def rotate_leaves_for_face_rec(ags_net, gtopt_net, plygn, plyln):
"""
rotates the leaves of the gtopt_net and adds them to ags_net to facilitate face recognition.
"""
ags_net_rot=gtopt_net.copy()
leaf_pair_dic=leaf_pair_dict(ags_net)
for key, pair in leaf_pair_dic.items():
coor_key=ags_net.node_coordinates(pair[0][0]) # the common coordinate
if len(pair)>1: # if they are two pairs (sup/load) at one node
coor_12=ags_net.node_coordinates(pair[0][1])
coor_22=ags_net.node_coordinates(pair[1][1])
plyln_bln_1=is_point_on_polyline(coor_12, plyln.points, tol=0.1)
plyln_bln_2=is_point_on_polyline(coor_22, plyln.points, tol=0.1)
if plyln_bln_1 or plyln_bln_2: # the case when one is on polyline
if plyln_bln_1:
key_g=pair[0][1]
key_o=pair[1][1]
coor_g=coor_12
coor_o=coor_22
elif plyln_bln_2:
key_g=pair[1][1]
key_o=pair[0][1]
coor_g=coor_22
coor_o=coor_12
add_vec=add_vectors(vector_create(coor_o, coor_key).tolist(), vector_create(coor_g, coor_key).tolist())
add_pt=subtract_vectors(coor_key, add_vec) # bcs the origin is the key_coor
ags_net_rot.add_node(key_g, {'x': add_pt[0], 'y': add_pt[1], 'z': add_pt[2]})
ags_net_rot.add_node(key_o, {'x': coor_o[0], 'y': coor_o[1], 'z': coor_o[2]})
ags_net_rot.add_edge(key, key_g)
ags_net_rot.add_edge(key, key_o)
else: # the case when both are not on polyline
ags_net_rot.add_node(pair[0][1], {'x': coor_12[0], 'y': coor_12[1], 'z': coor_12[2]})
ags_net_rot.add_node(pair[1][1], {'x': coor_22[0], 'y': coor_22[1], 'z': coor_22[2]})
ags_net_rot.add_edge(key, pair[0][1])
ags_net_rot.add_edge(key, pair[1][1])
else: # for single leaf
coor_12=ags_net.node_coordinates(pair[0][1])
plyln_bln=is_point_on_polyline(coor_12, plyln.points, tol=0.1)
if plyln_bln:
uv=unit_vector(vector_create(coor_key, coor_12))
if uv[0]-0.0<0.01: # x=0
coor_g=add_vectors(coor_12, (1.0, 0.0, 0.0))
plygn_bln=is_point_in_polygon_xy(coor_g, plygn.points)
if plygn_bln:
coor_g=add_vectors(coor_12, (-1.0, 0.0, 0.0))
elif uv[1]-0.0<0.01: # y=0
coor_g=add_vectors(coor_12, (0.0, 1.0, 0.0))
plygn_bln=is_point_in_polygon_xy(coor_12, plygn.points)
if plygn_bln:
coor_g=add_vectors(coor_g, (0.0,-1.0, 0.0))
ags_net_rot.add_node(pair[0][1], {'x': coor_g[0], 'y': coor_g[1], 'z': coor_g[2]})
ags_net_rot.add_edge(key, pair[0][1])
else: # when already in the correct position
ags_net_rot.add_node(pair[0][1], {'x': coor_12[0], 'y': coor_12[1], 'z': coor_12[2]})
ags_net_rot.add_edge(key, pair[0][1])
# plot_network(ags_net_rot)
return ags_net_rot
def add_vertex_edge_for_load_support(network, sup_dic, load_dic, bars_len, key_removed_dic):
"""
Post-Processing Function:
Adds vertices and edges in accordance with supports and loads
returns the cured network
"""
if not key_removed_dic:
load_sup_dic=merge_two_dicts(sup_dic, load_dic)
else:
load_dic_2=load_dic.copy()
for key in key_removed_dic:
load_dic_2.pop(key)
load_dic_2=merge_two_dicts(load_dic_2, key_removed_dic[key])
load_sup_dic=merge_two_dicts(sup_dic, load_dic_2)
# define arbitrary r to be added to get leaf vertex coordinates
max_len=max(bars_len)
r=max_len/3.0
# make a polygon and polyline from outer vertices of network
points = network.to_points()
cycles = network_find_cycles(network)
mesh = Mesh.from_vertices_and_faces(points, cycles)
if 0 in mesh.face and len(mesh.face)>1:
mesh.delete_face(0)
if len(mesh.face)==1:
ver_lis=[key for key in mesh.vertices()]
else:
ver_lis=mesh.vertices_on_boundary(ordered=True)
ver_lis_plyln=ver_lis[:]
ver_lis_plyln.append(ver_lis[0])
pt_lis_plygn=[mesh.vertex_coordinates(key) for key in ver_lis]
pt_lis_plyln=[mesh.vertex_coordinates(key) for key in ver_lis_plyln]
plygn=Polygon(pt_lis_plygn)
plyln=Polyline(pt_lis_plyln)
# add leaf vertices
for key in load_sup_dic:
if load_sup_dic[key][0]!=0.0:
pt_1=add_vectors(network.node_coordinates(key), (+r, 0.0, 0.0))
plyln_bln=is_point_on_polyline(pt_1, plyln.points, tol=0.001)
plygn_bln=is_point_in_polygon_xy(pt_1, plygn.points)
if plyln_bln or plygn_bln:
pt_1=add_vectors(network.node_coordinates(key), (-r, 0.0, 0.0))
key_2=network.add_node(x=np.asscalar(pt_1[0]), y=pt_1[1], z=0.0)
network.add_edge(key, key_2)
if load_sup_dic[key][1]!=0.0:
pt_2=add_vectors(network.node_coordinates(key), (0.0,+r, 0.0))
plyln_bln=is_point_on_polyline(pt_2, plyln.points, tol=0.001)
plygn_bln=is_point_in_polygon_xy(pt_2, plygn.points)
if plyln_bln or plygn_bln:
pt_2=add_vectors(network.node_coordinates(key), (0.0,-r, 0.0))
key_2=network.add_node(x=pt_2[0], y=np.asscalar(pt_2[1]), z=0.0)
network.add_edge(key, key_2)
return network, plygn, plyln
def boundary_triangulation(outer_boundary, inner_boundaries, polyline_features = [], point_features = [], src='numpy_rpc'):
"""Generate Delaunay triangulation between a planar outer boundary and planar inner boundaries. All vertices lie the boundaries.
Parameters
----------
outer_boundary : list
Planar outer boundary as list of vertex coordinates.
inner_boundaries : list
List of planar inner boundaries as lists of vertex coordinates.
polyline_features : list
List of planar polyline_features as lists of vertex coordinates.
point_features : list
List of planar point_features as lists of vertex coordinates.
src : str
Source of Delaunay triangulation. Default is NumPy via RPC.
Returns
-------
delaunay_mesh : Mesh
The Delaunay mesh.
"""
# generate planar Delaunay triangulation
vertices = [pt for boundary in [outer_boundary] + inner_boundaries + polyline_features for pt in boundary] + point_features
if src == 'numpy_rpc':
faces = delaunay_numpy_rpc(vertices)
elif src == 'numpy':
faces = delaunay_numpy(vertices)
else:
delaunay_compas(vertices)
delaunay_mesh = Mesh.from_vertices_and_faces(vertices, faces)
# delete false faces with aligned vertices
for fkey in list(delaunay_mesh.faces()):
a, b, c = [delaunay_mesh.vertex_coordinates(vkey) for vkey in delaunay_mesh.face_vertices(fkey)]
ab = subtract_vectors(b, a)
ac = subtract_vectors(c, a)
if length_vector(cross_vectors(ab, ac)) == 0:
delaunay_mesh.delete_face(fkey)
# delete faces outisde the borders
for fkey in list(delaunay_mesh.faces()):
centre = trimesh_face_circle(delaunay_mesh, fkey)[0]
if not is_point_in_polygon_xy(centre, outer_boundary) or any([is_point_in_polygon_xy(centre, inner_boundary) for inner_boundary in inner_boundaries]):
delaunay_mesh.delete_face(fkey)
# topological cut along the feature polylines through unwelding
vertex_map = {geometric_key(delaunay_mesh.vertex_coordinates(vkey)): vkey for vkey in delaunay_mesh.vertices()}
edges = [edge for polyline in polyline_features for edge in pairwise([vertex_map[geometric_key(point)] for point in polyline])]
mesh_unweld_edges(delaunay_mesh, edges)
return delaunay_mesh
def in_polygon(self, polygon):
"""Determine if the point lies inside the given polygon.
Parameters
----------
polygon : :class:`compas.geometry.Polygon` or list of points.
The polygon.
Returns
-------
bool
True, if the point lies in the polygon.
False, otherwise.
Examples
--------
>>> from compas.geometry import Polygon
>>> poly = Polygon([Point(0.0, 0.0, 0.0), Point(1.0, 0.0, 0.0), Point(1.0, 1.0, 0.0), Point(0.0, 1.0, 0.0)])
>>> point = Point(0.5, 0.5, 0.0)
>>> point.in_polygon(poly)
True
"""
if is_polygon_convex_xy(polygon):
return is_point_in_convex_polygon_xy(self, polygon)
return is_point_in_polygon_xy(self, polygon)
def get_distance(self, point):
"""
single point distance function
Parameters
----------
point: :class:`compas.geometry.Point`
The point in R<sup>3</sup> space to query for it's distance.
Returns
-------
float
The distance from the query point to the surface of the object.
"""
if not isinstance(point, Point):
point = Point(*point)
point.transform(self.inversetransform)
tp = Point(point[0], point[1], 0)
cp = closest_point_on_polyline_xy(tp, self.polyline)
d = tp.distance_to_point(cp)
if is_point_in_polygon_xy(tp, self.polyline):
d = -1.*d
d = max(d, abs(point.z) - self.height / 2.0)
return d
def in_polygon(self, polygon, convex=None):
"""Determine if the point lies inside the given polygon.
Parameters
----------
polygon : :class:`compas.geometry.Polygon` or list of points.
The polygon.
convex : {None, True, False}, optional
Is the polygon convex.
If ``None``, determine if the polygon is convex.
If ``False``, use the non-convex algorithm.
If ``True``, use the convex algorithm.
Returns
-------
bool
True, if the point lies in the polygon.
False, otherwise.
Examples
--------
>>> from compas.geometry import Polygon
>>> poly = Polygon([Point(0.0, 0.0, 0.0), Point(1.0, 0.0, 0.0), Point(1.0, 1.0, 0.0), Point(0.0, 1.0, 0.0)])
>>> point = Point(0.5, 0.5, 0.0)
>>> point.in_polygon(poly)
True
"""
if convex is None:
convex = is_polygon_convex_xy(polygon)
if convex:
return is_point_in_convex_polygon_xy(self, polygon)
return is_point_in_polygon_xy(self, polygon)
def in_polygon(self, polygon, convex=None):
"""Determine if the point lies inside the given polygon.
Parameters
----------
polygon : sequence[point] | :class:`compas.geometry.Polygon`
The polygon.
convex : Literal[None, True, False], optional
If None, determine if the polygon is convex.
If False, use the non-convex algorithm.
If True, use the convex algorithm.
Returns
-------
bool
True, if the point lies in the polygon.
False, otherwise.
Examples
--------
>>> from compas.geometry import Polygon
>>> poly = Polygon([Point(0.0, 0.0, 0.0), Point(1.0, 0.0, 0.0), Point(1.0, 1.0, 0.0), Point(0.0, 1.0, 0.0)])
>>> point = Point(0.5, 0.5, 0.0)
>>> point.in_polygon(poly)
True
"""
if convex is None:
convex = is_polygon_convex_xy(polygon)
if convex:
return is_point_in_convex_polygon_xy(self, polygon)
return is_point_in_polygon_xy(self, polygon)
def gluepath_creator(int_surf, path_width):
def interval_checker(dimension):
underflow = dimension % path_width
if underflow > 0.2:
no_paths = dimension // path_width + 1
new_path_width = dimension / no_paths
return new_path_width
else:
return path_width
wid_gap = int_surf[1] - int_surf[0]
wid_vec = Vector(wid_gap[0], wid_gap[1], wid_gap[2])
wid = wid_vec.length
wid_vec.unitize()
len_gap = int_surf[2] - int_surf[1]
len_vec = Vector(len_gap[0], len_gap[1], len_gap[2])
len = len_vec.length
len_vec.unitize()
wid_path = interval_checker(wid)
len_path = interval_checker(len)
path_dims = [wid_path, len_path]
path_points = []
iteration = 0
path_unfinished = True
current_pt = int_surf[0] + scale_vector(
wid_vec, wid_path / 2) + scale_vector(len_vec, len_path / 2)
current_vec = len_vec.unitized()
len_left = len - len_path
wid_left = wid - wid_path
dims_left = [len_left, wid_left]
path_points.append(current_pt)
R = Rotation.from_axis_and_angle([0, 0, 1], -math.pi / 2)
while path_unfinished:
current_index = iteration % 2
current_dim = dims_left[current_index]
if iteration > 2:
current_dim -= path_dims[current_index]
dims_left[current_index] = current_dim
if current_dim < path_width * 0.95:
break
current_pt = current_pt + scale_vector(current_vec,
current_dim)
path_points.append(current_pt)
current_vec.transform(R)
current_vec.unitize()
iteration += 1
if not is_point_in_polygon_xy(current_pt, int_surf):
print("Error: Point not in polygon")
return path_points
def get_distance(self, point):
if not isinstance(point, Point):
point = Point(*point)
m = matrix_from_frame(self.frame)
mi = matrix_inverse(m)
point.transform(mi)
tp = Point(point[0], point[1], 0)
cp = closest_point_on_polyline_xy(tp, self.polyline)
d = tp.distance_to_point(cp)
if is_point_in_polygon_xy(tp, self.polyline):
d = -1. * d
d = max(d, abs(point.z) - self.height / 2.0)
return d
def delaunay_from_points(points, boundary=None, holes=None, tiny=1e-12):
"""Computes the delaunay triangulation for a list of points.
Parameters
----------
points : sequence of tuple
XYZ coordinates of the original points.
boundary : sequence of tuples
list of ordered points describing the outer boundary (optional)
holes : list of sequences of tuples
list of polygons (ordered points describing internal holes (optional)
Returns
-------
list
The faces of the triangulation.
Each face is a triplet of indices referring to the list of point coordinates.
Notes
-----
For more info, see [1]_.
References
----------
.. [1] Sloan, S. W., 1987 *A fast algorithm for constructing Delaunay triangulations in the plane*
Advances in Engineering Software 9(1): 34-55, 1978.
Example
-------
.. plot::
:include-source:
from compas.datastructures import Mesh
from compas.geometry import pointcloud_xy
from compas.geometry import delaunay_from_points
from compas_plotters import MeshPlotter
points = pointcloud_xy(20, (0, 50))
faces = delaunay_from_points(points)
delaunay = Mesh.from_vertices_and_faces(points, faces)
plotter = MeshPlotter(delaunay)
plotter.draw_vertices(radius=0.1)
plotter.draw_faces()
plotter.show()
"""
from compas.datastructures import Mesh
from compas.datastructures import trimesh_swap_edge
def super_triangle(coords):
centpt = centroid_points(coords)
bbpts = bounding_box(coords)
dis = distance_point_point(bbpts[0], bbpts[2])
dis = dis * 300
v1 = (0 * dis, 2 * dis, 0)
v2 = (1.73205 * dis, -1.0000000000001 * dis, 0) # due to numerical issues
v3 = (-1.73205 * dis, -1 * dis, 0)
pt1 = add_vectors(centpt, v1)
pt2 = add_vectors(centpt, v2)
pt3 = add_vectors(centpt, v3)
return pt1, pt2, pt3
mesh = Mesh()
# to avoid numerical issues for perfectly structured point sets
points = [(point[0] + random.uniform(-tiny, tiny), point[1] + random.uniform(-tiny, tiny), 0.0) for point in points]
# create super triangle
pt1, pt2, pt3 = super_triangle(points)
# add super triangle vertices to mesh
n = len(points)
super_keys = n, n + 1, n + 2
mesh.add_vertex(super_keys[0], {'x': pt1[0], 'y': pt1[1], 'z': pt1[2]})
mesh.add_vertex(super_keys[1], {'x': pt2[0], 'y': pt2[1], 'z': pt2[2]})
mesh.add_vertex(super_keys[2], {'x': pt3[0], 'y': pt3[1], 'z': pt3[2]})
mesh.add_face(super_keys)
# iterate over points
for i, pt in enumerate(points):
key = i
# newtris should be intialised here
# check in which triangle this point falls
for fkey in list(mesh.faces()):
# abc = mesh.face_coordinates(fkey) #This is slower
# This is faster:
keya, keyb, keyc = mesh.face_vertices(fkey)
dicta = mesh.vertex[keya]
dictb = mesh.vertex[keyb]
dictc = mesh.vertex[keyc]
a = [dicta['x'], dicta['y']]
b = [dictb['x'], dictb['y']]
c = [dictc['x'], dictc['y']]
if is_point_in_triangle_xy(pt, [a, b, c], True):
# generate 3 new triangles (faces) and delete surrounding triangle
key, newtris = mesh.insert_vertex(fkey, key=key, xyz=pt, return_fkeys=True)
break
while newtris:
fkey = newtris.pop()
# get opposite_face
keys = mesh.face_vertices(fkey)
s = list(set(keys) - set([key]))
u, v = s[0], s[1]
fkey1 = mesh.halfedge[u][v]
if fkey1 != fkey:
fkey_op, u, v = fkey1, u, v
else:
fkey_op, u, v = mesh.halfedge[v][u], u, v
if fkey_op:
keya, keyb, keyc = mesh.face_vertices(fkey_op)
dicta = mesh.vertex[keya]
a = [dicta['x'], dicta['y']]
dictb = mesh.vertex[keyb]
b = [dictb['x'], dictb['y']]
dictc = mesh.vertex[keyc]
c = [dictc['x'], dictc['y']]
circle = circle_from_points_xy(a, b, c)
if is_point_in_circle_xy(pt, circle):
fkey, fkey_op = trimesh_swap_edge(mesh, u, v)
newtris.append(fkey)
newtris.append(fkey_op)
# Delete faces adjacent to supertriangle
for key in super_keys:
mesh.delete_vertex(key)
# Delete faces outside of boundary
if boundary:
for fkey in list(mesh.faces()):
centroid = mesh.face_centroid(fkey)
if not is_point_in_polygon_xy(centroid, boundary):
mesh.delete_face(fkey)
# Delete faces inside of inside boundaries
if holes:
for polygon in holes:
for fkey in list(mesh.faces()):
centroid = mesh.face_centroid(fkey)
if is_point_in_polygon_xy(centroid, polygon):
mesh.delete_face(fkey)
return [mesh.face_vertices(fkey) for fkey in mesh.faces()]
#process holes/openings
if not crvs_openings: crvs_openings = []
#divide curves per hole based on target length
crvs_openings_pts = [
rs.DivideCurve(crv, max(rs.CurveLength(crv) / trg_length, 3))
for crv in crvs_openings
]
#check which holes are inside which face / assign holes to faces
for fkey, attr in mesh.faces(True):
polygon = attr['polygon']
holes = []
for crvs_opening_pts in crvs_openings_pts:
if is_point_in_polygon_xy(crvs_opening_pts[0], polygon):
holes.append(crvs_opening_pts)
# could be more efficient since holes already
# assigned to another face are checked again
attr['hole_polygons'] = holes
#create triangular mesh for each face
delaunay_meshes = []
count = 1
for fkey, attr in mesh.faces(True):
polygon = attr['polygon']
holes = attr['hole_polygons']
#create flat list of all points
points = polygon + [item for hole in holes for item in hole]
#compute initial delaunay mesh based on all points for the current face
def delaunay_from_points(points, boundary=None, holes=None, tiny=1e-12):
"""Computes the delaunay triangulation for a list of points.
Parameters
----------
points : sequence[[float, float, float] | :class:`compas.geometry.Point`]
XYZ coordinates of the original points.
boundary : sequence[[float, float, float] | :class:`compas.geometry.Point`] | :class:`compas.geometry.Polygon`, optional
List of ordered points describing the outer boundary.
holes : sequence[sequence[[float, float, float] | :class:`compas.geometry.Point`] | :class:`compas.geometry.Polygon`], optional
List of polygons (ordered points describing internal holes.
Returns
-------
list[[int, int, int]]
The faces of the triangulation.
Each face is a triplet of indices referring to the list of point coordinates.
Notes
-----
For more info, see [1]_.
References
----------
.. [1] Sloan, S. W., 1987 *A fast algorithm for constructing Delaunay triangulations in the plane*
Advances in Engineering Software 9(1): 34-55, 1978.
Examples
--------
>>>
"""
from compas.datastructures import Mesh
from compas.datastructures import trimesh_swap_edge
def super_triangle(coords, ccw=True):
centpt = centroid_points(coords)
bbpts = bounding_box(coords)
dis = distance_point_point(bbpts[0], bbpts[2])
dis = dis * 300
v1 = (0 * dis, 2 * dis, 0)
v2 = (1.73205 * dis, -1.0000000000001 * dis, 0
) # due to numerical issues
v3 = (-1.73205 * dis, -1 * dis, 0)
pt1 = add_vectors(centpt, v1)
pt2 = add_vectors(centpt, v2)
pt3 = add_vectors(centpt, v3)
if ccw:
return pt1, pt3, pt2
return pt1, pt2, pt3
mesh = Mesh()
# to avoid numerical issues for perfectly structured point sets
points = [(point[0] + random.uniform(-tiny, tiny),
point[1] + random.uniform(-tiny, tiny), 0.0)
for point in points]
# create super triangle
pt1, pt2, pt3 = super_triangle(points)
# add super triangle vertices to mesh
n = len(points)
super_keys = n, n + 1, n + 2
mesh.add_vertex(super_keys[0], {'x': pt1[0], 'y': pt1[1], 'z': pt1[2]})
mesh.add_vertex(super_keys[1], {'x': pt2[0], 'y': pt2[1], 'z': pt2[2]})
mesh.add_vertex(super_keys[2], {'x': pt3[0], 'y': pt3[1], 'z': pt3[2]})
mesh.add_face(super_keys)
# iterate over points
for key, point in enumerate(points):
# newtris should be intialised here
# check in which triangle this point falls
for fkey in list(mesh.faces()):
abc = mesh.face_coordinates(fkey)
if is_point_in_triangle_xy(point, abc, True):
# generate 3 new triangles (faces) and delete surrounding triangle
key, newtris = mesh.insert_vertex(fkey,
key=key,
xyz=point,
return_fkeys=True)
break
while newtris:
fkey = newtris.pop()
face = mesh.face_vertices(fkey)
i = face.index(key)
u = face[i - 2]
v = face[i - 1]
nbr = mesh.halfedge[v][u]
if nbr is not None:
a, b, c = mesh.face_coordinates(nbr)
circle = circle_from_points_xy(a, b, c)
if is_point_in_circle_xy(point, circle):
fkey, nbr = trimesh_swap_edge(mesh, u, v)
newtris.append(fkey)
newtris.append(nbr)
# Delete faces adjacent to supertriangle
for key in super_keys:
mesh.delete_vertex(key)
# Delete faces outside of boundary
if boundary:
for fkey in list(mesh.faces()):
centroid = mesh.face_centroid(fkey)
if not is_point_in_polygon_xy(centroid, boundary):
mesh.delete_face(fkey)
# Delete faces inside of inside boundaries
if holes:
for polygon in holes:
for fkey in list(mesh.faces()):
centroid = mesh.face_centroid(fkey)
if is_point_in_polygon_xy(centroid, polygon):
mesh.delete_face(fkey)
return [mesh.face_vertices(fkey) for fkey in mesh.faces()]
plotter.zoom_extents()
plotter.pause(1)
# move points in the direction of the randomly assigned translation vectors
# bounce the points of the walls of the box
# color points red when they paas through the polygon
for _ in range(100):
for i in range(N):
T = transformations[i]
a = cloud[i]
b = a.transformed(T)
artist = plotter.find(a)
for side in box.lines:
x = intersection_segment_segment_xy((a, b), side)
if x:
x1 = Point(*x)
x2 = Point(* mirror_points_line_xy([x1 + (b - a)], side)[0])
T = Translation.from_vector(x2 - x1)
transformations[i] = T
break
a.transform(T)
artist.facecolor = (1, 0, 0) if is_point_in_polygon_xy(a, polygon) else (1, 1, 1)
# redraw the plotter view with a specific timeout
plotter.redraw(pause=0.1)
# keep the window alive after completion of the script
plotter.show()
def mesh_delaunay_from_points(points, polygon=None, polygons=None):
"""Computes the delaunay triangulation for a list of points.
Parameters:
points (sequence of tuple): XYZ coordinates of the original points.
polygon (sequence of tuples): list of ordered points describing the outer boundary (optional)
polygons (list of sequences of tuples): list of polygons (ordered points describing internal holes (optional)
Returns:
list of lists: list of faces (face = list of vertex indices as integers)
References:
Sloan, S. W. (1987) A fast algorithm for constructing Delaunay triangulations in the plane
Example:
.. plot::
:include-source:
import compas
from compas.datastructures.mesh import Mesh
from compas.visualization.plotters import MeshPlotter
from compas.datastructures.mesh.algorithms import mesh_delaunay_from_points
mesh = Mesh.from_obj(compas.get_data('faces.obj'))
vertices = [mesh.vertex_coordinates(key) for key in mesh]
faces = mesh_delaunay_from_points(vertices)
delaunay = Mesh.from_vertices_and_faces(vertices, faces)
plotter = MeshPlotter(delaunay)
plotter.draw_vertices(radius=0.1)
plotter.draw_faces()
plotter.show()
"""
def super_triangle(coords):
centpt = centroid_points(coords)
bbpts = bounding_box(coords)
dis = distance_point_point(bbpts[0], bbpts[2])
dis = dis * 300
v1 = (0 * dis, 2 * dis, 0)
v2 = (1.73205 * dis, -1.0000000000001 * dis, 0
) # due to numerical issues
v3 = (-1.73205 * dis, -1 * dis, 0)
pt1 = add_vectors(centpt, v1)
pt2 = add_vectors(centpt, v2)
pt3 = add_vectors(centpt, v3)
return pt1, pt2, pt3
mesh = Mesh()
# to avoid numerical issues for perfectly structured point sets
tiny = 1e-8
pts = [(point[0] + random.uniform(-tiny, tiny),
point[1] + random.uniform(-tiny, tiny), 0.0) for point in points]
# create super triangle
pt1, pt2, pt3 = super_triangle(points)
# add super triangle vertices to mesh
n = len(points)
super_keys = n, n + 1, n + 2
mesh.add_vertex(super_keys[0], {'x': pt1[0], 'y': pt1[1], 'z': pt1[2]})
mesh.add_vertex(super_keys[1], {'x': pt2[0], 'y': pt2[1], 'z': pt2[2]})
mesh.add_vertex(super_keys[2], {'x': pt3[0], 'y': pt3[1], 'z': pt3[2]})
mesh.add_face(super_keys)
# iterate over points
for i, pt in enumerate(pts):
key = i
# check in which triangle this point falls
for fkey in list(mesh.faces()):
# abc = mesh.face_coordinates(fkey) #This is slower
# This is faster:
keya, keyb, keyc = mesh.face_vertices(fkey)
dicta = mesh.vertex[keya]
dictb = mesh.vertex[keyb]
dictc = mesh.vertex[keyc]
a = [dicta['x'], dicta['y']]
b = [dictb['x'], dictb['y']]
c = [dictc['x'], dictc['y']]
if is_point_in_triangle_xy(pt, [a, b, c]):
# generate 3 new triangles (faces) and delete surrounding triangle
newtris = mesh.insert_vertex(fkey, key=key, xyz=pt)
break
while newtris:
fkey = newtris.pop()
# get opposite_face
keys = mesh.face_vertices(fkey)
s = list(set(keys) - set([key]))
u, v = s[0], s[1]
fkey1 = mesh.halfedge[u][v]
if fkey1 != fkey:
fkey_op, u, v = fkey1, u, v
else:
fkey_op, u, v = mesh.halfedge[v][u], u, v
if fkey_op:
keya, keyb, keyc = mesh.face_vertices(fkey_op)
dicta = mesh.vertex[keya]
a = [dicta['x'], dicta['y']]
dictb = mesh.vertex[keyb]
b = [dictb['x'], dictb['y']]
dictc = mesh.vertex[keyc]
c = [dictc['x'], dictc['y']]
circle = circle_from_points_xy(a, b, c)
if is_point_in_circle_xy(pt, circle):
fkey, fkey_op = trimesh_swap_edge(mesh, u, v)
newtris.append(fkey)
newtris.append(fkey_op)
# Delete faces adjacent to supertriangle
for key in super_keys:
mesh.remove_vertex(key)
# Delete faces outside of boundary
if polygon:
for fkey in list(mesh.faces()):
cent = mesh.face_centroid(fkey)
if not is_point_in_polygon_xy(cent, polygon):
mesh.delete_face(fkey)
# Delete faces inside of inside boundaries
if polygons:
for polygon in polygons:
for fkey in list(mesh.faces()):
cent = mesh.face_centroid(fkey)
if is_point_in_polygon_xy(cent, polygon):
mesh.delete_face(fkey)
return [[int(key) for key in mesh.face_vertices(fkey, True)]
for fkey in mesh.faces()]