geometry - How to find the orientation of a plane?

Question

I have three non-colinear 3D points, let's say pt1, pt2, pt3. I've computed the plane P using the sympy.Plane. How can I find the orientation of this plane(P) i.e. RPY(euler angles) or in quaternion?

Answer 1

I never used sympy, but you should be able to find a function to get the angle between 2 vectors (your normal vector and the world Y axis.)

theta = yaxis.angle_between(P.normal_vector)

then get the rotation axis, which is the normalized cross product of those same vectors.

axis = yaxis.cross(P.normal_vector).normal()

Then construct a quaternion from the axis and angle

q = Quaternion.from_axis_angle(axis, theta)