def from_axis_angle_vector(cls, axis_angle_vector, point=[0, 0, 0]):
"""Construct a frame from an axis-angle vector representing the rotation.
Parameters
----------
axis_angle_vector : :obj:`list` of :obj:`float`
Three numbers that represent the axis of rotation and angle of
rotation by its magnitude.
point : :obj:`list` of :obj:`float`, optional
The point of the frame.
Defaults to [0, 0, 0].
Returns
-------
Frame
The constructed frame.
Examples
--------
>>> from compas.geometry import Frame
>>> aav1 = [-0.043, -0.254, 0.617]
>>> f = Frame.from_axis_angle_vector(aav1, point = [0, 0, 0])
>>> aav2 = f.axis_angle_vector
>>> allclose(aav1, aav2)
True
"""
R = matrix_from_axis_angle_vector(axis_angle_vector)
xaxis, yaxis = basis_vectors_from_matrix(R)
return cls(point, xaxis, yaxis)
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 from_quaternion(cls, quaternion, point=[0, 0, 0]):
"""Construct a frame from a rotation represented by quaternion coefficients.
Parameters
----------
quaternion : :obj:`list` of :obj:`float`
Four numbers that represent the four coefficient values of a quaternion.
point : :obj:`list` of :obj:`float`, optional
The point of the frame.
Defaults to [0, 0, 0].
Returns
-------
Frame
The constructed frame.
Examples
--------
>>> from compas.geometry import Frame
>>> q1 = [0.945, -0.021, -0.125, 0.303]
>>> f = Frame.from_quaternion(q1, point = [1., 1., 1.])
>>> q2 = f.quaternion
>>> allclose(q1, q2, tol=1e-03)
True
"""
R = matrix_from_quaternion(quaternion)
xaxis, yaxis = basis_vectors_from_matrix(R)
return cls(point, xaxis, yaxis)
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 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 basis_vectors(self):
"""The basis vectors from the rotation component of the transformation matrix.
Returns
-------
tuple of :class:`compas.geometry.Vector`
The basis vectors of the rotation component of the tranformation.
"""
from compas.geometry import Vector
x, y = basis_vectors_from_matrix(self.rotation.matrix)
return Vector(*x), Vector(*y)
def basis_vectors(self):
"""Returns the basis vectors of the ``Rotation``.
Returns
-------
tuple of (:class:`Vector`, :class:`Vector`)
The basis vectors.
"""
from compas.geometry import Vector
xaxis, yaxis = basis_vectors_from_matrix(self.matrix)
return Vector(*xaxis), Vector(*yaxis)
def from_euler_angles(cls,
euler_angles,
static=True,
axes='xyz',
point=[0, 0, 0]):
"""Construct a frame from a rotation represented by Euler angles.
Parameters
----------
euler_angles : :obj:`list` of :obj:`float`
Three numbers that represent the angles of rotations about the defined axes.
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'.
point : :obj:`list` of :obj:`float`, optional
The point of the frame.
Defaults to [0, 0, 0].
Returns
-------
Frame
The constructed frame.
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_euler_angles(euler_angles, static, axes)
xaxis, yaxis = basis_vectors_from_matrix(R)
return cls(point, xaxis, yaxis)
def basis_vectors(self):
"""Returns the basis vectors of the ``Rotation``.
"""
return basis_vectors_from_matrix(self.matrix)
def basis_vectors(self):
from compas.geometry import Vector
xaxis, yaxis = basis_vectors_from_matrix(self.matrix)
return Vector(*xaxis), Vector(*yaxis)
def basis_vectors(self):
from compas.geometry import Vector
x, y = basis_vectors_from_matrix(self.rotation.matrix)
return Vector(*x), Vector(*y)
