确定地球上某个点是在一条线的左侧还是右侧
我在地球表面有三个点。我想确定当沿着该线沿某个方向行驶时，其中一个点是否位于连接其他两点的线的左侧或右侧。
所以，参数是：
globe (x,y,z,radius)
journey_start(x,y,z)
journey_end(x,y,z)
point(x,y,z)
到目前为止我的推理得到了这个：
地球仪原点、旅程起点和终点是大圆上的三个点并描述一个平面。我想知道另一个点是在这个平面之上还是之下。
但我还没有设法将其扩展到一个方程。
我该如何解决这个问题？
I have three points that are on the surface of a globe. I want to determine if one of the points lays to the left or right of a line that joins the other two points, when travelling in a certain direction down that line.
So, parameters are:
globe (x,y,z,radius)
journey_start (x,y,z)
journey_end (x,y,z)
point (x,y,z)
My reasoning so far has got me this:
globe origin, journey start and end are three points on a great circle and describe a plane. I want to know if the other point is above or below this plane.
but I haven't managed to extend that to an equation.
How can I solve this?
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将向量 S 和 E 定义为从地球中心到旅程开始和旅程结束的向量。它们的叉积是 S 和 E 所在平面的法线 N。当然，这个平面将地球分为两个半球，分别对应于您的左侧和右侧。随后，您可以计算该法线与从中心到第三点的向量的内积。它可以是正值（右）、负值（左）或零（在同一个大圆上）
Define the vectors S and E as the vectors from the center of the globe to journey_start and journey_end. Their crossproduct is the normal N of the plane in which S and E lie. This plane of course divides the globe in two hemispheres, which correspond to your left and right. You can subsequently calculate the inner product of this normal with the vector from the center to your third point. It's either positive (right), negative (left) or zero (on the same great circle)
求两点与圆心所在的平面、经过第三点的平行平面、两平面之间的偏移量、两点与圆心的叉积以及偏移的方向是否与叉积的方向相同。
Find the plane that the two points and the center are on, the parallel plane that passes through the third point, the offset between the two planes, the cross product of the two points and the center, and whether or not the direction of the offset is the same as the direction of the cross product.