Calculate Projected Point location (x,y) on given line start(x,y) end(x,y)

Question

If i have three points P1, P2, P3 with their coordinates(x,y)

P1(x,y) and P3(x,y) are coordinate of line(start, end) and P3 is a point need to be projected.

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

Answer 1

This solution extends to points with any geometric dimensions (2D, 3D, 4D, ...). It assumes all points are one dimensional numpy arrays (or two dimensional with one dimension shape 1). I am not sure if you require the projection to fall onto line segment or the extension of segment so I include both. You can pick whichever fits your question the best:

#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)