def represent_vector_in_local_coordinates(self, vector):
"""Represents a vector in the frame's local coordinate system.
Parameters
----------
vector : :obj:`list` of :obj:`float` or :class:`Vector`
A vector in world XY.
Returns
-------
:class:`Vector`
A vector in the local coordinate system of the frame.
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 = inverse(matrix_from_basis_vectors(self.xaxis, self.yaxis))
vec = Vector(*vector)
vec.transform(T)
return vec
def represent_point_in_local_coordinates(self, point):
"""Represents a point in the frame's local coordinate system.
Parameters
----------
point : :obj:`list` of :obj:`float` or :class:`Point`
A point in world XY.
Returns
-------
:class:`Point`
A point in the local coordinate system of the frame.
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
"""
pt = Point(*subtract_vectors(point, self.point))
T = inverse(matrix_from_basis_vectors(self.xaxis, self.yaxis))
pt.transform(T)
return pt
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.transform(T)
>>> f1 == f2
True
"""
T1 = cls.from_frame(frame_from)
T2 = cls.from_frame(frame_to)
return cls(multiply_matrices(T2.matrix, inverse(T1.matrix)))
def inverse(self):
"""Returns the inverse transformation.
Example:
>>> from compas.geometry import Frame
>>> f = Frame([1, 1, 1], [0.68, 0.68, 0.27], [-0.67, 0.73, -0.15])
>>> T = Transformation.from_frame(f)
>>> I = Transformation() # identity matrix
>>> I == T * T.inverse()
True
"""
cls = type(self)
return cls(inverse(self.matrix))
