测地线上的点 [英] Points on a geodesic line

问题描述

我正在单位球上工作。我有兴趣将N个点放置在两个任意点之间的球体（大地）表面的海峡线上。这些点的坐标是球面坐标（弧度）。

I am working on a unit sphere. I am interested to place N points on a strait line over the surface of the sphere (geodesic) between two arbitrary points. The coordinate of these points are in spherical coordinate (radians).

如何计算沿着这条线的N个等距点的集合。我想在计算时考虑球体的曲率。

How do I compute a set of N equally spaced points along such line. I would like to take the curvature of the sphere into account in my calculation.

我正在使用python 2.7.9

I am using python 2.7.9

推荐答案

您可以考虑 SLERP-球面线性插值

P = P0*Sin(Omega*(1-t))/Sin(Omega) + P1*Sin(Omega * t)/Sin(Omega)

其中，Omega是起点和终点之间的中心角（大弧圆），对于第i个点 t（i）= i / N

where Omega is central angle between start and end points (arc of great circle), t is parameter in range [0..1], for i-th point t(i) = i/N

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