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# Gives the rotation matrix which rotates theta degrees about
# vecU
# Generates the rotation matrix that rotate theta degrees about the vecU
def rotate_about_vec(vecU, theta):
import numpy as np
vecU = np.array(vecU)
vecU = vecU / (sum(vecU ** 2) ** 0.5)
ux, uy, uz = vecU
st = np.sin(theta)
ct = np.cos(theta)
mat = np.array([[ux ** 2 + ct * (1 - ux ** 2),
ux * uy * (1 - ct) - uz * st,
uz * ux * (1 - ct) + uy * st],
[ux * uy * (1 - ct) + uz * st,
uy ** 2 + ct * (1 - uy ** 2),
uy * uz * (1 - ct) - ux * st],
[uz * ux * (1 - ct) - uy * st,
uy * uz * (1 - ct) + ux * st,
uz ** 2 + ct * (1 - uz **2)]])
return (mat)
# Generates the rotation matrix which rotates aVec into intoVec
def rotate_vec_into_newvec(aVec, intoVec):
def length(v):
return((sum(v ** 2)) ** 0.5)
import numpy as np
from math import acos
fac = 1.0
aVec = np.array(aVec)
intoVec = np.array(intoVec)
nor = np.cross(aVec, intoVec)
if length(nor) == 0:
nor = np.array([1, 0, 0])
nor = nor / length(nor)
theta = acos(np.dot(aVec, intoVec) / (length(aVec) * length(intoVec)))
if np.dot(aVec, intoVec) < 0:
theta = theta + np.pi
fac = -1
return(fac * rotate_about_vec(nor, theta))
# Applies the rotation matrix to the vector and returns the rotated vector
def rotate_vec (rot_mat, vec):
import numpy as np
rot_vec = np.dot(rot_mat, vec)
return (rot_vec)
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