障碍物周围的质心Voronoi细分
我正在尝试在有边界的矩形空间中实现质心Voronoi细分算法，以使边界矩形中包含许多障碍物（多边形）。
以下代码在没有障碍物（多边形）的情况下在包围盒中给出了质心voronoi镶嵌。蓝色点是生成器，红色点是质心，黄色点是蓝色和红色点之间的中间点。 
import matplotlib.pyplot as pl
import numpy as np
import scipy as sp
import scipy.spatial
import sys
np.random.seed(1)
eps = sys.float_info.epsilon
n_robots = 10
robots = np.random.rand(n_robots, 2)
#print(robots)
bounding_box = np.array([0., 1., 0., 1.])
def in_box(robots, bounding_box):
return np.logical_and(np.logical_and(bounding_box[0] <= robots[:, 0],
robots[:, 0] <= bounding_box[1]),
np.logical_and(bounding_box[2] <= robots[:, 1],
robots[:, 1] <= bounding_box[3]))
def voronoi(robots, bounding_box):
i = in_box(robots, bounding_box)
points_center = robots[i, :]
points_left = np.copy(points_center)
points_left[:, 0] = bounding_box[0] - (points_left[:, 0] - bounding_box[0])
points_right = np.copy(points_center)
points_right[:, 0] = bounding_box[1] + (bounding_box[1] - points_right[:, 0])
points_down = np.copy(points_center)
points_down[:, 1] = bounding_box[2] - (points_down[:, 1] - bounding_box[2])
points_up = np.copy(points_center)
points_up[:, 1] = bounding_box[3] + (bounding_box[3] - points_up[:, 1])
points = np.append(points_center,
np.append(np.append(points_left,
points_right,
axis=0),
np.append(points_down,
points_up,
axis=0),
axis=0),
axis=0)
# Compute Voronoi
vor = sp.spatial.Voronoi(points)
# Filter regions and select corresponding points
regions = []
points_to_filter = [] # we'll need to gather points too
ind = np.arange(points.shape[0])
ind = np.expand_dims(ind,axis= 1)
for i,region in enumerate(vor.regions): # enumerate the regions
if not region: # nicer to skip the empty region altogether
continue
flag = True
for index in region:
if index == -1:
flag = False
break
else:
x = vor.vertices[index, 0]
y = vor.vertices[index, 1]
if not(bounding_box[0] - eps <= x and x <= bounding_box[1] + eps and
bounding_box[2] - eps <= y and y <= bounding_box[3] + eps):
flag = False
break
if flag:
regions.append(region)
# find the point which lies inside
points_to_filter.append(vor.points[vor.point_region == i][0,:])
vor.filtered_points = np.array(points_to_filter)
vor.filtered_regions = regions
return vor
def centroid_region(vertices):
A = 0
C_x = 0
C_y = 0
for i in range(0, len(vertices) - 1):
s = (vertices[i, 0] * vertices[i + 1, 1] - vertices[i + 1, 0] * vertices[i, 1])
A = A + s
C_x = C_x + (vertices[i, 0] + vertices[i + 1, 0]) * s
C_y = C_y + (vertices[i, 1] + vertices[i + 1, 1]) * s
A = 0.5 * A
C_x = (1.0 / (6.0 * A)) * C_x
C_y = (1.0 / (6.0 * A)) * C_y
return np.array([[C_x, C_y]])
def plot(r,index):
vor = voronoi(r, bounding_box)
fig = pl.figure()
ax = fig.gca()
#ax.plot(pol2[:,0],pol2[:,1],'k-')
# Plot initial points
ax.plot(vor.filtered_points[:, 0], vor.filtered_points[:, 1], 'b.')
print("initial",vor.filtered_points)
# Plot ridges points
for region in vor.filtered_regions:
vertices = vor.vertices[region, :]
ax.plot(vertices[:, 0], vertices[:, 1], 'go')
# Plot ridges
for region in vor.filtered_regions:
vertices = vor.vertices[region + [region[0]], :]
ax.plot(vertices[:, 0], vertices[:, 1], 'k-')
# Compute and plot centroids
centroids = []
for region in vor.filtered_regions:
vertices = vor.vertices[region + [region[0]], :]
centroid = centroid_region(vertices)
centroids.append(list(centroid[0, :]))
ax.plot(centroid[:, 0], centroid[:, 1], 'r.')
centroids = np.asarray(centroids)
rob = np.copy(vor.filtered_points)
# the below code is for the plotting purpose the update happens in the update function
interim_x = np.asarray(centroids[:,0] - rob[:,0])
interim_y = np.asarray(centroids[:,1] - rob[:,1])
magn = [np.linalg.norm(centroids[i,:] - rob[i,:]) for i in range(rob.shape[0])]
x = np.copy(interim_x)
x = np.asarray([interim_x[i]/magn[i] for i in range(interim_x.shape[0])])
y = np.copy(interim_y)
y = np.asarray([interim_y[i]/magn[i] for i in range(interim_y.shape[0])])
nor = np.copy(rob)
for i in range(x.shape[0]):
nor[i,0] = x[i]
nor[i,1] = y[i]
temp = np.copy(rob)
temp[:,0] = [rob[i,0] + 0.5*interim_x[i] for i in range(rob.shape[0])]
temp[:,1] = [rob[i,1] + 0.5*interim_y[i] for i in range(rob.shape[0])]
pol = [[]]
ax.plot(temp[:,0] ,temp[:,1], 'y.' )
ax.set_xlim([-0.1, 1.1])
ax.set_ylim([-0.1, 1.1])
pl.savefig("voronoi" + str(index) + ".png")
return centroids
def update(rob,centroids):
interim_x = np.asarray(centroids[:,0] - rob[:,0])
interim_y = np.asarray(centroids[:,1] - rob[:,1])
magn = [np.linalg.norm(centroids[i,:] - rob[i,:]) for i in range(rob.shape[0])]
x = np.copy(interim_x)
x = np.asarray([interim_x[i]/magn[i] for i in range(interim_x.shape[0])])
y = np.copy(interim_y)
y = np.asarray([interim_y[i]/magn[i] for i in range(interim_y.shape[0])])
nor = [np.linalg.norm([x[i],y[i]]) for i in range(x.shape[0])]
temp = np.copy(rob)
temp[:,0] = [rob[i,0] + 0.5*interim_x[i] for i in range(rob.shape[0])]
temp[:,1] = [rob[i,1] + 0.5*interim_y[i] for i in range(rob.shape[0])]
return np.asarray(temp)
if __name__ == '__main__':
for i in range(1):
centroids = plot(robots,i)
robots = update(robots,centroids)
现在，我想将此特殊代码扩展到遇到障碍的情况，即我想做类似
的事情，除了我不想要红色多边形中的任何东西。
我尝试的一种方法是使用不理想的空闲区域来划分空间。 
。
方法一的代码：
import random
from shapely.geometry import Polygon, Point
import numpy as np
import matplotlib.pyplot as pl
def get_random_point_in_polygon(poly,polygons,num):
(minx, miny, maxx, maxy) = poly.bounds
points =[]
while num != 0:
p = Point(random.uniform(minx, maxx), random.uniform(miny, maxy))
if any(poly.contains(p) for poly in polygons):
continue
else:
num = num-1
#print(num)
points.append([p.x,p.y])
return np.asarray(points)
def polysplit(poly,polygons):
(minx, miny, maxx, maxy) = poly.bounds
pols =[]
return pols
def randomRects(p,poly):
(minx, miny, maxx, maxy) = poly.bounds
rect = []
while True:
w = round(random.uniform(0, 1),3)
h = round(random.uniform(0, 1),3)
if (((p[:,0]+w) < maxx) and ((p[:,1]+h) < maxy)):
rect.append(np.squeeze([np.squeeze(p[:,0]),np.squeeze(p[:,1])]))
rect.append(np.squeeze([np.squeeze(p[:,0]+w),np.squeeze(p[:,1])]))
rect.append(np.squeeze([np.squeeze(p[:,0]+w),np.squeeze(p[:,1]+h)]))
rect.append(np.squeeze([np.squeeze(p[:,0]),np.squeeze(p[:,1]+h)]))
rect.append(np.squeeze([np.squeeze(p[:,0]),np.squeeze(p[:,1])]))
break
else:
continue
return np.asarray(rect)
def rect(poly,polygons):
rec =[]
area = poly.area
areas = 0
for i in polygons:
areas = areas+i.area
#print(area - areas)
flag = False
while (area - areas) > 0.4:
p = get_random_point_in_polygon(poly,polygons,1)
#print(p)
rect = randomRects(p,poly)
if any(poly.intersects(Polygon(rect)) for poly in polygons):
continue
#elif any(poly.intersects(Polygon(rect)) for poly in rec):
#continue
else:
if rec == []:
rec.append(Polygon(rect))
print("hi")
elif any(pol.intersects(Polygon(rect)) for pol in rec):
continue
else:
areas = areas+Polygon(rect).area
print(area-areas)
rec.append(Polygon(rect))
return rec
p = Polygon([(0, 0), (1, 0), (1, 1), (0, 1), (0, 0)])
p2 = Polygon([(0, 0), (.2,0), (.2,.2), (0, 0.2), (0,0)])
p3 = Polygon([(0.4, 0.4), (0.8,0.4), (.8,.8), (0.4, 0.8), (0.4,0.4)])
p4 = Polygon([(0.1,0.6),(0.3,.6),(0.3,0.9),(0.1,0.9),(0.1,0.6)])
p5 = Polygon([(0.25,0.25),(0.85,.25),(0.85,0.35),(0.25,0.35),(0.25,0.25)])
polygons = []
polygons.append(p2)
polygons.append(p3)
polygons.append(p4)
polygons.append(p5)
point_in_poly = get_random_point_in_polygon(p,polygons,10000)
fig = pl.figure()
ax = fig.gca()
#ax.plot(point_in_poly[:,0],point_in_poly[:,1],'b.')
area = 0
for po in polygons:
#area = area +po.area
x,y = po.exterior.xy
#print [x,y]
ax.plot(x,y,'r-')
#print(p.area - area)
r = rect(p,polygons)
for rr in r:
#area = area +po.area
x,y = rr.exterior.xy
#print [x,y]
ax.plot(x,y,'b-')
ax.set_xlim([-0.1, 1.1])
ax.set_ylim([-0.1, 1.1])
pl.savefig("test1.png")
第二种方法，我认为是使用二进制空间分区将可用区域划分为矩形，并将上述代码应用于这些可用区域的矩形。但我不确定如何在python中执行此操作。
第三种方法：我使用Python三角形库来计算自由空间的符合约束的Delaunay三角剖分，并尝试将其移植回voronoi图。结果与预期不符。
就是
下面的代码是我尝试过的所有方法的汇编，因此可能很乱。我尝试在Scipy，Triangle库中使用Voronoi函数，还尝试使用自定义方法将三角剖分转换为voronoi。该代码不能很好地工作，并且还存在一些错误。
from numpy import array
import numpy as np
def read_poly(file_name):
"""
Simple poly-file reader, that creates a python dictionary
with information about vertices, edges and holes.
It assumes that vertices have no attributes or boundary markers.
It assumes that edges have no boundary markers.
No regional attributes or area constraints are parsed.
"""
output = {'vertices': None, 'holes': None, 'segments': None}
# open file and store lines in a list
file = open(file_name, 'r')
lines = file.readlines()
file.close()
lines = [x.strip('\n').split() for x in lines]
# Store vertices
vertices= []
N_vertices, dimension, attr, bdry_markers = [int(x) for x in lines[0]]
# We assume attr = bdrt_markers = 0
for k in range(N_vertices):
label, x, y = [items for items in lines[k+1]]
vertices.append([float(x), float(y)])
output['vertices']=array(vertices)
# Store segments
segments = []
N_segments, bdry_markers = [int(x) for x in lines[N_vertices+1]]
for k in range(N_segments):
label, pointer_1, pointer_2 = [items for items in lines[N_vertices+k+2]]
segments.append([int(pointer_1)-1, int(pointer_2)-1])
output['segments'] = array(segments)
# Store holes
N_holes = int(lines[N_segments+N_vertices+2][0])
holes = []
for k in range(N_holes):
label, x, y = [items for items in lines[N_segments + N_vertices + 3 + k]]
holes.append([float(x), float(y)])
output['holes'] = array(holes)
print(holes)
return output
from triangle import triangulate,voronoi, plot as tplot
import matplotlib.pyplot as plt
image = read_poly("/home/pranav/catkin_ws/src/beginner_tutorials/scripts/test.poly")
cncfq20adt = triangulate(image, 'pq20a.01D')
#print(cncfq20adt['vertices'])
#print(cncfq20adt['triangles'])
plt.figure(figsize=(10, 10))
ax = plt.subplot(111, aspect='equal')
tplot.plot(ax, **cncfq20adt)
plt.savefig("image.png")
import triangle
from scipy.spatial import Delaunay
pts = cncfq20adt['vertices']
tri = Delaunay(pts)
p = tri.points[tri.vertices]
#print(pts)
# Triangle vertices
A = p[:,0,:].T
B = p[:,1,:].T
C = p[:,2,:].T
print(C)
# See http://en.wikipedia.org/wiki/Circumscribed_circle#Circumscribed_circles_of_triangles
# The following is just a direct transcription of the formula there
a = A - C
b = B - C
def dot2(u, v):
return u[0]*v[0] + u[1]*v[1]
def cross2(u, v, w):
"""u x (v x w)"""
return dot2(u, w)*v - dot2(u, v)*w
def ncross2(u, v):
"""|| u x v ||^2"""
return sq2(u)*sq2(v) - dot2(u, v)**2
def sq2(u):
return dot2(u, u)
cc = cross2(sq2(a) * b - sq2(b) * a, a, b) / (2*ncross2(a, b)) + C
# Grab the Voronoi edges
vc = cc[:,tri.neighbors]
vc[:,tri.neighbors == -1] = np.nan # edges at infinity, plotting those would need more work...
lines = []
lines.extend(zip(cc.T, vc[:,:,0].T))
lines.extend(zip(cc.T, vc[:,:,1].T))
lines.extend(zip(cc.T, vc[:,:,2].T))
# Plot it
import matplotlib.pyplot as plt
from matplotlib.collections import LineCollection
lines = LineCollection(lines, edgecolor='b')
#plt.hold(1)
plt.plot(pts[:,0], pts[:,1], '.')
plt.plot(cc[0], cc[1], '*')
plt.gca().add_collection(lines)
plt.axis('equal')
plt.xlim(-0.1, 1.1)
plt.ylim(-0.1, 1.1)
plt.savefig("vor2.png")
ax1 = plt.subplot(121, aspect='equal')
triangle.plot.plot(ax1, vertices=pts)
lim = ax1.axis()
points, edges, ray_origin, ray_direct = triangle.voronoi(pts)
d = dict(vertices=points, edges=edges, ray_origins=ray_origin, ray_directions=ray_direct)
ax2 = plt.subplot(111, aspect='equal')
triangle.plot.plot(ax2, **d)
ax2.axis(lim)
plt.savefig("vor.png")
import matplotlib.pyplot as pl
import scipy as sp
import scipy.spatial
import sys
from shapely.geometry import Polygon,Point
import random
np.random.seed(1)
eps = sys.float_info.epsilon
"""
n_robots = 50
#robots = np.random.rand(n_robots, 2)
def get_random_point_in_polygon(poly,polygons,num):
(minx, miny, maxx, maxy) = poly.bounds
points =[]
while num != 0:
p = Point(random.uniform(minx, maxx), random.uniform(miny, maxy))
if any(poly.contains(p) for poly in polygons):
continue
else:
num = num-1
print(num)
points.append([p.x,p.y])
return np.asarray(points)
def polysplit(poly,polygons):
rectangles = []
return rectangles
p = Polygon([(0, 0), (1, 0), (1, 1), (0, 1), (0, 0)])
p2 = Polygon([(0, 0), (.2,0), (.2,.2), (0, 0.2), (0,0)])
p3 = Polygon([(0.4, 0.4), (0.7,0.4), (.7,.7), (0.4, 0.7), (0.4,0.4)])
polygons = []
polygons.append(p2)
polygons.append(p3)
#point_in_poly = get_random_point_in_polygon(p,polygons,10)
robots = get_random_point_in_polygon(p,polygons,n_robots)
#print(sampl)
print(robots)
bounding_box = np.array([0., 1, 0., 1])
box = np.array([0.2, 0.6, 0, 0.6])
box2 = np.array([0, 0.6, 0.2, 0.6])
boxes =[]
boxes.append(box)
boxes.append(box2)
"""
robots = cncfq20adt['vertices']
print("length",len(robots))
bounding_box = np.array([0., 1., 0., 1.])
def in_box(robots, bounding_box):
return np.logical_and(np.logical_and(bounding_box[0] <= robots[:, 0],
robots[:, 0] <= bounding_box[1]),
np.logical_and(bounding_box[2] <= robots[:, 1],
robots[:, 1] <= bounding_box[3]))
def voronoi(robots, bounding_box):
i = in_box(robots, bounding_box)
points_center = robots[i, :]
points_left = np.copy(points_center)
points_left[:, 0] = bounding_box[0] - (points_left[:, 0] - bounding_box[0])
points_right = np.copy(points_center)
points_right[:, 0] = bounding_box[1] + (bounding_box[1] - points_right[:, 0])
points_down = np.copy(points_center)
points_down[:, 1] = bounding_box[2] - (points_down[:, 1] - bounding_box[2])
points_up = np.copy(points_center)
points_up[:, 1] = bounding_box[3] + (bounding_box[3] - points_up[:, 1])
points = np.append(points_center,
np.append(np.append(points_left,
points_right,
axis=0),
np.append(points_down,
points_up,
axis=0),
axis=0),
axis=0)
# Compute Voronoi
vor = sp.spatial.Voronoi(points)
# Filter regions and select corresponding points
regions = []
points_to_filter = [] # we'll need to gather points too
ind = np.arange(points.shape[0])
ind = np.expand_dims(ind,axis= 1)
for i,region in enumerate(vor.regions): # enumerate the regions
if not region: # nicer to skip the empty region altogether
continue
flag = True
for index in region:
if index == -1:
flag = False
break
else:
x = vor.vertices[index, 0]
y = vor.vertices[index, 1]
if not(bounding_box[0] - eps <= x and x <= bounding_box[1] + eps and
bounding_box[2] - eps <= y and y <= bounding_box[3] + eps):
flag = False
break
if flag:
regions.append(region)
# find the point which lies inside
points_to_filter.append(vor.points[vor.point_region == i][0,:])
vor.filtered_points = np.array(points_to_filter)
vor.filtered_regions = regions
return vor
def centroid_region(vertices):
A = 0
C_x = 0
C_y = 0
for i in range(0, len(vertices) - 1):
s = (vertices[i, 0] * vertices[i + 1, 1] - vertices[i + 1, 0] * vertices[i, 1])
A = A + s
C_x = C_x + (vertices[i, 0] + vertices[i + 1, 0]) * s
C_y = C_y + (vertices[i, 1] + vertices[i + 1, 1]) * s
A = 0.5 * A
C_x = (1.0 / (6.0 * A)) * C_x
C_y = (1.0 / (6.0 * A)) * C_y
return np.array([[C_x, C_y]])
def plot(r,index):
vor = voronoi(r, bounding_box)
fig = pl.figure()
ax = fig.gca()
#ax.plot(pol2[:,0],pol2[:,1],'k-')
# Plot initial points
ax.plot(vor.filtered_points[:, 0], vor.filtered_points[:, 1], 'b.')
print("initial",vor.filtered_points)
# Plot ridges points
for region in vor.filtered_regions:
vertices = vor.vertices[region, :]
ax.plot(vertices[:, 0], vertices[:, 1], 'go')
# Plot ridges
for region in vor.filtered_regions:
vertices = vor.vertices[region + [region[0]], :]
ax.plot(vertices[:, 0], vertices[:, 1], 'k-')
# Compute and plot centroids
centroids = []
for region in vor.filtered_regions:
vertices = vor.vertices[region + [region[0]], :]
centroid = centroid_region(vertices)
centroids.append(list(centroid[0, :]))
ax.plot(centroid[:, 0], centroid[:, 1], 'r.')
centroids = np.asarray(centroids)
rob = np.copy(vor.filtered_points)
# the below code is for the plotting purpose the update happens in the update function
interim_x = np.asarray(centroids[:,0] - rob[:,0])
interim_y = np.asarray(centroids[:,1] - rob[:,1])
magn = [np.linalg.norm(centroids[i,:] - rob[i,:]) for i in range(rob.shape[0])]
x = np.copy(interim_x)
x = np.asarray([interim_x[i]/magn[i] for i in range(interim_x.shape[0])])
y = np.copy(interim_y)
y = np.asarray([interim_y[i]/magn[i] for i in range(interim_y.shape[0])])
nor = np.copy(rob)
for i in range(x.shape[0]):
nor[i,0] = x[i]
nor[i,1] = y[i]
temp = np.copy(rob)
temp[:,0] = [rob[i,0] + 0.5*interim_x[i] for i in range(rob.shape[0])]
temp[:,1] = [rob[i,1] + 0.5*interim_y[i] for i in range(rob.shape[0])]
pol = [[]]
ax.plot(temp[:,0] ,temp[:,1], 'y.' )
ax.set_xlim([-0.1, 1.1])
ax.set_ylim([-0.1, 1.1])
pl.savefig("voronoi" + str(index) + ".png")
return centroids
def update(rob,centroids):
interim_x = np.asarray(centroids[:,0] - rob[:,0])
interim_y = np.asarray(centroids[:,1] - rob[:,1])
magn = [np.linalg.norm(centroids[i,:] - rob[i,:]) for i in range(rob.shape[0])]
x = np.copy(interim_x)
x = np.asarray([interim_x[i]/magn[i] for i in range(interim_x.shape[0])])
y = np.copy(interim_y)
y = np.asarray([interim_y[i]/magn[i] for i in range(interim_y.shape[0])])
nor = [np.linalg.norm([x[i],y[i]]) for i in range(x.shape[0])]
temp = np.copy(rob)
temp[:,0] = [rob[i,0] + 0.5*interim_x[i] for i in range(rob.shape[0])]
temp[:,1] = [rob[i,1] + 0.5*interim_y[i] for i in range(rob.shape[0])]
return np.asarray(temp)
if __name__ == '__main__':
for i in range(1):
centroids = plot(robots,i)
robots = update(robots,centroids)
如果有人可以帮助我，我将非常感激。
0 个答案:
没有答案
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