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 euler_angles(self, static=True, axes='xyz'):
"""The Euler angles from the rotation given by the frame.
Parameters
----------
static : :obj:`bool`, optional
If true the rotations are applied to a static frame.
If not, to a rotational.
Defaults to True.
axes : :obj:`str`, optional
A 3 character string specifying the order of the axes.
Defaults to 'xyz'.
Returns
-------
:obj:`list` of :obj:`float`
Three numbers that represent the angles of rotations about the defined axes.
Examples
--------
>>> from compas.geometry import Frame
>>> ea1 = 1.4, 0.5, 2.3
>>> f = Frame.from_euler_angles(ea1, static = True, axes = 'xyz')
>>> ea2 = f.euler_angles(static = True, axes = 'xyz')
>>> allclose(ea1, ea2)
True
"""
R = matrix_from_basis_vectors(self.xaxis, self.yaxis)
return euler_angles_from_matrix(R, static, axes)
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 test_matrix_from_basis_vectors():
xaxis = [0.68, 0.68, 0.27]
yaxis = [-0.67, 0.73, -0.15]
R = matrix_from_basis_vectors(xaxis, yaxis)
r = [[0.6807833515407016, -0.6687681611113407, -0.29880282253789103, 0.0],
[0.6807833515407016, 0.7282315114847181, -0.07882160714891209, 0.0],
[0.2703110366411609, -0.14975954908850603, 0.9510541192112079, 0.0],
[0.0, 0.0, 0.0, 1.0]]
assert np.allclose(R, r)
def axis_angle_vector(self):
"""vector : The axis-angle vector from the rotation given by the frame."""
R = matrix_from_basis_vectors(self.xaxis, self.yaxis)
return Vector(*axis_angle_vector_from_matrix(R))
def quaternion(self):
""":class:`Quaternion` : The quaternion from the rotation given by the frame.
"""
rotation = matrix_from_basis_vectors(self.xaxis, self.yaxis)
return Quaternion(*quaternion_from_matrix(rotation))
def quaternion(self):
""":obj:`list` of :obj:`float` : The 4 quaternion coefficients from the rotation given by the frame.
"""
rotation = matrix_from_basis_vectors(self.xaxis, self.yaxis)
return quaternion_from_matrix(rotation)
