Add dual_quaternion_double

doc/source/api.rst

@@ -362,6 +362,7 @@ Dual Quaternion
 
    ~check_dual_quaternion
    ~dual_quaternion_requires_renormalization
+   ~dual_quaternion_double
    ~dq_conj
    ~dq_q_conj
    ~concatenate_dual_quaternions

pytransform3d/test/test_transformations.py

@@ -938,3 +938,13 @@ def test_pq_slerp():
 def test_transform_requires_renormalization():
     assert pt.transform_requires_renormalization(np.eye(4) + 1e-6)
     assert not pt.transform_requires_renormalization(np.eye(4))
+
+
+def test_dual_quaternion_double():
+    rng = np.random.default_rng(4183)
+    A2B = pt.random_transform(rng)
+    dq = pt.dual_quaternion_from_transform(A2B)
+    dq_double = pt.dual_quaternion_double(dq)
+    pt.assert_unit_dual_quaternion_equal(dq, dq_double)
+    assert_array_almost_equal(
+        A2B, pt.transform_from_dual_quaternion(dq_double))

pytransform3d/transformations/__init__.py

@@ -31,8 +31,8 @@
     vectors_to_directions, transform)
 from ._pq_operations import pq_slerp
 from ._dual_quaternion_operations import (
-    dq_q_conj, dq_conj, concatenate_dual_quaternions, dual_quaternion_sclerp,
-    dual_quaternion_power, dq_prod_vector)
+    dual_quaternion_double, dq_q_conj, dq_conj, concatenate_dual_quaternions,
+    dual_quaternion_sclerp, dual_quaternion_power, dq_prod_vector)
 from ._random import (
     random_transform, random_screw_axis, random_exponential_coordinates)
 from ._plot import plot_transform, plot_screw
@@ -74,8 +74,9 @@
     "vectors_to_directions", "transform",
     "random_transform", "random_screw_axis", "random_exponential_coordinates",
     "pq_slerp",
-    "dq_q_conj", "dq_conj", "concatenate_dual_quaternions",
-    "dual_quaternion_sclerp", "dual_quaternion_power", "dq_prod_vector",
+    "dual_quaternion_double", "dq_q_conj", "dq_conj",
+    "concatenate_dual_quaternions", "dual_quaternion_sclerp",
+    "dual_quaternion_power", "dq_prod_vector",
     "plot_transform", "plot_screw",
     "assert_transform", "assert_exponential_coordinates_equal",
     "assert_screw_parameters_equal", "assert_unit_dual_quaternion_equal",

pytransform3d/transformations/_dual_quaternion_operations.py

@@ -6,6 +6,26 @@
 from ..rotations import concatenate_quaternions
 
 
+def dual_quaternion_double(dq):
+    """Create another dual quaternion that represents the same transformation.
+
+    The unit dual quaternions sigma and -sigma represent the same
+    transformation (double cover).
+
+    Parameters
+    ----------
+    dq : array-like, shape (8,)
+        Unit dual quaternion to represent transform:
+        (pw, px, py, pz, qw, qx, qy, qz)
+
+    Returns
+    -------
+    dq_double : array, shape (8,)
+        -dq
+    """
+    return -check_dual_quaternion(dq, unit=True)
+
+
 def dq_conj(dq):
     """Conjugate of dual quaternion.
 

pytransform3d/transformations/_dual_quaternion_operations.pyi

@@ -2,6 +2,9 @@ import numpy as np
 import numpy.typing as npt
 
 
+def dual_quaternion_double(dq: npt.ArrayLike) -> np.ndarray: ...
+
+
 def dq_conj(dq: npt.ArrayLike) -> np.ndarray: ...