CODEWITHSUNDEEP
pythonnumpymath3d
Sergio Moura
Sergio Moura

Reputation: 4942

Move a vertex along a plane, given the plane normal

I have a 3D vector and a 3D face normal. How do I go along to move this vector along the given face normal using Python (with or without numpy)?

Ideally, I'd build a matrix using the face normal with the x and y and multiply it by the original vector or something like that, but I can't get my head around on how to build it. It's been a while since Linear Algebra.

EDIT:

Thanks for pointing out that my question was too broad.

My goal is to get a new point, that is x and y units away from the original point, along the face defined by its normal.

Example: If the point is (0,0,0) and the normal is (0, 0, 1), the result would be (x, y, 0).

Example 2: If the point is (1, 0, 0) and the normal is (0, 1, 0), the result would be (1+x, 0, y).

I'd need to extrapolate that to work with any point, normal, x and y.

Upvotes: 1

Views: 1424

Answers (2)

Cihan
Cihan

Reputation: 157

def give_me_a_new_vertex_position_along_normal(old_vertex_position, normal):
  new_vertex_position = old_vertex_position + normal
  return new_vertex_position

There is a difference between affine spaces (your normals) and euclidean/linear spaces (your vertices).

Vectors in linear space have coordinates associated with them, while vectors in affine space do not.

Adding an affine-spaced vector to a linear-spaced vector is called projection and that is what you are looking to do.

Upvotes: 0

Andy Hayden
Andy Hayden

Reputation: 375475

The projection of a vector to a plane defined by its normal is:

def projection(vector, normal):
    return vector - vector.dot(normal) * normal

Presumably this means you want something like:

x + projection(y, normal)

Upvotes: 2

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