quaternion.txt

https://math.stackexchange.com/questions/40164/how-do-you-rotate-a-vector-by-a-unit-quaternion
https://www.3dgep.com/understanding-quaternions/
https://math.stackexchange.com/questions/180418/calculate-rotation-matrix-to-align-vector-a-to-vector-b-in-3d/897677#897677
https://stackoverflow.com/questions/1171849/finding-quaternion-representing-the-rotation-from-one-vector-to-another
https://stackoverflow.com/questions/14812005/rotate-plane-so-its-normal-is-the-same-direction-as-another-planes-normal
https://answers.unity.com/questions/1221564/rotate-plane-by-normal-how-to-calculate-new-positi.html
https://stackoverflow.com/questions/1023948/rotate-normal-vector-onto-axis-plane
https://stackoverflow.com/questions/57694061/how-can-i-use-the-rotation-angle-and-axis-to-rotate-a-3d-plane

Rotate plane by normal, how to calculate new position?

I hava a plane, which I know the normal(normal0), and 2 points(pointA, pointB).

Now I have another normal:normal1.

I need to rotate plane from normal0 to normal1 around pointA, How can I know the new position pointB after rotation? 

      
      Vector3 changeNormal(Vector3 normal0, Vector3 normal2, Vector3 pointA, Vector3 pointB) {
         Quaternion rotation = Quaternion.FromToRotation(normal0, normal2); //Get rotation between both normals
         Vector3 rotationDir = pointB - pointA; // Get point direction relative to pivot
         rotationDir = rotation * rotationDir; // Rotate it
         pointB = rotationDir + pointA; // Calculate rotated point
         return pointB;
     }

Calculate Rotation Matrix to align Vector A to Vector B in 3d?
import numpy as np
import math


def rotation_matrix(A,B):
# a and b are in the form of numpy array

   ax = A[0]
   ay = A[1]
   az = A[2]

   bx = B[0]
   by = B[1]
   bz = B[2]

   au = A/(np.sqrt(ax*ax + ay*ay + az*az))
   bu = B/(np.sqrt(bx*bx + by*by + bz*bz))

   R=np.array([[bu[0]*au[0], bu[0]*au[1], bu[0]*au[2]], [bu[1]*au[0], bu[1]*au[1], bu[1]*au[2]], [bu[2]*au[0], bu[2]*au[1], bu[2]*au[2]] ])


   return(R)