def test_matrix_inverse(R, T):
assert matrix_inverse(
R.matrix) == [[1.0, -0.0, 0.0, -0.0],
[-0.0, -0.4480736161291701, 0.8939966636005579, 0.0],
[0.0, -0.8939966636005579, -0.4480736161291701, -0.0],
[-0.0, 0.0, -0.0, 1.0]]
assert matrix_inverse(T.matrix) == [[1.0, -0.0, 0.0, -1.0],
[-0.0, 1.0, -0.0, -2.0],
[0.0, -0.0, 1.0, -3.0],
[-0.0, 0.0, -0.0, 1.0]]
def from_change_of_basis(cls, frame_from, frame_to):
"""Computes a change of basis transformation between two frames.
A basis change is essentially a remapping of geometry from one
coordinate system to another.
Parameters
----------
frame_from : :class:`Frame`
A frame defining the original Cartesian coordinate system.
frame_to : :class:`Frame`
A frame defining the targeted Cartesian coordinate system.
Examples
--------
>>> from compas.geometry import Point, Frame
>>> 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_change_of_basis(f1, f2)
>>> p_f1 = Point(1, 1, 1) # point in f1
>>> p_f1.transformed(T) # point represented in f2
Point(1.395, 0.955, 1.934)
>>> Frame.local_to_local_coordinates(f1, f2, p_f1)
Point(1.395, 0.955, 1.934)
"""
T1 = cls.from_frame(frame_from)
T2 = cls.from_frame(frame_to)
return cls(multiply_matrices(matrix_inverse(T2.matrix), T1.matrix))
def from_frame_to_frame(cls, frame_from, frame_to):
"""Computes a transformation between two frames.
This transformation allows to transform geometry from one Cartesian
coordinate system defined by "frame_from" to another Cartesian
coordinate system defined by "frame_to".
Parameters
----------
frame_from : :class:`Frame`
A frame defining the original Cartesian coordinate system.
frame_to : :class:`Frame`
A frame defining the targeted Cartesian coordinate system.
Returns
-------
Transformation
The ``Transformation`` object representing a change of basis.
Examples
--------
>>> from compas.geometry import Frame
>>> 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)
>>> f1 == f2
True
"""
T1 = cls.from_frame(frame_from)
T2 = cls.from_frame(frame_to)
return cls(multiply_matrices(T2.matrix, matrix_inverse(T1.matrix)))
def from_factors(cls, factors, frame=None):
"""Construct a scale transformation from scale factors.
Parameters
----------
factors : list of float
The scale factors along X, Y, Z.
frame : :class:`compas.geometry.Frame`, optional
The anchor frame for the scaling transformation.
Defaults to ``None``.
Returns
-------
Scale
A scale transformation.
Examples
--------
>>> point = Point(2, 5, 0)
>>> frame = Frame(point, (1, 0, 0), (0, 1, 0))
>>> points = [point, Point(2, 10, 0)]
>>> S = Scale.from_factors([2.] * 3, frame)
>>> [p.transformed(S) for p in points]
[Point(2.000, 5.000, 0.000), Point(2.000, 15.000, 0.000)]
"""
S = cls()
if frame:
Tw = matrix_from_frame(frame)
Tl = matrix_inverse(Tw)
Sc = matrix_from_scale_factors(factors)
S.matrix = multiply_matrices(multiply_matrices(Tw, Sc), Tl)
else:
S.matrix = matrix_from_scale_factors(factors)
return S
def invert(self):
"""Invert this transformation.
Returns
-------
None
The transformation is transposed in-place.
"""
self.matrix = matrix_inverse(self.matrix)
def invert(self):
"""Invert this transformation."""
self.matrix = matrix_inverse(self.matrix)
