How May I Project Vectors Onto A Plane Defined By Its Orthogonal Vector In Python?

I have a plane, plane A, defined by its orthogonal vector, say (a, b, c). (i.e. the vector (a, b, c) is orthogonal to plane A) I wish to project a vector (d, e, f) onto plane A. Ho

Solution 1:

Take (d, e, f) and subtract off the projection of it onto the normalized normal to the plane (in your case (a, b, c)). So:

v =(d, e, f)-sum((d, e, f)*. (a, b,c))*(a, b,c)/sum((a, b,c)*. (a, b,c))

Here, by *. I mean the component-wise product. So this would mean:

sum([x * y for x, y in zip([d, e, f], [a, b, c])])

or

d * a + e * b + f * c

if you just want to be clear but pedantic

and similarly for (a, b, c) *. (a, b, c). Thus, in Python:

from math import sqrt

defdot_product(x, y):
    returnsum([x[i] * y[i] for i inrange(len(x))])

defnorm(x):
    return sqrt(dot_product(x, x))

defnormalize(x):
    return [x[i] / norm(x) for i inrange(len(x))]

defproject_onto_plane(x, n):
    d = dot_product(x, n) / norm(n)
    p = [d * normalize(n)[i] for i inrange(len(n))]
    return [x[i] - p[i] for i inrange(len(x))]

Then you can say:

p = project_onto_plane([3, 4, 5], [1, 2, 3])