论文标题
在球形衣服上
On the spherical clothoid
论文作者
论文摘要
我们重新审视一个由Mehlum首先研究的三个空间的非线性样条原始型。它是球形衣服，是带有大地曲率的球形曲线，是弧长的线性函数。我们使用汇合的高几何函数（Kummer函数）及其在复杂平面上的立体投影介绍其笛卡尔坐标函数。新的Humbert系列结果以及与相关的Meixner-Pollaczek多项式相关的生成函数公式也会呈现。
We revisit a nonlinear spline primitive for 3-space first studied by Even Mehlum. It is the spherical clothoid, the spherical curve with geodesic curvature a linear function of arc length. We present its Cartesian coordinate functions using confluent hypergeometric functions (the Kummer functions) and its stereographic projection onto the complex plane. New Humbert series results are also presented along with generating function formulas related to the associated Meixner-Pollaczek polynomials.
