def transform(self, transformation):
"""Transform the frame.
Parameters
----------
transformation : :class:`Transformation`
The transformation used to transform the Frame.
Examples
--------
>>> from compas.geometry import Frame
>>> from compas.geometry import Transformation
>>> f1 = Frame([1, 1, 1], [0.68, 0.68, 0.27], [-0.67, 0.73, -0.15])
>>> T = Transformation.from_frame(f1)
>>> f2 = Frame.worldXY()
>>> f2.transform(T)
>>> f1 == f2
True
"""
T = transformation * Transformation.from_frame(self)
point = T.translation
xaxis, yaxis = T.basis_vectors
self.point = point
self.xaxis = xaxis
self.yaxis = yaxis
def to_world_coords(self, object_in_lcs):
"""Returns the object's coordinates in the global coordinate frame.
Parameters
----------
object_in_lcs : :class:`Point` or :class:`Vector` or :class:`Frame` or list of float
An object in local coordinate system of the frame.
Returns
-------
:class:`Point` or :class:`Vector` or :class:`Frame`
The object in the world coordinate frame.
Notes
-----
If you pass a list of float, it is assumed to represent a point.
Examples
--------
>>> from compas.geometry import Frame
>>> frame = Frame([1, 1, 1], [0.68, 0.68, 0.27], [-0.67, 0.73, -0.15])
>>> pl = Point(1.632, -0.090, 0.573) # point in frame
>>> pw = frame.to_world_coords(pl) # point in wcf
>>> frame.to_local_coords(pw)
Point(1.632, -0.090, 0.573)
"""
T = Transformation.change_basis(self, Frame.worldXY())
if isinstance(object_in_lcs, list):
return Point(*object_in_lcs).transformed(T)
else:
return object_in_lcs.transformed(T)
def local_to_local_coords(frame1, frame2, object_in_frame1):
"""Returns the object's coordinates in frame1 in the local coordinates of frame2.
Parameters
----------
frame1 : :class:`Frame`
A frame representing one local coordinate system.
frame2 : :class:`Frame`
A frame representing another local coordinate system.
object_in_frame1 : :class:`Point` or :class:`Vector` or :class:`Frame` or list of float
An object in the coordinate frame1. If you pass a list of float, it is assumed to represent a point.
Returns
-------
:class:`Point` or :class:`Vector` or :class:`Frame`
The object in the local coordinate system of frame2.
Examples
--------
>>> from compas.geometry import Point, Frame
>>> frame1 = Frame([1, 1, 1], [0.68, 0.68, 0.27], [-0.67, 0.73, -0.15])
>>> frame2 = Frame([2, 1, 3], [1., 0., 0.], [0., 1., 0.])
>>> p1 = Point(2, 2, 2) # point in frame1
>>> p2 = Frame.local_to_local_coords(frame1, frame2, p1) # point in frame2
>>> Frame.local_to_local_coords(frame2, frame1, p2)
Point(2.000, 2.000, 2.000)
"""
T = Transformation.change_basis(frame1, frame2)
if isinstance(object_in_frame1, list):
return Point(*object_in_frame1).transformed(T)
else:
return object_in_frame1.transformed(T)
def test_reflection():
point = [1, 1, 1]
normal = [0, 0, 1]
R1 = Reflection(point, normal)
R2 = Transformation.from_matrix([[1, 0, 0, 0], [0, 1, 0, 0], [0, 0, -1, 2],
[0, 0, 0, 1]])
assert R1 == R2
def test_reflection_from_frame():
point = [1, 1, 1]
x = [1, 0, 0]
y = [0, 1, 0]
f = Frame(point, x, y)
R1 = Reflection.from_frame(f)
R2 = Transformation.from_matrix([[1, 0, 0, 0], [0, 1, 0, 0], [0, 0, -1, 2],
[0, 0, 0, 1]])
assert R1 == R2
def test_from_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)
assert np.allclose(f1, f2)
def test_transformation():
assert Transformation().matrix == [[1.0, 0.0, 0.0, 0.0],
[0.0, 1.0, 0.0, 0.0],
[0.0, 0.0, 1.0, 0.0],
[0.0, 0.0, 0.0, 1.0]]
def test_inverse():
f = Frame([1, 1, 1], [0.68, 0.68, 0.27], [-0.67, 0.73, -0.15])
T = Transformation.from_frame(f)
assert Transformation() == T * T.inverse()
def test_rotation_property():
T = Transformation()
r = T.rotation
assert type(r) == Rotation
assert r.matrix == [[1, 0, 0, 0], [0, 1, 0, 0], [0, 0, 1, 0], [0, 0, 0, 1]]
def test_from_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)
assert f1 == f2
def test_from_list():
numbers = [1, 0, 0, 3, 0, 1, 0, 4, 0, 0, 1, 5, 0, 0, 0, 1]
T = Transformation.from_list(numbers)
assert T.matrix == [[1.0, 0.0, 0.0, 3.0], [0.0, 1.0, 0.0, 4.0],
[0.0, 0.0, 1.0, 5.0], [0.0, 0.0, 0.0, 1.0]]
def test_from_matrix():
t = Transformation().matrix
assert Transformation.from_matrix(t).matrix == t
def test_copy():
T = Transformation()
assert T.matrix == T.copy().matrix
def test_list():
T = Transformation()
assert T.list == [
1.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0,
0.0, 1.0
]