015-07-28

Spiral-preserving geometric subdivision scheme for admissible G2 Hermite interpolation

  • Online:2012-04-27 Published:2015-07-28

摘要: 为使几何细分方法生成的平面螺线段插值平面容许G2Hermite 数据,基于
平面双圆弧插值理论提出了该方法首末端点处新的细分规则。理论分析表明,修改后的细分
方法所得极限曲线是曲率单调、不变号的螺线段,且插值首末端点处的点、切向、曲率。数
值算例表明,修改后的细分方法收敛速度较快,极限曲线具有较好的形状。

关键词: 平面螺线, 容许G2Hermite 数据, Hermite 插值

Abstract: To interpolate admissible G2 Hermite data, this paper proposes a modified
geometric subdivision scheme with new subdivision rules near the end points of the curve. The
method is based on the theory of planar biarc curve interpolation. Theoretical analysis shows that
the limit curves of the modified subdivision scheme are planar spirals, which are curves of
one-signed, monotone increasing or decreasing curvature. Numerical examples show that the
modified subdivision scheme converge rapidly, and the limit curves are with nice shape.

Key words: planar spiral, admissible G2 Hermite data, Hermite interpolation