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