def from_frame_to_frame(cls, frame_from, frame_to):
"""Computes a change of basis transformation between two frames.
This transformation maps geometry from one Cartesian coordinate system
defined by "frame_from" to the other Cartesian coordinate system
defined by "frame_to".
Args:
frame_from (:class:`Frame`): a frame defining the original
Cartesian coordinate system
frame_to (:class:`Frame`): a frame defining the targeted
Cartesian coordinate system
Example:
>>> 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 == f1.transform(T)
True
"""
T1 = matrix_from_frame(frame_from)
T2 = matrix_from_frame(frame_to)
return cls(multiply_matrices(T2, inverse(T1)))
def from_frame(cls, frame):
"""Computes a transformation from world XY to frame.
Parameters
----------
frame : :class:`Frame`
A frame describing the targeted Cartesian coordinate system.
Returns
-------
Transformation
The ``Transformation`` object.
Examples
--------
>>> from compas.geometry import Frame
>>> f1 = Frame([1, 1, 1], [0.68, 0.68, 0.27], [-0.67, 0.73, -0.15])
>>> T = Transformation.from_frame(f1)
>>> f2 = Frame.from_transformation(T)
>>> f1 == f2
True
Notes
-----
It is the same as from_frame_to_frame(Frame.worldXY(), frame).
"""
return cls(matrix_from_frame(frame))
def from_frame(cls, frame):
"""Computes the rotational transformation from world XY to frame.
Notes
-----
Creating a rotation from a frame means that we omit all translational
components. If that is unwanted, use ``Transformation.from_frame(frame)``.
Parameters
----------
frame : :class:`Frame`
A frame describing the targeted Cartesian coordinate system.
Examples
--------
>>> from compas.geometry import Frame
>>> f1 = Frame([1, 1, 1], [0.68, 0.68, 0.27], [-0.67, 0.73, -0.15])
>>> T = Transformation.from_frame(f1)
>>> f2 = Frame.from_transformation(T)
>>> f1 == f2
True
"""
R = cls()
matrix = matrix_from_frame(frame)
matrix[0][3] = 0.0
matrix[1][3] = 0.0
matrix[2][3] = 0.0
R.matrix = matrix
return R
def represent_vector_in_global_coordinates(self, vector):
"""Represents a vector in local coordinates in the world coordinate system.
Parameters
----------
vector: :obj:`list` of :obj:`float` or :class:`Vector`
A vector in local coordinates.
Returns
-------
:class:`Vector`
A vector in the world coordinate system.
Examples
--------
>>> from compas.geometry import Frame
>>> f = Frame([1, 1, 1], [0.68, 0.68, 0.27], [-0.67, 0.73, -0.15])
>>> pw1 = [2, 2, 2]
>>> pf = f.represent_vector_in_local_coordinates(pw1)
>>> pw2 = f.represent_vector_in_global_coordinates(pf)
>>> allclose(pw1, pw2)
True
"""
T = matrix_from_frame(self)
vec = Vector(*vector)
vec.transform(T)
return vec
def represent_point_in_global_coordinates(self, point):
"""Represents a point from local coordinates in the world coordinate system.
Parameters
----------
point : :obj:`list` of :obj:`float` or :class:`Point`
A point in local coordinates.
Returns
-------
:class:`Point`
A point in the world coordinate system.
Examples
--------
>>> from compas.geometry import Frame
>>> f = Frame([1, 1, 1], [0.68, 0.68, 0.27], [-0.67, 0.73, -0.15])
>>> pw1 = [2, 2, 2]
>>> pf = f.represent_point_in_local_coordinates(pw1)
>>> pw2 = f.represent_point_in_global_coordinates(pf)
>>> allclose(pw1, pw2)
True
"""
T = matrix_from_frame(self)
pt = Point(*point)
pt.transform(T)
return pt
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 test_basis_vectors_from_matrix():
f = Frame([0, 0, 0], [0.68, 0.68, 0.27], [-0.67, 0.73, -0.15])
R = matrix_from_frame(f)
xaxis, yaxis = basis_vectors_from_matrix(R)
assert np.allclose(
xaxis, [0.6807833515407016, 0.6807833515407016, 0.2703110366411609])
assert np.allclose(
yaxis, [-0.6687681911461376, 0.7282315441900513, -0.14975955581430114])
def test_matrix_from_frame():
f = Frame([1, 1, 1], [0.68, 0.68, 0.27], [-0.67, 0.73, -0.15])
T = matrix_from_frame(f)
t = [[0.6807833515407016, -0.6687681911461376, -0.29880283595731283, 1.0],
[0.6807833515407016, 0.7282315441900513, -0.0788216106888398, 1.0],
[0.2703110366411609, -0.14975955581430114, 0.9510541619236438, 1.0],
[0.0, 0.0, 0.0, 1.0]]
assert np.allclose(T, t)
def from_frame(cls, frame):
"""Computes a change of basis transformation from world XY to frame.
It is the same as from_frame_to_frame(Frame.worldXY(), frame).
Args:
frame (:class:`Frame`): a frame describing the targeted Cartesian
coordinate system
Example:
>>> from compas.geometry import Frame
>>> f1 = Frame([1, 1, 1], [0.68, 0.68, 0.27], [-0.67, 0.73, -0.15])
>>> T = Transformation.from_frame(f1)
>>> f2 = Frame.from_transformation(T)
>>> f1 == f2
True
"""
T = cls()
T.matrix = matrix_from_frame(frame)
return T
def from_frame(cls, frame):
"""Computes a change of basis transformation from world XY to frame.
It is the same as from_frame_to_frame(Frame.worldXY(), frame).
Parameters
----------
frame : :class:`Frame`
A frame describing the targeted Cartesian coordinate system.
Examples
--------
>>> from compas.geometry import Frame
>>> f1 = Frame([1, 1, 1], [0.68, 0.68, 0.27], [-0.67, 0.73, -0.15])
>>> T = Transformation.from_frame(f1)
>>> f2 = Frame.from_transformation(T)
>>> f1 == f2
True
"""
R = cls()
R.matrix = matrix_from_frame(frame)
R.matrix[0][3], R.matrix[1][3], R.matrix[2][3] = [0., 0., 0.]
return R
