查找点是否位于线段上 [英] Find if point lies on line segment

问题描述

我有由以下两点定义的线段:A(x1,y1,z1) 和 B(x2,y2,z2).我有一点p(x,y,z).如何检查点是否位于线段上?

I have line segment defined by these two points: A(x1,y1,z1) and B(x2,y2,z2). I have point p(x,y,z). How can I check if the point lies on the line segment?

推荐答案

如果点是在线那么:

(x - x1) / (x2 - x1) = (y - y1) / (y2 - y1) = (z - z1) / (z2 - z1)

计算所有三个值，如果它们相同(在某种程度的公差)，你的点就在这条线上.

Calculate all three values, and if they are the same (to some degree of tolerance), your point is on the line.

要测试点是否在段中，而不仅仅是在线上，您可以检查是否

To test if the point is in the segment, not just on the line, you can check that

x1 < x < x2, assuming x1 < x2, or
y1 < y < y2, assuming y1 < y2, or
z1 < z < z2, assuming z1 < z2

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