在直线上找一个点 [英] Finding a point on a line

问题描述

我知道线段上的起点和终点.对于此示例，假设线段的距离为 5.现在我想知道与终点的距离为 3 的点.知道如何用数学来做到这一点吗?

I know the start and end points on a line segment. For this example say that the line segment has a distance of 5. Now I want to know the point that has a distance of three away from the end point. Any idea how to do this with math?

起点 (0,0)终点 (0,5)

Start Point (0,0) End Point (0,5)

我要找的点(0,2)

推荐答案

如果你的点是 (x1, y1) 和 (x2, y2)，并且你想要找到距离点 2 n 个单位的点 (x3, y3):

If your points are (x1, y1) and (x2, y2), and you want to find the point (x3, y3) that is n units away from point 2:

d = sqrt((x2-x1)^2 + (y2 - y1)^2) #distance
r = n / d #segment ratio

x3 = r * x2 + (1 - r) * x1 #find point that divides the segment
y3 = r * y2 + (1 - r) * y1 #into the ratio (1-r):r

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