Using cascaded_union to combine shapes gives "ValueError: Impossible to create Shapely geometry from zero value"

Question

I have a cluster of seven overlapping circles and ellipses that I try to combine into one shape, but when I run cascaded_union() I get an error:

 ValueError: No Shapely geometry can be created from null value 

Here is what I have written so far:

 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) 

My goal is to get something like the picture on the right: , where the rest of my code will determine how many points in the random distribution fall into irregularly shaped borders. I am confused about what the error refers to when it returns the comment "null value". Do I take into account the coincidence of individual figures correctly? From what I was looking, cascaded_union already takes the input of an array of shapes, but for some reason this does not work in this case.

Answer 1

All of your geometries are invalid.

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

If you look closely at your plot, the lines used for each LinearRing intersect near the beginning and end. This makes polygons invalid, which inevitably gives unpredictable results.

Here is my version of what you are doing:

 # 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...