Arc length preserving approximation of circular arcs by Pythagorean-hodograph curves of degree seven

二维毕达哥拉斯- hodograph 样条曲线

Pythagorean-Hodograph B-Spline Curves

本文介绍了一种新的二维毕达哥拉斯- hodograph (PH) 样条曲线，扩展了1990年Farouki和Sakkalis提出的经典PH贝塞尔曲线。该曲线具有弧长为样条函数的特性，其偏移曲线为非均匀有理样条曲线，适用于CAD、CAM、机器人、路径规划等领域。

复多项式度量在平面Pythagorean-hodograph曲线有界修改中的应用

Application of a metric for complex polynomials to bounded modification of planar Pythagorean-hodograph curves

本文通过将平面多项式曲线解释为复值函数并定义度量，应用于生成PH曲线的复原像多项式，实现了保持PH性质的有界修改，并解决了端点约束及弧长增加等问题。

Rational Framing Motions and Spatial Rational Pythagorean Hodograph Curves

We propose a new method for constructing rational spatial Pythagorean Hodograph (PH) curves based on determining a suitable rational framing motion. While the spherical component of the framing motion is arbitrary, the translation part is determined be a modestly sized and nicely structured system of linear equations. Rather surprisingly, generic input data will only result in polynomial PH curves. We provide a complete characterization of all cases that admit truly rational (non-polynomial) solutions. Examples illustrate our ideas and relate them to existing literature.

使用空间有理 Pythagorean hodograph 曲线的最优插值

Optimal interpolation with spatial rational Pythagorean hodograph curves

本文用残差方法刻画给定切向方向的有理空间曲线空间，显式给出其基，使多种插值、尖点避免及能量、长度优化可转化为线性约束或二次规划。

具有指定弧长的 $G^2$ 平面 Hermite 插值曲线的构造

Construction of $G^2$ planar Hermite interpolants with prescribed arc lengths

提出用 7 次 PH 双圆弧局部构造满足点、切向、曲率及指定弧长的 $G^2$ 平面插值样条，并通过弯曲能量选解，数值验证逼近阶为 5。