Numpy Line-Plane intersection

Question

I have two planes in 3D space as shown below.

Point "e" on plane2 represents the intersection of the line which passes from point "P" of plane1 and has the direction vector of "S". Let P be the edge of plane 1.

Which are the "e" point coordinates (xe,ye, 0) with respect to the coordinates system of the plane it belongs (plane2), using Numpy?

I have the following data available:

1. Coordinates of the centers of each plane with respect of the global coordinate system "C".

   • x = np.array([x1, x2])

   • y = np.array([y1, y2])

   • z = np.array([z1, z2])

2. Sun direction vector S = np.array([Sz, Sx, Sy])

3. Point "P" location with respect to the coordinate system of plane1: P(xp,yp,0)

4. Each plane has the same width and length dimensions: Hw, Hl

5. Unit vectors normal to the plane surfaces

   • n = np.array([[n1z, n1x, n1y], [n2z, n2x, n2y]])

6. Also the azimuthial and elevation angles for both planes with respect to the global coordinate system "c" are known:

   • alphaH = np.array([alphaH1, alphaH2])

   • aH = np.array([aH1, aH2])

Answer 1

You have the position vector for c2 and the position vector for e in the global coordinate system then all you need to do is calculate c2-e and this will give you the position vector of e relative to c2.