def decomposed(self):
"""Decompose the `Transformation` into its components.
Returns
-------
:class:`compas.geometry.Scale`
The scale component of the current transformation.
:class:`compas.geometry.Shear`
The shear component of the current transformation.
:class:`compas.geometry.Rotation`
The rotation component of the current transformation.
:class:`compas.geometry.Translation`
The translation component of the current transformation.
:class:`compas.geometry.Projection`
The projection component of the current transformation.
Examples
--------
>>> from compas.geometry import Scale, Translation, Rotation
>>> trans1 = [1, 2, 3]
>>> angle1 = [-2.142, 1.141, -0.142]
>>> scale1 = [0.123, 2, 0.5]
>>> T1 = Translation.from_vector(trans1)
>>> R1 = Rotation.from_euler_angles(angle1)
>>> S1 = Scale.from_factors(scale1)
>>> M = T1 * R1 * S1
>>> S, H, R, T, P = M.decomposed()
>>> S1 == S
True
>>> R1 == R
True
>>> T1 == T
True
"""
from compas.geometry import Scale # noqa: F811
from compas.geometry import Shear
from compas.geometry import Rotation # noqa: F811
from compas.geometry import Translation # noqa: F811
from compas.geometry import Projection
s, h, a, t, p = decompose_matrix(self.matrix)
S = Scale.from_factors(s)
H = Shear.from_entries(h)
R = Rotation.from_euler_angles(a, static=True, axes='xyz')
T = Translation.from_vector(t)
P = Projection.from_entries(p)
return S, H, R, T, P
def decomposed(self):
"""Decompose the ``Transformation`` into its ``Scale``, ``Shear``,
``Rotation``, ``Translation`` and ``Perspective`` components.
Returns
-------
5-tuple of Transformation
The scale, shear, rotation, tranlation, and projection components
of the current transformation.
Examples
--------
>>> trans1 = [1, 2, 3]
>>> angle1 = [-2.142, 1.141, -0.142]
>>> scale1 = [0.123, 2, 0.5]
>>> T1 = Translation(trans1)
>>> R1 = Rotation.from_euler_angles(angle1)
>>> S1 = Scale(scale1)
>>> M = (T1 * R1) * S1
>>> Sc, Sh, R, T, P = M.decomposed()
>>> S1 == Sc
True
>>> R1 == R
True
>>> T1 == T
True
"""
from compas.geometry import Scale # noqa: F811
from compas.geometry import Shear
from compas.geometry import Rotation # noqa: F811
from compas.geometry import Translation # noqa: F811
from compas.geometry import Projection
sc, sh, a, t, p = decompose_matrix(self.matrix)
Sc = Scale(sc)
Sh = Shear.from_entries(sh)
R = Rotation.from_euler_angles(a, static=True, axes='xyz')
T = Translation(t)
P = Projection.from_entries(p)
return Sc, Sh, R, T, P
def test_from_entries():
shear1 = [-0.41, -0.14, -0.35]
S = Shear.from_entries(shear1)
s = [[1.0, -0.41, -0.14, 0.0], [0.0, 1.0, -0.35, 0.0],
[0.0, 0.0, 1.0, 0.0], [0.0, 0.0, 0.0, 1.0]]
assert np.allclose(S, s)
def from_entries(cls, shear_entries):
"""Creates a ``Shear`` from the 3 factors for x-y, x-z, and y-z axes.
Parameters
----------
shear_factors : :obj:`list` of :obj:`float`
The 3 shear factors for x-y, x-z, and y-z axes.
Examples
--------
>>> S = Shear.from_entries([1, 2, 3])
"""
M = matrix_from_shear_entries(shear_entries)
return cls.from_matrix(M)
# ==============================================================================
# Main
# ==============================================================================
if __name__ == "__main__":
from compas.geometry import Frame
from compas.geometry import Shear
shear1 = [-0.41, -0.14, -0.35]
Sh1 = Shear.from_entries(shear1)
S2, Sh, R2, T2, P = Sh1.decompose()
print(Sh)