Voronoi泰森多边形应用案例-python
Voronoi泰森多边形应用案例-python
下面代码为Voronoi泰森多边形的应用案例。在下面代码中，我们会对输入的数据集，计算泰森多边形，之后在这个基础上，再对泰森多边形进行分割，之后我们可以通过书输入点，然后直接计算出其在我们分割的那个框里，再次基础上，结合泰森多边形的边界线知识，就可以很快的判断输入点的坐标距离输入数据集那个点最近。
import random
import math
from scipy.spatial import Voronoi, voronoi_plot_2d
import os
from scipy.spatial import cKDTree
import numpy as np
import matplotlib .pyplot as plt
import cv2
from sklearn.datasets import make_classification
x_min = -100
x_max =100
a=-1
b=1
num=10
y_min = -100
y_max =100
divide_num=5
x_lmin = -2
x_lmax =2
y_lmin = -2
y_lmax =2
#判断点是否在框中
def judge_frame(point):
x, y = point[0], point[1]
flag = (x >= x_min and x <= x_max and y >= y_min and y <= y_max)
return flag
# 判断两线段相交
def judge_inter(A, B, C, D):
def vector(piont_1, point_2): # 输入numpy格式
return point_2 - piont_1
def vector_product(vec_1, vec_2): # 计算向量
return vec_1[0] * vec_2[1] - vec_2[0] * vec_1[1]
AC = vector(A, C)
AD = vector(A, D)
BC = vector(B, C)
BD = vector(B, D)
CA = vector(C, A)
CB = vector(C, B)
DA = vector(D, A)
DB = vector(D, B)
# 相交返回true
return (vector_product(AC, AD) * vector_product(BC, BD) <= 0 ) \
and (vector_product(CA, CB) * vector_product(DA, DB) <= 0)
# 判断得出两线段的交点
def intersection(point_1, point_2):
point_bound = [[[x_min, y_min], [x_max, y_min]], [[x_max, y_min], [x_max, y_max]],
[[x_min, y_max], [x_max, y_max]], [[x_min, y_max], [x_min, y_min]]]
for line in point_bound:
if judge_inter(point_1, point_2, line[0], line[1]):
x1, x2, x3, x4 = point_1[0], point_2[0], line[0][0], line[1][0]
y1, y2, y3, y4 = point_1[1], point_2[1], line[0][1], line[1][1]
px = ((x1 * y2 - y1 * x2) * (x3 - x4) - (x1 - x2) * (x3 * y4 - y3 * x4)) / ((x1 - x2) * (y3 - y4) - (y1 - y2) * (x3 - x4))
py = ((x1 * y2 - y1 * x2) * (y3 - y4) - (y1 - y2) * (x3 * y4 - y3 * x4)) / ((x1 - x2) * (y3 - y4) - (y1 - y2) * (x3 - x4))
return [px, py]
# 求射线方程
def ray(barr, piont):
# 计算障碍的中垂线
def medLine(x1, y1, x2, y2):
A = 2 * (x2 - x1)
B = 2 * (y2 - y1)
C = x1 ** 2 - x2 ** 2 + y1 ** 2 - y2 ** 2
return A, B, C
A, B, C = medLine(barr[0][0], barr[0][1], barr[1][0], barr[1][1])
return [A, B, C]
#判断两线段是否相交
def Intersect(l1, l2):
v1 = (l1[0] - l2[0], l1[1] - l2[1])
v2 = (l1[0] - l2[2], l1[1] - l2[3])
v0 = (l1[0] - l1[2], l1[1] - l1[3])
a = v0[0] * v1[1] - v0[1] * v1[0]
b = v0[0] * v2[1] - v0[1] * v2[0]
temp = l1
l1 = l2
l2 = temp
v1 = (l1[0] - l2[0], l1[1] - l2[1])
v2 = (l1[0] - l2[2], l1[1] - l2[3])
v0 = (l1[0] - l1[2], l1[1] - l1[3])
c = v0[0] * v1[1] - v0[1] * v1[0]
d = v0[0] * v2[1] - v0[1] * v2[0]
if a*b < 0 and c*d < 0:
return True
else:
return False
# 判断直线与线段相交并求出交点
def ray_inter_point(ray, point, barr):
point_bound = [[[x_min, y_min], [x_max, y_min]], [[x_max, y_min], [x_max, y_max]],
[[x_min, y_max], [x_max, y_max]], [[x_min, y_max], [x_min, y_min]]]
list_inter = []
for bound in point_bound:
sPoint, ePoint = bound[0], bound[1]
line = [sPoint[1] - ePoint[1], ePoint[0] - sPoint[0], sPoint[0] * ePoint[1] - ePoint[0] * sPoint[1]]
a0, b0, c0 = ray[0], ray[1], ray[2]
a1, b1, c1 = line[0], line[1], line[2]
D = a0 * b1 - a1 * b0
x = (b0 * c1 - b1 * c0) / D
y = (a1 * c0 - a0 * c1) / D
list_inter.append([x, y])
result=[]
for i in list_inter:
result.append(i)
return(result)
path="C:/Users/gaoxi/Desktop/data/input.png"
# 使用 make_classification 创建数据
def save_point(self,vor):
with open('C:/Users/gaoxi/Desktop/data/vor/input_vor.txt','w',encoding='utf-8') as file:
#vor.vertices
for i in vor.vertices:
file.write(str(i[0])+" "+str(i[1])+'\n')
#points=[]
#for i in range(num):
# c=a + (b-a)*np.random.random()
# d=a + (b-a)*np.random.random()
# points.append([c,d])
#points = np.array(points)
points = np.load('C:/Users/gaoxi/Desktop/data/data/pose_det_results_list.npy')
barr_center = points
# 计算Voronoi图
vor = Voronoi(barr_center)
vertices, ridge_vertices = [], []
my_dict={}
new_dict = []
for k,v in vor.ridge_dict.items():
my_dict[str(v[0])+str(v[1])]=k
if -1 in v:
new_dict.append(list(k))
print("my_dict",my_dict)
vers=[]
pots=[]
### l1 [xa, ya, xb, yb] l2 [xa, ya, xb, yb]
#求解voronio线段
for ver_rela in vor.ridge_vertices:
print("ver_rela:",ver_rela)
if -1 in ver_rela:
continue
else:
# 两个都在
if vor.vertices[ver_rela[0]].tolist() not in vertices:
vertices.append(vor.vertices[ver_rela[0]].tolist())
if vor.vertices[ver_rela[1]].tolist() not in vertices:
vertices.append(vor.vertices[ver_rela[1]].tolist())
pots.append(my_dict[str(ver_rela[0])+str(ver_rela[1])])
vers.append([vor.vertices[ver_rela[0]].tolist(),vor.vertices[ver_rela[1]].tolist()])
# 一个都不在
#求解voronio射线
for ver_rela in vor.ridge_vertices:
# print("ver_rela:",ver_rela)
if -1 in ver_rela:
pots.append(my_dict[str(ver_rela[0])+str(ver_rela[1])])
temp = [0, 1]
temp.pop(ver_rela.index(-1))
if judge_frame(vor.vertices[ver_rela[temp[0]]]) or 1:
# 与边界的交点
barr_ind = new_dict.pop(0)
points1=vor.vertices[ver_rela[temp[0]]].tolist()
barr = [vor.points[barr_ind[0]], vor.points[barr_ind[1]]]
f_ray = ray(barr, vor.vertices[ver_rela[temp[0]]]) # 改为直线方程
# print(f_ray)
inter = ray_inter_point(f_ray, vor.vertices[ver_rela[temp[0]]], barr)
points2_list=inter
for i in points2_list:
l1=[points1[0],points1[1],i[0],i[1]]
flag=0
#plt.plot([i[0], points1[0]],
# [i[1], points1[1]],
# color = 'r')
for pointsz in vers:
l2=[pointsz[0][0],pointsz[0][1],pointsz[1][0],pointsz[1][1]]
if Intersect(l1,l2) :
flag=1
break
if flag==0 :
# print("true")
vertices.append(i)
vers.append([points1,i])
break
#print("points1:",points1)
#print("points2:",points2_list)
vertices = np.array(vertices)
ridge_vertices = np.array(ridge_vertices)
#绘图
def test1():
for i in range(num):
plt.annotate(str(i), (vor.points[i][0], vor.points[i][1]), size = 10)
for i in range(len(vor.vertices)):
plt.annotate(str(i), (vor.vertices[i][0], vor.vertices[i][1]), size = 10,color='r')
plt.xlim((-4, 4))
plt.ylim((-4, 4))
plt.scatter(vertices[:, 0], vertices[:, 1])
plt.scatter(points[:, 0], points[:, 1])
for pointsz in vers:
plt.plot([pointsz[0][0], pointsz[1][0]],
[pointsz[0][1], pointsz[1][1]],
color = 'k')
# voronoi_plot_2d(vor)
# print(vers)
#print(pots)
#plt.show()
test1()################################################
x_list=np.linspace(x_lmin, x_lmax, num=divide_num)
y_list=np.linspace(y_lmin, x_lmax, num=divide_num)
print("x_list",x_list)
print("y_list",y_list)
frame=[]
for i in range(len(x_list)-1):
x1=x_list[i]
x2=x_list[i+1]
for j in range(len(y_list)-1):
y1=y_list[j]
y2=y_list[j+1]
frame.append([[x1,y1],[x2,y1],[x2,y2],[x1,y2]])
print(frame)
def test2():
for points in frame:
for i in range(4):
if i<3:
plt.plot([points[i][0], points[i+1][0]],
[points[i][1], points[i+1][1]],
color = 'k')
else:
plt.plot([points[i][0], points[0][0]],
[points[i][1], points[0][1]],
color = 'k')
plt.show()
### l1 [xa, ya, xb, yb] l2 [xa, ya, xb, yb]
index=[]
#检测框中通过那些射线或者线段
def frame_points():
for j in range(len(frame)):
print(j)
fra=frame[j]
x_minz=fra[0][0]
x_maxz=fra[1][0]
y_minz=fra[0][1]
y_maxz=fra[2][1]
a=[]
for i in range(len(vers)):
#print(vers[i])
posts=vers[i]
l2=[posts[0][0],posts[0][1],posts[1][0],posts[1][1]]
if x_minz<posts[0][0] and posts[0][0]<x_maxz and x_minz<posts[1][0] and posts[1][0]<x_maxz:
if y_minz<posts[0][1] and posts[0][1]<y_maxz and y_minz<posts[1][1] and posts[1][1]<y_maxz:
a.append(pots[i][0])
a.append(pots[i][1])
continue
for z in range(4):
if z<3:
l1=[fra[z][0],fra[z][1],fra[z+1][0],fra[z+1][1]]
if Intersect(l1, l2):
a.append(pots[i][0])
a.append(pots[i][1])
break
else:
l1=[fra[z][0],fra[z][1],fra[0][0],fra[0][1]]
if Intersect(l1, l2):
a.append(pots[i][0])
a.append(pots[i][1])
break
if len(a)==0:
x=(x_minz+x_maxz)/2
y=(y_minz+y_maxz)/2
min_distance=(points[0][0]-x)**2+(points[0][1]-y)**2
index_min=0
for k in range(1,len(points)):
if (points[k][0]-x)**2+(points[k][1]-y)**2<min_distance:
index_min=k
min_distance=(points[k][0]-x)**2+(points[k][1]-y)**2
index.append([index_min])
else:
a=list(set(a))
index.append(a)
frame_points()
po=[1.48,0.52]
#寻找查找点在那个框中
def find(po):
position=0
for i in range(len(x_list)-1):
x1=x_list[i]
x2=x_list[i+1]
if x1<=po[0] and po[0]<=x2:
for j in range(len(y_list)-1):
y1=y_list[j]
y2=y_list[j+1]
print(y1,y2)
if y1<=po[1] and po[1]<=y2:
return position
else:
position=position+1
# print("position",position)
else:
# print("sucess")
position=position+len(x_list)-1
# print("position",position)
position=find(po)
print("position:",position)
print("index of position is:",index[position])
#寻找最近点得索引
def find_min_index(po,index_list):
x=po[0]
y=po[1]
min_distance=(points[index_list[0]][0]-x)**2+(points[index_list[0]][1]-y)**2
index_min=index_list[0]
for k in range(1,len(index_list)):
if (points[index_list[k]][0]-x)**2+(points[index_list[k]][1]-y)**2<min_distance:
index_min=index_list[k]
min_distance=(points[index_list[k]][0]-x)**2+(points[index_list[k]][1]-y)**2
return index_min
find_index=find_min_index(po,index[position])
print("find_index:",find_index)
test2()
os.system("pause")