def test_projection_perspective():
point = [0, 0, 0]
normal = [0, 0, 1]
perspective = [1, 1, 0]
P = Projection.perspective(point, normal, perspective)
assert P.matrix == [[0.0, 0.0, -1.0, 0.0], [0.0, 0.0, -1.0, 0.0],
[0.0, 0.0, 0.0, 0.0], [0.0, 0.0, -1.0, 0.0]]
def test_projection_parallel():
point = [0, 0, 0]
normal = [0, 0, 1]
direction = [1, 1, 1]
P = Projection.parallel(point, normal, direction)
assert P.matrix == [[1.0, 0.0, -1.0, 0.0], [0.0, 1.0, -1.0, 0.0],
[0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 1.0]]
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
from compas_rhino.artists import MeshArtist
from compas_rhino.artists import PlaneArtist # not implemented
from compas.datastructures import Mesh
# Define a Frame, which is not in the origin and a bit tilted to the world frame
frame = Frame(Point(1, 1, 3), Vector(1, 0, 1), Vector(0, 1, 1))
# Create a Box with that frame
box = Box(frame, 2, 3, 6)
# create a plane for the projection
planexy = Plane.worldXY()
# Create a Projection (can be orthogonal, parallel or perspective)
P3 = Projection.from_plane(
planexy) # orthogonal Projection to project onto a plane
P4 = Projection.from_plane_and_direction(planexy, direction=Vector(
-2, 2, 1)) # parallel projection
P5 = Projection.from_plane_and_point(planexy,
Point(3, -3,
-1)) # perspective Projection
# Create a Mesh from the Box
mesh = Mesh.from_shape(box)
# Apply the Projection onto the mesh
mesh_projected3 = mesh.transformed(P3)
mesh_projected4 = mesh.transformed(P4)
mesh_projected5 = mesh.transformed(P5)
# Create artists
def test_projection_orthogonal():
point = [0, 0, 0]
normal = [0, 0, 1]
P = Projection.from_plane((point, normal))
assert P.matrix == [[1.0, 0.0, 0.0, 0.0], [0.0, 1.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 1.0]]
def test_projection_entries():
persp1 = [0.3, 0.1, 0.1, 1]
P1 = Projection.from_entries(persp1)
assert P1.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], [0.3, 0.1, 0.1, 1.0]]
def test_projection_perspective():
point = [0, 0, 0]
normal = [0, 0, 1]
perspective = [1, 1, 0]
P = Projection.from_plane_and_point((point, normal), perspective)
assert P.matrix == [[0.0, 0.0, -1.0, 0.0], [0.0, 0.0, -1.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, -1.0, 0.0]]
def test_projection_parallel():
point = [0, 0, 0]
normal = [0, 0, 1]
direction = [1, 1, 1]
P = Projection.from_plane_and_direction((point, normal), direction)
assert P.matrix == [[1.0, 0.0, -1.0, 0.0], [0.0, 1.0, -1.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 1.0]]
from compas_rhino.artists import MeshArtist from compas.datastructures import Mesh # Define a Frame, which is not in the origin and a bit tilted to the world frame frame = Frame([4, 4, 4], [.5, 1, 2], [0, 1, 2]) # Create a Box with that frame width, length, height = 1, 1, 1 box = Box(frame, width, length, height) # Create a Projection (can be orthogonal, parallel or perspective) point = [0, 0, 0] normal = [0, 0, 1] plane = Plane(point, normal) direction = [1, 1, 1] P = Projection.from_plane_and_direction(plane, direction) # Create a Mesh from the Box mesh = Mesh.from_shape(box) # Apply the Projection onto the mesh mesh_projected = mesh.transformed(P) # Create artists artist1 = BoxArtist(box) artist2 = MeshArtist(mesh_projected) # Draw artist1.draw() artist2.draw_edges(color="#00ff00")
print("Translation:\n", T)
#create concantinated transformation of Frame
X1 = R * T
F.transform(X1)
print(F)
"""
CREATE BOX AND PROJECTION
"""
width, length, height = 1, 1, 8
box = Box(F, width, length, height)
#create projection
projection_plane = Plane([0, 0, 0], [0, 0, 1]) #world XY plane
P = Projection.from_plane(projection_plane) #orthogonal projection
print("Projection:\n", P)
"""
CREATE PROJECTED MESH
"""
mesh_01 = Mesh.from_shape(box)
projected_mesh = mesh_01
try:
projected_mesh.transform(P)
except:
print("Something went wrong with the projection")
"""
ARTISTS
"""
from compas.geometry import Box from compas.geometry import Frame from compas.geometry import Projection, Plane, Vector from compas_rhino.artists import BoxArtist from compas_rhino.artists import MeshArtist from compas.datastructures import Mesh # Define a Frame, which is not in the origin and a bit tilted to the world frame frame_1 = Frame([7, 7, 7], [0.5, 1, 0], [1, 0, 0.5]) # Create a Box with that frame box_1 = Box(frame_1, 1, 2, 3) # Create a Projection transformation (can be orthogonal, parallel or perspective) plane_1 = Plane([0, 0, 0], [0, 0, 1]) P = Projection.from_plane_and_point(plane_1, (10, 10, 10)) # Create a Mesh from the Box mesh = Mesh.from_shape(box_1) # Apply the Projection onto the mesh mesh_projected = mesh.transformed(P) # Create artists artist1 = BoxArtist(box_1) artist2 = MeshArtist(mesh_projected) # Draw artist1.draw() artist2.draw_edges(color="#00ff00")
frame = Frame.from_euler_angles([0.5, 1., 0.2]) translation_vector = [5, 3, 1] T = Translation.from_vector(translation_vector) # move frame from origin frame.transform(T) # Create a Box with that frame width, length, height = 1, 1, 1 box = Box(frame, width, length, height) # Create a Projection (can be orthogonal, parallel or perspective) point = [0, 0, 0] normal = [0, 0, 1] plane = Plane(point, normal) # An orthogonal projection transformation P = Projection.from_plane(plane) # Create a Mesh from the Box mesh = Mesh.from_shape(box) # Apply the Projection onto the mesh mesh_projected = Mesh.transformed(mesh, P) # Create artists artist1 = BoxArtist(box) artist2 = MeshArtist(mesh_projected) # Draw artist1.draw() artist2.draw_edges(color="#00ff00")
from compas.geometry import Scale
from compas.geometry import Reflection
from compas.geometry import Projection
from compas.geometry import Shear
axis, angle = [0.2, 0.4, 0.1], 0.3
R = Rotation.from_axis_and_angle(axis, angle)
print("Rotation:\n", R)
translation_vector = [5, 3, 1]
T = Translation.from_vector(translation_vector)
print("Translation:\n", T)
scale_factors = [0.1, 0.3, 0.4]
S = Scale.from_factors(scale_factors)
print("Scale:\n", S)
point, normal = [0.3, 0.2, 1], [0.3, 0.1, 1]
R = Reflection.from_plane((point, normal))
print("Reflection:\n", R)
point, normal = [0, 0, 0], [0, 0, 1]
perspective = [1, 1, 0]
P = Projection.from_plane_and_point((point, normal), perspective)
print("Perspective projection:\n", R)
angle, direction = 0.1, [0.1, 0.2, 0.3]
point, normal = [4, 3, 1], [-0.11, 0.31, -0.17]
S = Shear.from_angle_direction_plane(angle, direction, (point, normal))
print("Shear:\n", S)
""" from compas.geometry import Box from compas.geometry import Frame from compas.geometry import Projection from compas_rhino.artists import BoxArtist from compas_rhino.artists import MeshArtist from compas.datastructures import Mesh # Define a Frame, which is not in the origin and a bit tilted to the world frame frame = Frame([1, 2, 3], [-4, 5, 6], [7, 8, 9]) # Create a Box with that frame box = Box(frame, 3, 4, 5) # Create a Projection (can be orthogonal, parallel or perspective) point, normal = [0, 0, 0], [0, 0, 1] P = Projection.from_plane((point, normal)) # Create a Mesh from the Box mesh = Mesh.from_shape(box) # Apply the Projection onto the mesh mesh_projected = mesh.transformed(P) # Create artists artist1 = BoxArtist(box) artist2 = MeshArtist(mesh_projected) # Draw artist1.draw() artist2.draw_edges(color="#ff0000")
# Box in the world coordinate system frame = Frame([1, 0, 0], [-0.45, 0.1, 0.3], [1, 0, 0]) width, length, height = 1, 1, 1 box = Box(frame, width, length, height) # Frame F representing a coordinate system F = Frame([2, 2, 2], [0.978, 0.010, -0.210], [0.090, 0.882, 0.463]) # Get transformation between frames and apply transformation on box. T = Transformation.from_frame_to_frame(Frame.worldXY(), F) box_transformed = box.transformed(T) # make Mesh from box mesh_transformed = Mesh.from_shape(box_transformed) # create Projection P = Projection.from_plane_and_direction(Plane((0, 0, 0), (0, 0, 1)), (3, 5, 5)) P = Projection.from_plane(Plane((0, 0, 0), (0, 0, 1))) P = Projection.from_plane_and_point(Plane((0, 0, 0), (0, 0, 1)), (3, 5, 5)) # apply transformation on mesh mesh_projected = mesh_transformed.transformed(P) # create artists artist1 = BoxArtist(box_transformed) artist2 = MeshArtist(mesh_projected) # draw artist1.draw() artist2.draw()
frame = Frame((
1,
0,
0,
), (1, 0, 0), (0, 1, 0))
# Create a Box with that frame
box = Box(frame, 0.3, 0.3, 0.3)
# Create a Projection (can be orthogonal, parallel or perspective)
point = [0, 0, 0]
normal = [0, 0, 1]
XYplane = Plane(point, normal)
direction = [1, 1, 1]
P = Projection.from_plane_and_direction(XYplane, normal)
# Create a Mesh from the Box
mesh = Mesh.from_shape(box)
# Apply the Projection onto the mesh
mesh_projected = mesh.projected(P)
# Create artists
artist1 = BoxArtist(box)
artist2 = MeshArtist(mesh_projected)
# Draw
artist1.draw()
artist2.draw_edges(color="#00ff00")
from compas.geometry import Scale
from compas.geometry import Reflection
from compas.geometry import Projection
from compas.geometry import Shear
axis, angle = [0.2, 0.4, 0.1], 0.3
R = Rotation.from_axis_and_angle(axis, angle)
print("Rotation:\n", R)
translation_vector = [5, 3, 1]
T = Translation(translation_vector)
print("Translation:\n", T)
scale_factors = [0.1, 0.3, 0.4]
S = Scale(scale_factors)
print("Scale:\n", S)
point, normal = [0.3, 0.2, 1], [0.3, 0.1, 1]
R = Reflection(point, normal)
print("Reflection:\n", R)
point, normal = [0, 0, 0], [0, 0, 1]
perspective = [1, 1, 0]
P = Projection.perspective(point, normal, perspective)
print("Perspective projection:\n", R)
angle, direction = 0.1, [0.1, 0.2, 0.3]
point, normal = [4, 3, 1], [-0.11, 0.31, -0.17]
S = Shear(angle, direction, point, normal)
print("Shear:\n", S)
"""Assignment 01: Project box to xy-plane """ from compas.geometry import Box from compas.geometry import Frame, Plane from compas.geometry import Projection from compas_rhino.artists import BoxArtist from compas_rhino.artists import MeshArtist from compas.datastructures import Mesh # Define a Frame, which is not in the origin and a bit tilted to the world frame frame = Frame([1, 2, 3], [-0.45, 0.1, 0.3], [1, 2, 1]) # Create a Box with that frame box = Box(frame, 2, 3, 5) # Create a Projection (can be orthogonal, parallel or perspective) P = Projection.from_plane(Plane([0, 0, 0], [0, 0, 1])) # Create a Mesh from the Box mesh = Mesh.from_shape(box) # Apply the Projection onto the mesh mesh_projected = mesh.transformed(P) # Create artists artist1 = BoxArtist(box) artist2 = MeshArtist(mesh_projected) # Draw artist1.draw() artist2.draw_edges(color="#00ff00")