使用级联_并集组合形状会产生“ValueError:无法从空值创建任何形状几何体”

Question

我有一个由七个重叠的圆圈和椭圆组成的集群，我试图将它们组合成一个形状，但是当我运行cascaded_union（）时，我得到了错误：

ValueError: No Shapely geometry can be created from null value

以下是我到目前为止所写的内容：

import numpy as np
import matplotlib.pyplot as plt
from shapely.geometry import Polygon
from shapely.ops import cascaded_union

x = [-1.86203523, -1.91255406, -2.03575331, -2.16247874, -2.22159676, -2.17992322,
     -2.06085035, -1.93121615, -1.86378696, -1.89641216, -1.838166,   -1.88166833,
     -1.98775658, -2.09688125, -2.14778844, -2.1119029,  -2.00936791, -1.89773847,
     -1.83967446, -1.86776838, -1.55136662, -1.60188546, -1.72508471, -1.85181013,
     -1.91092815, -1.86925461, -1.75018174, -1.62054755, -1.55311836, -1.58574355,
     -1.29187795, -1.33538028, -1.44146853, -1.5505932,  -1.60150039, -1.56561485,
     -1.46307986, -1.35145041, -1.2933864,  -1.32148032, -1.07173048, -1.11382951,
     -1.21649555, -1.32210007, -1.37136508, -1.33663714, -1.23740975, -1.12938125,
     -1.07319027, -1.10037793, -1.87340556, -1.79563936, -1.5818673,  -1.35208399,
     -1.23527147, -1.29699902, -1.50261769, -1.73670954, -1.86787402, -1.82248584,
     -1.98180156, -1.89591919, -1.66476691, -1.4180952,  -1.29436593, -1.36303087,
     -1.58554696, -1.83701142, -1.97627207, -1.92515911]
y = [0.80459679,  0.9296353,   0.98448714,  0.93836285,  0.81715295,  0.68889502,
     0.62558285,  0.66275485,  0.77954562,  0.91039814,  0.63006386,  0.73773591,
     0.78496944,  0.74525131,  0.6408761,   0.53043177,  0.47591296,  0.50792219,
     0.60849203,  0.72117057,  0.6981317,   0.82317021,  0.87802205,  0.83189777,
     0.71068786,  0.58242993,  0.51911776,  0.55628977,  0.67308054,  0.80393305,
     0.60213859,  0.70981064,  0.75704417,  0.71732605,  0.61295084,  0.50250651,
     0.44798769,  0.47999693,  0.58056676,  0.6932453,   0.77841685,  0.8826156,
     0.92832546,  0.88988856,  0.78888032,  0.6819987,   0.62923856,  0.66021523,
     0.75754088,  0.86658463,  0.84706981,  0.76282008,  0.69418295,  0.67968584,
     0.7274663,   0.81070415,  0.88267631,  0.90298332,  0.86022645,  0.77840601,
     0.56517702,  0.48654992,  0.41794253,  0.39786557,  0.43758864,  0.51481438,
     0.5861944,   0.61166165,  0.57692084,  0.50147268]

m = 7
n = 10

x_1 = np.zeros(shape=(m,n))
y_1 = np.zeros(shape=(m,n))
for i in range(m):
    for j in range(n):
        x_1[i][j] = x[j+(n*i)]
        y_1[i][j] = y[j+(n*i)]
    plt.plot(x_1[i],y_1[i])
    plt.axis('scaled')
plt.show()

Poly1 = Polygon(zip(x_1[0],y_1[0]))
Poly2 = Polygon(zip(x_1[1],y_1[1]))
Poly3 = Polygon(zip(x_1[2],y_1[2]))
Poly4 = Polygon(zip(x_1[3],y_1[3]))
Poly5 = Polygon(zip(x_1[4],y_1[4]))
Poly6 = Polygon(zip(x_1[5],y_1[5]))
Poly7 = Polygon(zip(x_1[6],y_1[6]))

polygons = [Poly1,Poly2,Poly3,Poly4,Poly5,Poly6,Poly7]

boundary = cascaded_union(polygons)

Answer 1

您的所有几何图形都无效。

[p.is_valid for p in polygons]  # [False, False, False, ...]

如果仔细观察绘图，则用于每个线性化的线在起点和终点附近交叉。这会使多边形无效，从而不可避免地产生不可预测的结果。

以下是我对您所做工作的看法：

# Discard the first and last points from each list of coordinates
x_2 = x_1[:, 1:-1]
y_2 = y_1[:, 1:-1]
# Build a list of polygons
polygons = [Polygon(zip(x_2[i], y_2[i])) for i in range(x_2.shape[0])]
boundary = cascaded_union(polygons)  # POLYGON ((-1.343821678336245 0.4932102...