How to compare the orientation of a 3D vector against a plane in three dimensions

Question

I am currently trying to plot a plane in three dimensional space but not sure how to do it for the problem I have.

Currently I have code that defines a 3D vector according to co-ordinates I have, this includes the ability to rotate, translate, and work out the angle between vectors.

The next step is to define a plane. I am not sure the best way to do this, however. The plane will be in a 100,100,100 box, be flat, and likely exist at az height of around 30.

My issue comes because I need this plane to do a couple of things:

1: I need to be able to rotate it around the three axes.

2: I need to be able to measure the smallest angle between the plane and the vector I have defined where the vector intersects the plane.

I was initially playing around trying to fill a numpy array with 1s where the plane would be etc but I don't see this really working how I need it to.

Does anyone know of any other tool that I would be able to use in this situation? Many thanks.

Answer 1

First of all, you'll need the normal vector to the plane. From there and following this link it should be easy for you to figure it out :)

Basically you get arcsin of the scalar product of your vector and the normal vector of the plane divided by the product of the norms of both vectors.

PS: If the plane is paralel to the XY plane, then it's normal vector it's just (0,0,1).