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pythoncoordinateslinesurfaceplane

How do I create a line that is perpendicular to a plane of coordinates

I have three datasets (numpy arrays) of coordinates (X, Y and X) representing a planar surface. I need to create a line that is perpendicular to the plane surface.

A visual representation of the coordinates in a coordinate system

I got the data from another file, because I can't share it easily with you, I created a random pandas dataset the code I used to generate the data surface is as following:

cor_CTV = pd.DataFrame(np.random.randint(0,100,size=(100, 3)), columns = list('xyz'))

linear_data = np.c_[cor_CTV["x"], cor_CTV["y"], cor_CTV["z"]]
mn = np.min(linear_data, axis=0)
mx = np.max(linear_data, axis=0)
X,Y = np.meshgrid(np.linspace(mn[0], mx[0], 20), np.linspace(mn[1], mx[1], 20))

XX = X.flatten()
YY = Y.flatten()

A = np.c_[linear_data[:,0], linear_data[:,1], np.ones(linear_data.shape[0])]
C,_,_,_ = scipy.linalg.lstsq(A, linear_data[:,2])
Z = C[0]*X + C[1]*Y + C[2]

I would be very grateful if anyone can help me.

Solution

  • You can use the cross product of the relative position of any two non-colinear points:

    O = np.array([X[0][0], Y[0][0], Z[0][0]])   # Corner to be used as the origin

V1 = np.array([X[1][0], Y[1][0], Z[1][0]]) - O  # Relative vectors
V2 = np.array([X[0][1], Y[0][1], Z[0][1]]) - O

V1 = V1 / scipy.linalg.norm(V1)  # Normalise vectors
V2 = V2 / scipy.linalg.norm(V2)

# Take the cross product
perp = np.cross(V1, V2)

    Example result:

    [ 0.18336919 -0.0287231  -0.98260979]