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

Question

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。

我怎样才能找到点 r(x,y) 的坐标，它是 P3 在 P1 和 P2 上的投影

Answer 1

此解决方案扩展到具有任何几何尺寸(2D、3D、4D 等)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)。我不确定您是否需要投影落在线段或线段的延伸上，所以我将两者都包括在内。您可以选择最适合您的问题的:

#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)