def test_basis_vectors():
ea1 = 1.4, 0.5, 2.3
args = False, 'xyz'
R1 = Rotation.from_euler_angles(ea1, *args)
R2 = [[-0.5847122176808724, -0.18803656702967916, 0.789147560317086],
[-0.6544178905170501, -0.4655532858863264, -0.5958165511058404]]
assert np.allclose(R1.basis_vectors, R2)
def vertex_xyz(self):
"""dict : The view coordinates of the volmesh object."""
origin = Point(0, 0, 0)
stack = []
if self.scale != 1.0:
S = Scale.from_factors([self.scale] * 3)
stack.append(S)
if self.rotation != [0, 0, 0]:
R = Rotation.from_euler_angles(self.rotation)
stack.append(R)
if self.location != origin:
if self.anchor is not None:
xyz = self.volmesh.vertex_attributes(self.anchor, 'xyz')
point = Point(*xyz)
T1 = Translation.from_vector(origin - point)
stack.insert(0, T1)
T2 = Translation.from_vector(self.location)
stack.append(T2)
if stack:
X = reduce(mul, stack[::-1])
volmesh = self.volmesh.transformed(X)
else:
volmesh = self.volmesh
vertex_xyz = {
vertex: volmesh.vertex_attributes(vertex, 'xyz')
for vertex in volmesh.vertices()
}
return vertex_xyz
def concatenate():
trans1 = [1, 2, 3]
angle1 = [-2.142, 1.141, -0.142]
T1 = Translation(trans1)
R1 = Rotation.from_euler_angles(angle1)
M1 = T1.concatenate(R1)
assert np.allclose(M1, T1 * R1)
def test_concatenated():
trans1 = [1, 2, 3]
angle1 = [-2.142, 1.141, -0.142]
T1 = Translation.from_vector(trans1)
R1 = Rotation.from_euler_angles(angle1)
M1 = T1.concatenated(R1)
assert allclose(M1, T1 * R1)
def node_xyz(self):
"""dict : The view coordinates of the mesh object."""
origin = Point(0, 0, 0)
stack = []
if self.scale != 1.0:
S = Scale.from_factors([self.scale] * 3)
stack.append(S)
if self.rotation != [0, 0, 0]:
R = Rotation.from_euler_angles(self.rotation)
stack.append(R)
if self.location != origin:
if self.anchor is not None:
xyz = self.network.vertex_attributes(self.anchor, 'xyz')
point = Point(*xyz)
T1 = Translation.from_vector(origin - point)
stack.insert(0, T1)
T2 = Translation.from_vector(self.location)
stack.append(T2)
if stack:
X = reduce(mul, stack[::-1])
network = self.network.transformed(X)
else:
network = self.network
node_xyz = {
network: network.node_attributes(node, 'xyz')
for node in network.nodes()
}
return node_xyz
def test_rotation():
angle1 = [-2.142, 1.141, -0.142]
R = Rotation.from_euler_angles(angle1)
r = [[0.41249169135312663, -0.8335562904208867, -0.3674704277413451, 0.0],
[-0.05897071585157175, -0.4269749553355485, 0.9023385407861949, 0.0],
[-0.9090506362335324, -0.35053715668381935, -0.22527903264048646, 0.0],
[0.0, 0.0, 0.0, 1.0]]
assert np.allclose(R, r)
def vertex_xyz(self):
"""dict : The view coordinates of the mesh object."""
origin = Point(0, 0, 0)
if self.anchor is not None:
xyz = self.mesh.vertex_attributes(self.anchor, 'xyz')
point = Point(* xyz)
T1 = Translation.from_vector(origin - point)
S = Scale.from_factors([self.scale] * 3)
R = Rotation.from_euler_angles(self.rotation)
T2 = Translation.from_vector(self.location)
X = T2 * R * S * T1
else:
S = Scale.from_factors([self.scale] * 3)
R = Rotation.from_euler_angles(self.rotation)
T = Translation.from_vector(self.location)
X = T * R * S
mesh = self.mesh.transformed(X)
vertex_xyz = {vertex: mesh.vertex_attributes(vertex, 'xy') + [0.0] for vertex in mesh.vertices()}
return vertex_xyz
def test_basis_vectors():
trans1 = [1, 2, 3]
angle1 = [-2.142, 1.141, -0.142]
scale1 = [0.123, 2, 0.5]
T1 = Translation(trans1)
R1 = Rotation.from_euler_angles(angle1)
S1 = Scale(scale1)
M = (T1 * R1) * S1
x, y = M.basis_vectors
assert np.allclose(x, Vector(0.41249169135312663, -0.05897071585157175, -0.9090506362335324))
assert np.allclose(y, Vector(-0.8335562904208867, -0.4269749553355485, -0.35053715668381935))
def test_decomposed():
trans1 = [1, 2, 3]
angle1 = [-2.142, 1.141, -0.142]
scale1 = [0.123, 2, 0.5]
T1 = Translation(trans1)
R1 = Rotation.from_euler_angles(angle1)
S1 = Scale(scale1)
M = (T1 * R1) * S1
Sc, Sh, R, T, P = M.decomposed()
assert S1 == Sc
assert R1 == R
assert T1 == T
def node_xyz(self):
"""dict : The view coordinates of the mesh object."""
origin = Point(0, 0, 0)
if self.anchor is not None:
xyz = self.network.node_attributes(self.anchor, 'xyz')
point = Point(*xyz)
T1 = Translation.from_vector(origin - point)
S = Scale.from_factors([self.scale] * 3)
R = Rotation.from_euler_angles(self.rotation)
T2 = Translation.from_vector(self.location)
X = T2 * R * S * T1
else:
S = Scale.from_factors([self.scale] * 3)
R = Rotation.from_euler_angles(self.rotation)
T = Translation.from_vector(self.location)
X = T * R * S
network = self.network.transformed(X)
node_xyz = {
network: network.node_attributes(node, 'xyz')
for node in network.nodes()
}
return node_xyz
def test_from_euler_angles():
ea1 = 1.4, 0.5, 2.3
args = False, 'xyz'
R1 = Rotation.from_euler_angles(ea1, *args)
ea2 = R1.euler_angles(*args)
assert allclose(ea1, ea2)
alpha, beta, gamma = ea1
xaxis, yaxis, zaxis = [1, 0, 0], [0, 1, 0], [0, 0, 1]
Rx = Rotation.from_axis_and_angle(xaxis, alpha)
Ry = Rotation.from_axis_and_angle(yaxis, beta)
Rz = Rotation.from_axis_and_angle(zaxis, gamma)
R2 = Rx * Ry * Rz
assert np.allclose(R1, R2)
def decomposed(self):
"""Decompose the `Transformation` into its components.
Returns
-------
:class:`compas.geometry.Scale`
The scale component of the current transformation.
:class:`compas.geometry.Shear`
The shear component of the current transformation.
:class:`compas.geometry.Rotation`
The rotation component of the current transformation.
:class:`compas.geometry.Translation`
The translation component of the current transformation.
:class:`compas.geometry.Projection`
The projection component of the current transformation.
Examples
--------
>>> from compas.geometry import Scale, Translation, Rotation
>>> trans1 = [1, 2, 3]
>>> angle1 = [-2.142, 1.141, -0.142]
>>> scale1 = [0.123, 2, 0.5]
>>> T1 = Translation.from_vector(trans1)
>>> R1 = Rotation.from_euler_angles(angle1)
>>> S1 = Scale.from_factors(scale1)
>>> M = T1 * R1 * S1
>>> S, H, R, T, P = M.decomposed()
>>> S1 == S
True
>>> R1 == R
True
>>> T1 == T
True
"""
from compas.geometry import Scale # noqa: F811
from compas.geometry import Shear
from compas.geometry import Rotation # noqa: F811
from compas.geometry import Translation # noqa: F811
from compas.geometry import Projection
s, h, a, t, p = decompose_matrix(self.matrix)
S = Scale.from_factors(s)
H = Shear.from_entries(h)
R = Rotation.from_euler_angles(a, static=True, axes='xyz')
T = Translation.from_vector(t)
P = Projection.from_entries(p)
return S, H, R, T, P
def decomposed(self):
"""Decompose the ``Transformation`` into its ``Scale``, ``Shear``,
``Rotation``, ``Translation`` and ``Perspective`` components.
Returns
-------
5-tuple of Transformation
The scale, shear, rotation, tranlation, and projection components
of the current transformation.
Examples
--------
>>> trans1 = [1, 2, 3]
>>> angle1 = [-2.142, 1.141, -0.142]
>>> scale1 = [0.123, 2, 0.5]
>>> T1 = Translation(trans1)
>>> R1 = Rotation.from_euler_angles(angle1)
>>> S1 = Scale(scale1)
>>> M = (T1 * R1) * S1
>>> Sc, Sh, R, T, P = M.decomposed()
>>> S1 == Sc
True
>>> R1 == R
True
>>> T1 == T
True
"""
from compas.geometry import Scale # noqa: F811
from compas.geometry import Shear
from compas.geometry import Rotation # noqa: F811
from compas.geometry import Translation # noqa: F811
from compas.geometry import Projection
sc, sh, a, t, p = decompose_matrix(self.matrix)
Sc = Scale(sc)
Sh = Shear.from_entries(sh)
R = Rotation.from_euler_angles(a, static=True, axes='xyz')
T = Translation(t)
P = Projection.from_entries(p)
return Sc, Sh, R, T, P
"""There are several ways to construct a `Rotation`. """ import math from compas.geometry import Frame from compas.geometry import Rotation R = Rotation.from_axis_and_angle([1, 0, 0], math.radians(30)) R = Rotation.from_axis_and_angle([1, 0, 0], math.radians(30), point=[1, 0, 0]) R = Rotation.from_basis_vectors([0.68, 0.68, 0.27], [-0.67, 0.73, -0.15]) R = Rotation.from_frame(Frame([1, 1, 1], [0.68, 0.68, 0.27], [-0.67, 0.73, -0.15])) R = Rotation.from_axis_angle_vector([-0.043, -0.254, 0.617]) R = Rotation.from_quaternion([0.945, -0.021, -0.125, 0.303]) R = Rotation.from_euler_angles([1.4, 0.5, 2.3], static=True, axes='xyz') print(R)
def R():
return Rotation.from_euler_angles([90, 0, 0])
def test_euler_angles():
ea1 = 1.4, 0.5, 2.3
args = False, 'xyz'
R1 = Rotation.from_euler_angles(ea1, *args)
ea2 = R1.euler_angles(*args)
assert allclose(ea1, ea2)
"""Example: Rotations from euler angles, rotate an object based on 3 euler angles.
"""
from compas.geometry import Rotation
# euler angles
alpha, beta, gamma = -0.156, -0.274, 0.785
static, axes = True, 'xyz'
# Version 1: Create Rotation from angles
R1 = Rotation.from_euler_angles([alpha, beta, gamma], static, axes)
# Version 2: Concatenate 3 Rotations
xaxis, yaxis, zaxis = [1, 0, 0], [0, 1, 0], [0, 0, 1]
Rx = Rotation.from_axis_and_angle(xaxis, alpha)
Ry = Rotation.from_axis_and_angle(yaxis, beta)
Rz = Rotation.from_axis_and_angle(zaxis, gamma)
if static: # check difference between pre- and post-concatenation!
R2 = Rz * Ry * Rx
else:
R2 = Rx * Ry * Rz
# Check
print(R1 == R2)
