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 translate_points_xy(points, vector):
"""Translate points and in the XY plane.
Parameters
----------
points : sequence[[float, float, float] | :class:`compas.geometry.Point`]
A list of points.
vector : [float, float, float] | :class:`compas.geometry.Vector`
A translation vector.
Returns
-------
list[[float, float, float]]
The translated points in the XY plane (Z=0).
Examples
--------
>>>
"""
return [add_vectors_xy(point, vector) for point in points]
def translate_points_xy(points, vector):
"""Translate points and in the XY plane.
Parameters
----------
points : list of point
A list of points.
vector : vector
A translation vector.
Returns
-------
list of point
The translated points in the XY plane (Z=0).
Examples
--------
>>>
"""
return [add_vectors_xy(point, vector) for point in points]
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
