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_rotation_groups.py
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_rotation_groups.py
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import numpy as np
from scipy.constants import golden as phi
def icosahedral(cls):
g1 = tetrahedral(cls).as_quat()
a = 0.5
b = 0.5 / phi
c = phi / 2
g2 = np.array([[+a, +b, +c, 0],
[+a, +b, -c, 0],
[+a, +c, 0, +b],
[+a, +c, 0, -b],
[+a, -b, +c, 0],
[+a, -b, -c, 0],
[+a, -c, 0, +b],
[+a, -c, 0, -b],
[+a, 0, +b, +c],
[+a, 0, +b, -c],
[+a, 0, -b, +c],
[+a, 0, -b, -c],
[+b, +a, 0, +c],
[+b, +a, 0, -c],
[+b, +c, +a, 0],
[+b, +c, -a, 0],
[+b, -a, 0, +c],
[+b, -a, 0, -c],
[+b, -c, +a, 0],
[+b, -c, -a, 0],
[+b, 0, +c, +a],
[+b, 0, +c, -a],
[+b, 0, -c, +a],
[+b, 0, -c, -a],
[+c, +a, +b, 0],
[+c, +a, -b, 0],
[+c, +b, 0, +a],
[+c, +b, 0, -a],
[+c, -a, +b, 0],
[+c, -a, -b, 0],
[+c, -b, 0, +a],
[+c, -b, 0, -a],
[+c, 0, +a, +b],
[+c, 0, +a, -b],
[+c, 0, -a, +b],
[+c, 0, -a, -b],
[0, +a, +c, +b],
[0, +a, +c, -b],
[0, +a, -c, +b],
[0, +a, -c, -b],
[0, +b, +a, +c],
[0, +b, +a, -c],
[0, +b, -a, +c],
[0, +b, -a, -c],
[0, +c, +b, +a],
[0, +c, +b, -a],
[0, +c, -b, +a],
[0, +c, -b, -a]])
return cls.from_quat(np.concatenate((g1, g2)))
def octahedral(cls):
g1 = tetrahedral(cls).as_quat()
c = np.sqrt(2) / 2
g2 = np.array([[+c, 0, 0, +c],
[0, +c, 0, +c],
[0, 0, +c, +c],
[0, 0, -c, +c],
[0, -c, 0, +c],
[-c, 0, 0, +c],
[0, +c, +c, 0],
[0, -c, +c, 0],
[+c, 0, +c, 0],
[-c, 0, +c, 0],
[+c, +c, 0, 0],
[-c, +c, 0, 0]])
return cls.from_quat(np.concatenate((g1, g2)))
def tetrahedral(cls):
g1 = np.eye(4)
c = 0.5
g2 = np.array([[c, -c, -c, +c],
[c, -c, +c, +c],
[c, +c, -c, +c],
[c, +c, +c, +c],
[c, -c, -c, -c],
[c, -c, +c, -c],
[c, +c, -c, -c],
[c, +c, +c, -c]])
return cls.from_quat(np.concatenate((g1, g2)))
def dicyclic(cls, n, axis=2):
g1 = cyclic(cls, n, axis).as_rotvec()
thetas = np.linspace(0, np.pi, n, endpoint=False)
rv = np.pi * np.vstack([np.zeros(n), np.cos(thetas), np.sin(thetas)]).T
g2 = np.roll(rv, axis, axis=1)
return cls.from_rotvec(np.concatenate((g1, g2)))
def cyclic(cls, n, axis=2):
thetas = np.linspace(0, 2 * np.pi, n, endpoint=False)
rv = np.vstack([thetas, np.zeros(n), np.zeros(n)]).T
return cls.from_rotvec(np.roll(rv, axis, axis=1))
def create_group(cls, group, axis='Z'):
if not isinstance(group, str):
raise ValueError("`group` argument must be a string")
permitted_axes = ['x', 'y', 'z', 'X', 'Y', 'Z']
if axis not in permitted_axes:
raise ValueError("`axis` must be one of " + ", ".join(permitted_axes))
if group in ['I', 'O', 'T']:
symbol = group
order = 1
elif group[:1] in ['C', 'D'] and group[1:].isdigit():
symbol = group[:1]
order = int(group[1:])
else:
raise ValueError("`group` must be one of 'I', 'O', 'T', 'Dn', 'Cn'")
if order < 1:
raise ValueError("Group order must be positive")
axis = 'xyz'.index(axis.lower())
if symbol == 'I':
return icosahedral(cls)
elif symbol == 'O':
return octahedral(cls)
elif symbol == 'T':
return tetrahedral(cls)
elif symbol == 'D':
return dicyclic(cls, order, axis=axis)
elif symbol == 'C':
return cyclic(cls, order, axis=axis)
else:
assert False