测地线上的点 [英] Points on a geodesic line

问题描述

我正在研究一个单位球体.我有兴趣在两个任意点之间的球体(测地线)表面上的一条海峡线上放置 N 个点.这些点的坐标是球坐标(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).

我如何计算沿这条线的一组 N 个等距点.我想在计算中考虑球体的曲率.

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.

我使用的是 python 2.7.9

I am using python 2.7.9

推荐答案

你可以考虑 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(大圆弧)，t 是范围 [0..1] 内的参数，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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