计算给定线上的投影点位置 (x,y) start(x,y) end(x,y)

如果我有三个点 P1、P2、P3 及其坐标（x，y）

P1（x，y）和P3（x，y）是线（起点，终点）的坐标，P3是需要投影的点。

how can i find the coordinate of point r(x,y) which is projection of P3 over P1 and P2

该解决方案扩展到具有任何几何尺寸（2D、3D、4D...）的点。它假设所有点都是一维 numpy 数组（或一维形状为 1 的二维数组）。我不确定您是否需要投影落在线段上或线段的延伸上，所以我将两者都包括在内。您可以选择最适合您的问题的一个：

#distance between p1 and p2
l2 = np.sum((p1-p2)**2)
if l2 == 0:
  print('p1 and p2 are the same points')

#The line extending the segment is parameterized as p1 + t (p2 - p1).
#The projection falls where t = [(p3-p1) . (p2-p1)] / |p2-p1|^2

#if you need the point to project on line extention connecting p1 and p2
t = np.sum((p3 - p1) * (p2 - p1)) / l2

#if you need to ignore if p3 does not project onto line segment
if t > 1 or t < 0:
  print('p3 does not project onto p1-p2 line segment')

#if you need the point to project on line segment between p1 and p2 or closest point of the line segment
t = max(0, min(1, np.sum((p3 - p1) * (p2 - p1)) / l2))

projection = p1 + t * (p2 - p1)