def project_point_line_xy(point, line):
"""Project a point onto a line in the XY plane.
Parameters
----------
point : [float, float, float] | :class:`compas.geometry.Point`
XY(Z) coordinates of the point.
line : [point, point] | :class:`compas.geometry.Line`
Two points defining the projection line.
Returns
-------
[float, float, float]
XYZ coordinates of the projected point, with Z=0.
Notes
-----
For more info, see [1]_.
References
----------
.. [1] Wiki Books. *Linear Algebra/Orthogonal Projection Onto a Line*.
Available at: https://en.wikibooks.org/wiki/Linear_Algebra/Orthogonal_Projection_Onto_a_Line.
"""
a, b = line
ab = subtract_vectors_xy(b, a)
ap = subtract_vectors_xy(point, a)
c = vector_component_xy(ap, ab)
return add_vectors_xy(a, c)
def mirror_point_point_xy(point, mirror):
"""Mirror a point about a point.
Parameters
----------
point : [float, float, float] | :class:`compas.geometry.Point`
XY(Z) coordinates of the point to mirror.
mirror : [float, float, float] | :class:`compas.geometry.Point`
XY(Z) coordinates of the mirror point.
Returns
-------
[float, float, float]
The mirrored point, with Z=0.
"""
return add_vectors_xy(mirror, subtract_vectors_xy(mirror, point))
def mirror_point_point_xy(point, mirror):
"""Mirror a point about a point.
Parameters
----------
point : list of float
XY(Z) coordinates of the point to mirror.
mirror : list of float
XY(Z) coordinates of the mirror point.
Returns
-------
list of float
The mirrored point, with Z=0.
"""
return add_vectors_xy(mirror, subtract_vectors_xy(mirror, point))
def mirror_point_line_xy(point, line):
"""Mirror a point about a line.
Parameters
----------
point : [float, float, float] | :class:`compas.geometry.Point`
XY(Z) coordinates of the point to mirror.
line : [point, point] | :class:`compas.geometry.Line`
Two points defining the line.
XY(Z) coordinates of the two points defining the mirror line.
Returns
-------
[float, float, float]
The mirrored point, with Z=0.
"""
closest = closest_point_on_line_xy(point, line)
return add_vectors_xy(closest, subtract_vectors_xy(closest, point))
def mirror_point_line_xy(point, line):
"""Mirror a point about a line.
Parameters
----------
point : list of float
XY(Z) coordinates of the point to mirror.
line : tuple
Two points defining the line.
XY(Z) coordinates of the two points defining the mirror line.
Returns
-------
list of float
The mirrored point, with Z=0.
"""
closest = closest_point_on_line_xy(point, line)
return add_vectors_xy(closest, subtract_vectors_xy(closest, point))
def intersection_circle_circle_xy(circle1, circle2):
"""Calculates the intersection points of two circles in 2d lying in the XY plane.
Parameters
----------
circle1 : tuple
center, radius of the first circle in the xy plane.
circle2 : tuple
center, radius of the second circle in the xy plane.
Returns
-------
points : list of tuples
the intersection points if there are any
None
if there are no intersection points
"""
p1, r1 = circle1[0], circle1[1]
p2, r2 = circle2[0], circle2[1]
d = length_vector_xy(subtract_vectors_xy(p2, p1))
if d > r1 + r2:
return None
if d < fabs(r1 - r2):
return None
if (d == 0) and (r1 == r2):
return None
a = (r1 * r1 - r2 * r2 + d * d) / (2 * d)
h = (r1 * r1 - a * a)**0.5
cx2 = p1[0] + a * (p2[0] - p1[0]) / d
cy2 = p1[1] + a * (p2[1] - p1[1]) / d
i1 = ((cx2 + h * (p2[1] - p1[1]) / d), (cy2 - h * (p2[0] - p1[0]) / d), 0)
i2 = ((cx2 - h * (p2[1] - p1[1]) / d), (cy2 + h * (p2[0] - p1[0]) / d), 0)
return i1, i2
def intersection_circle_circle_xy(circle1, circle2):
"""Calculates the intersection points of two circles in 2d lying in the XY plane.
Parameters
----------
circle1 : [plane, float] | :class:`compas.geometry.Circle`
Circle defined by a point, with at least XY coordinates, and a radius.
circle2 : [plane, float] | :class:`compas.geometry.Circle`
Circle defined by a point, with at least XY coordinates, and a radius.
Returns
-------
tuple[[float, float, float], [float, float, float]] | None
The intersection points if there are any.
If the circles are tangent to each other, the two intersection points are identical.
None otherwise.
"""
p1, r1 = circle1[0], circle1[1]
p2, r2 = circle2[0], circle2[1]
d = length_vector_xy(subtract_vectors_xy(p2, p1))
if d > r1 + r2:
return None
if d < fabs(r1 - r2):
return None
if (d == 0) and (r1 == r2):
return None
a = (r1 * r1 - r2 * r2 + d * d) / (2 * d)
h = (r1 * r1 - a * a)**0.5
cx2 = p1[0] + a * (p2[0] - p1[0]) / d
cy2 = p1[1] + a * (p2[1] - p1[1]) / d
i1 = ((cx2 + h * (p2[1] - p1[1]) / d), (cy2 - h * (p2[0] - p1[0]) / d), 0)
i2 = ((cx2 - h * (p2[1] - p1[1]) / d), (cy2 + h * (p2[0] - p1[0]) / d), 0)
return i1, i2
def network_embed_in_plane(network, fixed=None, straightline=True):
"""Embed the network in the plane.
Parameters
----------
network : Network
A network object.
fixed : list (None)
Two fixed points.
straightline : bool (True)
Embed using straight lines.
Returns
-------
bool
True if the embedding was successful.
False otherwise.
Raises
------
ImportError
If NetworkX is not installed.
Examples
--------
>>>
"""
try:
import networkx as nx
except ImportError:
print(
"NetworkX is not installed. Get NetworkX at https://networkx.github.io/."
)
raise
x = network.nodes_attribute('x')
y = network.nodes_attribute('y')
xmin, xmax = min(x), max(x)
ymin, ymax = min(y), max(y)
xspan = xmax - xmin
yspan = ymax - ymin
edges = [(u, v) for u, v in network.edges()
if not network.is_leaf(u) and not network.is_leaf(v)]
is_embedded = False
count = 100
while count:
graph = nx.Graph(edges)
pos = nx.spring_layout(graph, iterations=100, scale=max(xspan, yspan))
if not _are_edges_crossed(edges, pos):
is_embedded = True
break
count -= 1
if not is_embedded:
return False
if fixed:
a, b = fixed
p0 = network.node_attributes(a, 'xy')
p1 = network.node_attributes(b, 'xy')
p2 = pos[b]
vec0 = subtract_vectors_xy(p1, p0)
vec1 = subtract_vectors_xy(pos[b], pos[a])
# rotate
angle = angle_vectors_xy(vec0, vec1)
if is_ccw_xy(p0, p1, p2):
angle = 2 * pi - angle
cosa = cos(angle)
sina = sin(angle)
for key in pos:
x, y = pos[key]
pos[key][0] = cosa * x - sina * y
pos[key][1] = sina * x + cosa * y
# scale
l0 = (vec0[0]**2 + vec0[1]**2)**0.5
l1 = (vec1[0]**2 + vec1[1]**2)**0.5
scale = l0 / l1
for key in pos:
pos[key][0] *= scale
pos[key][1] *= scale
# translate
t = subtract_vectors_xy(p0, pos[a])
for key in pos:
pos[key][0] += t[0]
pos[key][1] += t[1]
# update network node coordinates
for key in network.nodes():
if key in pos:
network.node_attributes(key, 'xy', pos[key])
return True
def add_feet(self, segments, feet=2):
""""""
def rotate(point, angle):
x = cos(angle) * point[0] - sin(angle) * point[1]
y = sin(angle) * point[0] + cos(angle) * point[1]
return x, y, 0
def cross_z(ab, ac):
return ab[0] * ac[1] - ab[1] * ac[0]
scale = self.attributes['feet.scale']
alpha = self.attributes['feet.alpha'] * pi / 180
tol = self.attributes['feet.tol']
key_foot = {}
key_xyz = {
key: self.vertex_coordinates(key, 'xyz')
for key in self.vertices()
}
for i, vertices in enumerate(segments):
key = vertices[0]
after = vertices[1]
before = segments[i - 1][-2]
b = key_xyz[before]
o = key_xyz[key]
a = key_xyz[after]
ob = normalize_vector_xy(subtract_vectors_xy(b, o))
oa = normalize_vector_xy(subtract_vectors_xy(a, o))
z = cross_z(ob, oa)
if z > +tol:
r = normalize_vector_xy(add_vectors_xy(oa, ob))
r = [-scale * axis for axis in r]
elif z < -tol:
r = normalize_vector_xy(add_vectors_xy(oa, ob))
r = [+scale * axis for axis in r]
else:
ba = normalize_vector_xy(subtract_vectors_xy(a, b))
r = cross_vectors([0, 0, 1], ba)
r = [+scale * axis for axis in r]
if feet == 1:
x, y, z = add_vectors_xy(o, r)
m = self.add_vertex(x=x,
y=y,
z=o[2],
is_fixed=True,
is_external=True)
key_foot[key] = m
elif feet == 2:
lx, ly, lz = add_vectors_xy(o, rotate(r, +alpha))
rx, ry, rz = add_vectors_xy(o, rotate(r, -alpha))
l = self.add_vertex(x=lx,
y=ly,
z=o[2],
is_fixed=True,
is_external=True)
r = self.add_vertex(x=rx,
y=ry,
z=o[2],
is_fixed=True,
is_external=True)
key_foot[key] = l, r
else:
pass
for vertices in segments:
l = vertices[0]
r = vertices[-1]
if feet == 1:
lm = key_foot[l]
rm = key_foot[r]
self.add_face([lm] + vertices + [rm], is_loaded=False)
self.set_edge_attribute((l, lm), 'is_external', True)
self.set_edge_attribute((rm, lm), 'is_edge', False)
elif feet == 2:
lb = key_foot[l][0]
la = key_foot[l][1]
rb = key_foot[r][0]
self.add_face([lb, l, la], is_loaded=False)
self.add_face([la] + vertices + [rb], is_loaded=False)
self.set_edge_attribute((l, lb), 'is_external', True)
self.set_edge_attribute((l, la), 'is_external', True)
self.set_edge_attribute((lb, la), 'is_edge', False)
self.set_edge_attribute((la, rb), 'is_edge', False)
else:
pass
