def world_to_local_coords(frame, xyz):
"""Convert global coordinates to local coordinates.
Parameters
----------
frame : :class:`Frame` or [point, xaxis, yaxis]
The local coordinate system.
xyz : array-like
The global coordinates of the points to convert.
Returns
-------
list of list of float
The coordinates of the given points in the local coordinate system.
Examples
--------
>>> import numpy as np
>>> f = Frame([0, 1, 0], [3, 4, 1], [1, 5, 9])
>>> xyz = [Point(2, 3, 5)]
>>> Point(*world_to_local_coords(f, xyz)[0])
Point(3.726, 4.088, 1.550)
"""
from compas.geometry.primitives import Frame
T = matrix_change_basis(Frame.worldXY(), frame)
return transform_points(xyz, T)
def local_to_world_coords(frame, xyz):
"""Convert local coordinates to global coordinates.
Parameters
----------
frame : :class:`Frame` or [point, xaxis, yaxis]
The local coordinate system.
xyz : list of `Points` or list of list of float
The global coordinates of the points to convert.
Returns
-------
list of list of float
The coordinates of the given points in the local coordinate system.
Examples
--------
>>> import numpy as np
>>> f = Frame([0, 1, 0], [3, 4, 1], [1, 5, 9])
>>> xyz = [Point(3.726, 4.088, 1.550)]
>>> Point(*local_to_world_coords(f, xyz)[0])
Point(2.000, 3.000, 5.000)
"""
from compas.geometry.primitives import Frame # noqa: F811
T = matrix_change_basis(frame, Frame.worldXY())
return transform_points(xyz, T)
def to_vertices_and_faces(self, **kwargs):
if 'u' in kwargs:
u = kwargs['u']
else:
u = 10
vertices = []
a = 2 * pi / u
for i in range(u):
x = self.circle.radius * cos(i * a)
y = self.circle.radius * sin(i * a)
z = self.height / 2
vertices.append([x, y, z])
vertices.append([x, y, -z])
# transform vertices to cylinder's plane
frame = Frame.from_plane(self.circle.plane)
M = matrix_from_frame(frame)
vertices = transform_points(vertices, M)
faces = []
for i in range(0, u*2, 2):
faces.append([i, i+1, (i+3)%(u*2), (i+2)%(u*2)])
faces.append([i for i in range(0, u*2, 2)])
faces.append([i for i in range(1, u*2, 2)])
faces[-1].reverse()
return vertices, faces
def to_vertices_and_faces(self, **kwargs):
"""Returns a list of vertices and faces, called by `Mesh.from_shape()`."""
if 'u' in kwargs:
u = kwargs['u']
else:
u = 10
vertices = []
a = 2 * pi / u
for i in range(u):
x = self.circle.radius * cos(i * a)
y = self.circle.radius * sin(i * a)
vertices.append([x, y, 0])
vertices.append([0, 0, self.height])
# transform vertices to cylinder's plane
frame = Frame.from_plane(self.circle.plane)
M = matrix_from_frame(frame)
vertices = transform_points(vertices, M)
faces = []
last = len(vertices) - 1
for i in range(u):
faces.append([i, (i + 1) % u, last])
faces.append([i for i in range(u)])
faces[-1].reverse()
return vertices, faces
def to_vertices_and_faces(self, **kwargs):
"""Returns a list of vertices and faces"""
u = kwargs.get('u') or 10
if u < 3:
raise ValueError('The value for u should be u > 3.')
vertices = []
a = 2 * pi / u
for i in range(u):
x = self.circle.radius * cos(i * a)
y = self.circle.radius * sin(i * a)
z = self.height / 2
vertices.append([x, y, z])
vertices.append([x, y, -z])
# transform vertices to cylinder's plane
frame = Frame.from_plane(self.circle.plane)
M = matrix_from_frame(frame)
vertices = transform_points(vertices, M)
faces = []
for i in range(0, u * 2, 2):
faces.append([i, i + 1, (i + 3) % (u * 2), (i + 2) % (u * 2)])
faces.append([i for i in range(0, u * 2, 2)])
faces.append([i for i in range(1, u * 2, 2)])
faces[-1].reverse()
return vertices, faces
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 test_matrix_from_frame():
f = Frame([1, 1, 1], [0.68, 0.68, 0.27], [-0.67, 0.73, -0.15])
T = matrix_from_frame(f)
t = [[0.6807833515407016, -0.6687681911461376, -0.29880283595731283, 1.0],
[0.6807833515407016, 0.7282315441900513, -0.0788216106888398, 1.0],
[0.2703110366411609, -0.14975955581430114, 0.9510541619236438, 1.0],
[0.0, 0.0, 0.0, 1.0]]
assert np.allclose(T, t)
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 from_bounding_box(cls, bbox):
a = bbox[0]
b = bbox[1]
d = bbox[3]
e = bbox[4]
xaxis = Vector(*subtract_vectors(d, a))
yaxis = Vector(*subtract_vectors(b, a))
zaxis = Vector(*subtract_vectors(e, a))
xsize = xaxis.length
ysize = yaxis.length
zsize = zaxis.length
frame = Frame(a, xaxis, yaxis)
return cls(frame, xsize, ysize, zsize)
def from_bounding_box(cls, bbox):
# this should put the frame at the centroid of the box
# not at the bottom left corner
a = bbox[0]
b = bbox[1]
d = bbox[3]
e = bbox[4]
xaxis = Vector(*subtract_vectors(d, a))
yaxis = Vector(*subtract_vectors(b, a))
zaxis = Vector(*subtract_vectors(e, a))
xsize = xaxis.length
ysize = yaxis.length
zsize = zaxis.length
frame = Frame(a, xaxis, yaxis)
frame.point += frame.xaxis * 0.5 * xsize + frame.yaxis * 0.5 * ysize + frame.zaxis * 0.5 * zsize
return cls(frame, xsize, ysize, zsize)
def from_width_height_depth(cls, width, height, depth):
"""Construct a box from its width, height and depth.
Parameters
----------
width : float
Width of the box.
height : float
Height of the box.
depth : float
Depth of the box.
Returns
-------
Box
The resulting box.
Notes
-----
The bottom left corner of the box is positioned at the origin of the
coordinates system. The box is axis-aligned.
Examples
--------
>>> from compas.geometry import Box
>>> box = Box.from_width_height_depth(1.0, 2.0, 3.0)
"""
width = float(width)
height = float(height)
depth = float(depth)
if width == 0.0:
raise Exception('Width cannot be zero.')
if height == 0.0:
raise Exception('Height cannot be zero.')
if depth == 0.0:
raise Exception('Depth cannot be zero.')
return cls(Frame.worldXY(), width, depth, height)
def from_corner_corner_height(cls, corner1, corner2, height):
"""Construct a box from the opposite corners of its base and its height.
Parameters
----------
corner1 : point
The XYZ coordinates of the bottom left corner of the base of the box.
corner2 : point
The XYZ coordinates of the top right corner of the base of the box.
height : float
The height of the box.
Returns
-------
Box
The resulting box.
Examples
--------
>>> box = Box.from_corner_corner_height([0.0, 0.0, 0.0], [1.0, 1.0, 0.0], 1.0)
"""
# this should put the frame at the centroid of the box
# not at the bottom left corner
if height == 0:
raise Exception('The box should have a height.')
x1, y1, z1 = corner1
x2, y2, z2 = corner2
xaxis = Vector(x2 - x1, 0, 0)
yaxis = Vector(0, y2 - y1, 0)
width = xaxis.length
depth = yaxis.length
if z1 != z2:
raise Exception('Corners should be in the same horizontal plane.')
frame = Frame(corner1, xaxis, yaxis)
frame.point += frame.xaxis * 0.5 * width + frame.yaxis * 0.5 * depth + frame.zaxis * 0.5 * height
return cls(frame, width, depth, height)
def from_data(cls, data):
"""Construct a box from its data representation.
Parameters
----------
data : :obj:`dict`
The data dictionary.
Returns
-------
Box
The constructed box.
Examples
--------
>>> data = {'frame': Frame.worldXY().data, 'xsize': 1.0, 'ysize': 1.0, 'zsize': 1.0}
>>> box = Box.from_data(data)
"""
box = cls(Frame.worldXY(), 1, 1, 1)
box.data = data
return box
def from_diagonal(cls, diagonal):
"""Construct a box from its main diagonal.
Parameters
----------
diagonal : segment
The diagonal of the box, represented by a pair of points in space.
Returns
-------
Box
The resulting box.
Examples
--------
>>> diagonal = [0.0, 0.0, 0.0], [1.0, 1.0, 1.0]
>>> box = Box.from_diagonal(diagonal)
"""
# this should put the frame at the centroid of the box
# not at the bottom left corner
d1, d2 = diagonal
x1, y1, z1 = d1
x2, y2, z2 = d2
if z1 == z2:
raise Exception('The box has no height.')
xaxis = Vector(x2 - x1, 0, 0)
yaxis = Vector(0, y2 - y1, 0)
zaxis = Vector(0, 0, z2 - z1)
width = xaxis.length
depth = yaxis.length
height = zaxis.length
frame = Frame(d1, xaxis, yaxis)
frame.point += frame.xaxis * 0.5 * width + frame.yaxis * 0.5 * depth + frame.zaxis * 0.5 * height
return cls(frame, width, depth, height)
def to_vertices_and_faces(self, **kwargs):
"""Returns a list of vertices and faces"""
u = kwargs.get('u') or 10
v = kwargs.get('v') or 10
if u < 3:
raise ValueError('The value for u should be u > 3.')
if v < 3:
raise ValueError('The value for v should be v > 3.')
theta = pi * 2 / u
phi = pi * 2 / v
vertices = []
for i in range(u):
for j in range(v):
x = cos(i * theta) * (self.radius_axis +
self.radius_pipe * cos(j * phi))
y = sin(i * theta) * (self.radius_axis +
self.radius_pipe * cos(j * phi))
z = self.radius_pipe * sin(j * phi)
vertices.append([x, y, z])
# transform vertices to torus' plane
frame = Frame.from_plane(self.plane)
M = matrix_from_frame(frame)
vertices = transform_points(vertices, M)
faces = []
for i in range(u):
ii = (i + 1) % u
for j in range(v):
jj = (j + 1) % v
a = i * v + j
b = ii * v + j
c = ii * v + jj
d = i * v + jj
faces.append([a, b, c, d])
return vertices, faces
def from_diagonal(cls, diagonal):
"""Construct a box from its main diagonal.
Parameters
----------
diagonal : segment
The diagonal of the box, represented by a pair of points in space.
Returns
-------
Box
The resulting box.
Examples
--------
>>> from compas.geometry import Box
>>> diagonal = [0.0, 0.0, 0.0], [1.0, 1.0, 1.0]
>>> box = Box.from_diagonal(diagonal)
"""
d1, d2 = diagonal
x1, y1, z1 = d1
x2, y2, z2 = d2
if z1 == z2:
raise Exception('The box has no height.')
xaxis = Vector(x2 - x1, 0, 0)
yaxis = Vector(0, y2 - y1, 0)
zaxis = Vector(0, 0, z2 - z1)
width = xaxis.length
depth = yaxis.length
height = zaxis.length
frame = Frame(d1, xaxis, yaxis)
return cls(frame, width, depth, height)
def to_vertices_and_faces(self, **kwargs):
"""Returns a list of vertices and faces, called by `Mesh.from_shape()`."""
if 'u' in kwargs:
u = kwargs['u']
else:
u = 10
if 'v' in kwargs:
v = kwargs['v']
else:
v = 10
theta = pi*2 / u
phi = pi*2 / v
vertices = []
for i in range(u):
for j in range(v):
x = cos(i * theta) * (self.radius_axis + self.radius_pipe * cos(j * phi))
y = sin(i * theta) * (self.radius_axis + self.radius_pipe * cos(j * phi))
z = self.radius_pipe * sin(j * phi)
vertices.append([x, y, z])
# transform vertices to torus' plane
frame = Frame.from_plane(self.plane)
M = matrix_from_frame(frame)
vertices = transform_points(vertices, M)
faces = []
for i in range(u):
ii = (i + 1) % u
for j in range(v):
jj = (j + 1) % v
a = i * v + j
b = ii * v + j
c = ii * v + jj
d = i * v + jj
faces.append([a, b, c, d])
return vertices, faces
def to_vertices_and_faces(self, **kwargs):
"""Returns a list of vertices and faces"""
u = kwargs.get('u') or 10
if u < 3:
raise ValueError('The value for u should be u > 3.')
vertices = []
a = 2 * pi / u
z = self.height / 2
for i in range(u):
x = self.circle.radius * cos(i * a)
y = self.circle.radius * sin(i * a)
vertices.append([x, y, z])
vertices.append([x, y, -z])
# add v in bottom and top's circle center
vertices.append([0, 0, z])
vertices.append([0, 0, -z])
# transform vertices to cylinder's plane
frame = Frame.from_plane(self.circle.plane)
M = matrix_from_frame(frame)
vertices = transform_points(vertices, M)
faces = []
# side faces
for i in range(0, u * 2, 2):
faces.append([i, i + 1, (i + 3) % (u * 2), (i + 2) % (u * 2)])
# top and bottom circle faces
for i in range(0, u * 2, 2):
top = [i, (i + 2) % (u * 2), len(vertices) - 2]
bottom = [i + 1, (i + 3) % (u * 2), len(vertices) - 1]
faces.append(top)
faces.append(bottom[::-1])
return vertices, faces
>>> T = Transformation.from_frame(frame)
>>> circle_transformed = cylinder.transformed(T)
"""
cylinder = self.copy()
cylinder.transform(transformation)
return cylinder
# ==============================================================================
# Main
# ==============================================================================
if __name__ == "__main__":
from compas.geometry import Transformation
cylinder = Cylinder(Circle(Plane.worldXY(), 5), 7)
frame = Frame([1, 1, 1], [0.68, 0.68, 0.27], [-0.67, 0.73, -0.15])
print(frame.normal)
T = Transformation.from_frame(frame)
cylinder.transform(T)
print(cylinder)
print(Plane.worldXY().data)
data = {'circle': Circle(Plane.worldXY(), 5).data, 'height': 7.}
cylinder = Cylinder.from_data(data)
print(cylinder)
import doctest
doctest.testmod()
def frame(self, frame):
self._frame = Frame(frame[0], frame[1], frame[2])
def data(self, data):
self.frame = Frame.from_data(data['frame'])
self.xsize = data['xsize']
self.ysize = data['ysize']
self.zsize = data['zsize']
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()
>>> torus = Torus(Plane.worldXY(), 5, 2)
>>> frame = Frame([1, 1, 1], [0.68, 0.68, 0.27], [-0.67, 0.73, -0.15])
>>> T = Transformation.from_frame(frame)
>>> torus_transformed = torus.transformed(T)
"""
torus = self.copy()
torus.transform(transformation)
return torus
if __name__ == '__main__':
from compas.geometry import Frame
from compas.geometry import Plane
from compas.geometry import Transformation
torus = Torus(Plane.worldXY(), 5, 2)
frame = Frame([5, 0, 0], [0.68, 0.68, 0.27], [-0.67, 0.73, -0.15])
T = Transformation.from_frame(frame)
torus.transform(T)
print(torus)
torus = Torus(Plane.worldXY(), 5, 2)
print(torus.data)
print(torus)
torus = Torus.from_data(torus.data)
print(torus)
import doctest
doctest.testmod()
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