93 lines
3.0 KiB
Python
93 lines
3.0 KiB
Python
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import sympy
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import sys
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import unittest
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import sophus
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class DualQuaternion:
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""" Dual quaternion class """
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def __init__(self, real_q, inf_q):
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""" Dual quaternion consists of a real quaternion, and an infinitesimal
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quaternion """
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self.real_q = real_q
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self.inf_q = inf_q
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def __mul__(self, right):
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""" dual quaternion multiplication """
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return DualQuaternion(self.real_q * right.real_q,
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self.real_q * right.inf_q +
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self.inf_q * right.real_q)
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def __truediv__(self, scalar):
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""" scalar division """
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return DualQuaternion(self.real_q / scalar, self.inf_q / scalar)
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def __repr__(self):
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return "( " + repr(self.real_q) + \
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" + " + repr(self.inf_q) + ")"
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def __getitem__(self, key):
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assert (key >= 0 and key < 8)
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if key < 4:
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return self.real_q[i]
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else:
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return self.inf_q[i - 4]
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def squared_norm(self):
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""" squared norm when considering the dual quaternion as 8-tuple """
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return self.real_q.squared_norm() + self.inf_q.squared_norm()
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def conj(self):
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""" dual quaternion conjugate """
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return DualQuaternion(self.real_q.conj(), self.inf_q.conj())
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def inv(self):
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""" dual quaternion inverse """
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return DualQuaternion(self.real_q.inv(),
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-self.real_q.inv() * self.inf_q *
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self.real_q.inv())
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def simplify(self):
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return DualQuaternion(self.real_q.simplify(),
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self.inf_q.simplify())
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@staticmethod
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def identity():
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return DualQuaternion(sophus.Quaternion.identity(),
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sophus.Quaternion.zero())
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def __eq__(self, other):
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if isinstance(self, other.__class__):
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return self.real_q == other.real_q and self.inf_q == other.inf_q
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return False
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class TestDualQuaternion(unittest.TestCase):
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def setUp(self):
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w, s0, s1, s2 = sympy.symbols('w s0 s1 s2', real=True)
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x, t0, t1, t2 = sympy.symbols('x t0 t1 t2', real=True)
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y, u0, u1, u2 = sympy.symbols('y u0 u1 u2', real=True)
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z, v0, v1, v2 = sympy.symbols('z v0 v1 v2', real=True)
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s = sophus.Vector3(s0, s1, s2)
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t = sophus.Vector3(t0, t1, t2)
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u = sophus.Vector3(u0, u1, u2)
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v = sophus.Vector3(v0, v1, v2)
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self.a = DualQuaternion(sophus.Quaternion(w, s),
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sophus.Quaternion(x, t))
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self.b = DualQuaternion(sophus.Quaternion(y, u),
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sophus.Quaternion(z, v))
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def test_muliplications(self):
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product = self.a * self.a.inv()
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self.assertEqual(product.simplify(),
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DualQuaternion.identity())
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product = self.a.inv() * self.a
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self.assertEqual(product.simplify(),
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DualQuaternion.identity())
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if __name__ == '__main__':
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unittest.main()
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