def test_decompose_matrix(R, T):
assert decompose_matrix(R.matrix) == ([1.0, 1.0, 1.0], [0.0, 0.0, 0.0],
[2.035405699485789, 0.0,
0.0], [0.0, 0.0,
0.0], [0.0, 0.0, 0.0, 1.0])
assert decompose_matrix(T.matrix) == ([1.0, 1.0, 1.0], [0.0, 0.0, 0.0],
[0.0, -0.0,
0.0], [1.0, 2.0,
3.0], [0.0, 0.0, 0.0, 1.0])
def __init__(self, matrix=None):
if matrix:
_, _, _, _, perspective = decompose_matrix(matrix)
check = matrix_from_perspective_entries(perspective)
if not allclose(flatten(matrix), flatten(check)):
raise ValueError('This is not a proper projection matrix.')
super(Projection, self).__init__(matrix=matrix)
def __init__(self, matrix=None):
if matrix:
_, _, _, translation, _ = decompose_matrix(matrix)
check = matrix_from_translation(translation)
if not allclose(flatten(matrix), flatten(check)):
raise ValueError('This is not a proper translation matrix.')
super(Translation, self).__init__(matrix=matrix)
def __init__(self, matrix=None):
if matrix:
_, _, angles, _, _ = decompose_matrix(matrix)
check = matrix_from_euler_angles(angles)
if not allclose(flatten(matrix), flatten(check)):
raise ValueError('This is not a proper rotation matrix.')
super(Rotation, self).__init__(matrix=matrix)
def from_matrix(cls, matrix):
"""Construct a frame from a matrix.
Parameters
----------
matrix : :obj:`list` of :obj:`list` of :obj:`float`
The 4x4 transformation matrix in row-major order.
Returns
-------
Frame
The constructed frame.
Examples
--------
>>> from compas.geometry import Frame
>>> from compas.geometry import matrix_from_euler_angles
>>> ea1 = [0.5, 0.4, 0.8]
>>> M = matrix_from_euler_angles(ea1)
>>> f = Frame.from_matrix(M)
>>> ea2 = f.euler_angles()
>>> allclose(ea1, ea2)
True
"""
sc, sh, a, point, p = decompose_matrix(matrix)
R = matrix_from_euler_angles(a, static=True, axes='xyz')
xaxis, yaxis = basis_vectors_from_matrix(R)
return cls(point, xaxis, yaxis)
def __init__(self, matrix=None):
if matrix:
scale, _, _, _, _ = decompose_matrix(matrix)
check = matrix_from_scale_factors(scale)
if not allclose(flatten(matrix), flatten(check)):
raise ValueError('This is not a proper scale matrix.')
super(Scale, self).__init__(matrix=matrix)
def decompose(self):
"""Decomposes the ``Transformation`` into ``Scale``, ``Shear``, \
``Rotation``, ``Translation`` and ``Perspective``.
Example:
>>> 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.decompose()
>>> S1 == Sc
True
>>> R1 == R
True
>>> T1 == T
True
"""
from compas.geometry.xforms import Scale
from compas.geometry.xforms import Shear
from compas.geometry.xforms import Rotation
from compas.geometry.xforms import Translation
from compas.geometry.xforms 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 basis_vectors(self):
"""Returns the basis vectors from the ``Rotation`` component of the
``Transformation``.
"""
sc, sh, a, t, p = decompose_matrix(self.matrix)
R = matrix_from_euler_angles(a, static=True, axes='xyz')
xv, yv = basis_vectors_from_matrix(R)
return Vector(*xv), Vector(*yv)
def basis_vectors(self):
"""Returns the basis vectors from the ``Rotation`` component of the ``Transformation``.
"""
# this has to be here to avoid circular import
from compas.geometry.primitives import Vector
sc, sh, a, t, p = decompose_matrix(self.matrix)
R = matrix_from_euler_angles(a, static=True, axes='xyz')
xv, yv = basis_vectors_from_matrix(R)
return Vector(*xv), Vector(*yv)
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.transformations import Scale # noqa: F811
from compas.geometry.transformations import Shear
from compas.geometry.transformations import Rotation # noqa: F811
from compas.geometry.transformations import Translation # noqa: F811
from compas.geometry.transformations 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
f1 = Frame([2, 2, 2], [0.12, 0.58, 0.81], [-0.80, 0.53, -0.26])
f2 = Frame([1, 1, 1], [0.68, 0.68, 0.27], [-0.67, 0.73, -0.15])
T = Transformation.from_frame_to_frame(f1, f2)
f1.transform(T)
print(f1 == f2)
f = Frame([1, 1, 1], [0.68, 0.68, 0.27], [-0.67, 0.73, -0.15])
T = Transformation.from_frame(f)
p = Point(0, 0, 0)
p.transform(T)
print(allclose(f.point, p))
f1 = Frame([1, 1, 1], [0.68, 0.68, 0.27], [-0.67, 0.73, -0.15])
T = Transformation.from_frame(f1)
points = [[1.0, 1.0, 1.0], [1.68, 1.68, 1.27], [0.33, 1.73, 0.85]]
points = transform_points(points, T)
trans1 = [1, 2, 3]
angle1 = [-2.142, 1.141, -0.142]
scale1 = [0.123, 2, 0.5]
T = matrix_from_translation(trans1)
R = matrix_from_euler_angles(angle1)
S = matrix_from_scale_factors(scale1)
M = multiply_matrices(multiply_matrices(T, R), S)
# M = compose_matrix(scale1, None, angle1, trans1, None)
scale2, shear2, angle2, trans2, persp2 = decompose_matrix(M)
print(allclose(scale1, scale2))
print(allclose(angle1, angle2))
print(allclose(trans1, trans2))
