如何判断一个点是在一条线的右侧还是左侧

How to tell whether a point is to the right or left side of a line(如何判断一个点是在一条线的右侧还是左侧)

问题描述

我有一组点.我想将它们分成 2 个不同的集合.为此，我选择了两个点(a 和 b)并在它们之间画一条假想线.现在我想把这条线左边的所有点放在一组中，把这条线右边的点放在另一组中.

I have a set of points. I want to separate them into 2 distinct sets. To do this, I choose two points (a and b) and draw an imaginary line between them. Now I want to have all points that are left from this line in one set and those that are right from this line in the other set.

我如何判断任何给定点 z 是在左边还是在右边?我试图计算 a-z-b – 之间的角度.小于 180 的角度在右侧，大于 180 的角度在左侧.但由于 ArcCos 的定义，计算出的角度总是小于 180°.是否有计算大于 180° 的角度的公式(或任何其他选择右侧或左侧的公式)?

How can I tell for any given point z whether it is in the left or in the right set? I tried to calculate the angle between a-z-b – angles smaller than 180 are on the right hand side, greater than 180 on the left hand side – but because of the definition of ArcCos, the calculated angles are always smaller than 180°. Is there a formula to calculate angles greater than 180° (or any other formula to chose right or left side)?

推荐答案

使用向量行列式的符号(AB,AM)，其中M(X,Y)为查询点:

Use the sign of the determinant of vectors (AB,AM), where M(X,Y) is the query point:

position = sign((Bx - Ax) * (Y - Ay) - (By - Ay) * (X - Ax))

一行是0，一侧是+1，另一侧是-1.

It is 0 on the line, and +1 on one side, -1 on the other side.

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