Chimie Théorique » QMX

# 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)