A simple code that builds a 3D graph based on the coordinates of points:
import pandas as pd
import matplotlib.pyplot as plt
with open('data\PS.txt', 'r') as f:
df = pd.read_csv(f, sep=",")
x = df['x'].values.tolist()
y = df['y'].values.tolist()
z = df['z'].values.tolist()
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
ax.plot_trisurf(x, y, z)
plt.show()
Here is the 3D figure itself:
enter image description here
Now it is necessary to calculate the volume of this figure.
How do I calculate the volume of a figure?
File contents “PS.txt” it looks like this:
1,152691.129,213258.428,631.716
2,152691.316,213256.857,631.827
3,152692.729,213255.315,631.945
4,152695.035,213250.459,631.882
5,152696.787,213246.130,632.107
6,152698.298,213242.364,631.578
7,152699.839,213239.028,631.723
8,152700.217,213237.356,631.350
9,152701.883,213233.297,631.206
10,152702.981,213229.478,631.392
11,152705.247,213224.878,631.609
12,152706.485,213222.668,632.294
13,152708.542,213219.988,632.765
14,152708.552,213220.002,632.750
15,152711.060,213215.836,632.809
16,152713.617,213211.422,632.346
17,152718.564,213202.802,631.409
18,152722.731,213197.100,631.362
19,152726.272,213192.046,631.498
20,152730.236,213186.253,631.371
21,152734.179,213180.031,631.452
22,152737.690,213175.369,631.344
23,152741.310,213177.118,631.309
24,152748.978,213182.575,631.163
25,152756.270,213188.301,631.247
26,152759.305,213190.724,631.267
27,152762.942,213192.492,631.256
28,152765.987,213194.916,631.162
29,152769.216,213197.108,631.358
30,152771.065,213200.136,631.245
31,152769.791,213202.537,631.736
32,152767.962,213205.946,631.614
33,152764.967,213211.123,631.717
34,152762.501,213215.213,631.571
35,152758.903,213221.344,631.816
36,152757.514,213225.138,632.015
37,152754.682,213229.676,631.975
38,152751.918,213234.024,631.889
39,152748.804,213239.425,632.106
40,152745.263,213245.349,631.928
41,152741.336,213251.451,631.912
42,152737.827,213256.240,632.071
43,152733.422,213263.828,632.060
44,152729.597,213269.791,632.211
45,152727.207,213273.974,632.440
46,152725.795,213276.797,632.435
47,152725.042,213277.064,632.554
48,152723.422,213276.584,632.513
49,152715.066,213272.147,632.442
50,152709.221,213268.936,632.387
51,152702.480,213264.648,632.467
52,152697.043,213261.739,632.231
53,152693.678,213259.727,632.141
54,152718.231,213206.304,629.044
55,152720.573,213203.068,628.925
56,152723.331,213199.193,628.898
57,152723.927,213196.993,628.870
58,152728.193,213190.552,628.813
59,152731.767,213185.322,628.960
60,152735.617,213179.673,629.032
61,152737.550,213176.409,629.168
62,152740.349,213177.727,629.093
63,152747.789,213183.248,628.736
64,152755.001,213188.781,628.874
65,152758.970,213192.543,629.045
66,152761.357,213193.329,629.181
67,152766.041,213196.920,629.269
68,152767.944,213199.372,629.367
69,152768.401,213201.151,629.219
70,152764.862,213207.360,629.122
71,152761.754,213212.748,629.312
72,152757.478,213220.474,629.310
73,152753.623,213228.269,629.393
74,152748.167,213237.432,629.557
75,152742.455,213247.561,629.629
76,152737.519,213254.209,629.883
77,152733.522,213259.618,630.021
78,152732.286,213261.395,629.511
79,152728.106,213268.732,629.516
80,152726.549,213271.128,629.326
81,152723.805,213274.373,629.317
82,152721.984,213273.677,629.192
83,152716.138,213270.812,629.574
84,152710.821,213268.060,629.567
85,152706.132,213265.473,629.309
86,152701.330,213262.217,628.895
87,152697.388,213260.418,628.983
88,152694.490,213258.500,629.225
89,152693.393,213258.304,629.621
90,152694.345,213256.439,629.329
91,152696.949,213251.571,629.259
92,152698.927,213246.215,629.155
93,152700.346,213242.499,629.009
94,152702.244,213238.054,628.970
95,152703.983,213233.276,628.897
96,152705.018,213229.281,629.012
97,152706.526,213226.382,629.127
98,152707.929,213223.484,629.261
99,152711.127,213219.338,629.268
100,152713.425,213215.829,629.093
101,152716.183,213210.623,628.744
102,152699.816,213255.436,628.810
103,152703.999,213257.574,628.649
104,152708.446,213259.993,629.049
105,152715.256,213263.596,629.281
106,152719.561,213265.977,629.373
107,152724.048,213268.319,629.370
108,152726.984,213263.115,629.579
109,152724.089,213260.586,629.322
110,152718.138,213256.749,629.407
111,152713.111,213253.939,629.257
112,152709.817,213251.502,628.953
113,152707.199,213249.989,628.670
114,152702.574,213247.411,628.844
115,152705.577,213241.685,628.898
116,152710.906,213244.101,628.792
117,152715.875,213246.241,628.887
118,152717.636,213247.094,629.211
119,152725.472,213251.103,629.307
120,152728.123,213252.443,629.553
121,152731.916,213254.534,629.897
122,152736.446,213247.816,629.464
123,152732.745,213245.056,629.233
124,152727.080,213241.423,629.124
125,152721.365,213238.400,628.874
126,152714.975,213234.559,628.970
127,152708.530,213231.420,628.871
128,152712.677,213225.120,629.003
129,152716.666,213227.440,628.856
130,152722.213,213230.296,628.799
131,152726.407,213232.656,628.672
132,152731.916,213235.770,628.876
133,152736.523,213238.443,629.147
134,152740.674,213240.783,629.344
135,152744.868,213234.142,629.359
136,152740.977,213231.527,629.126
137,152735.601,213228.189,628.759
138,152730.823,213225.042,628.534
139,152726.882,213222.278,628.481
140,152722.476,213218.921,628.594
141,152718.191,213215.736,628.733
142,152722.108,213210.698,628.572
143,152727.304,213212.925,628.314
144,152732.755,213215.602,628.129
145,152738.899,213219.785,628.257
146,152741.104,213221.031,628.425
147,152745.450,213223.517,628.798
148,152749.876,213225.960,629.039
149,152753.427,213219.757,629.075
150,152748.345,213216.114,628.684
151,152743.630,213212.799,628.256
152,152737.131,213209.291,628.304
153,152730.671,213206.158,628.415
154,152726.464,213203.380,628.630
155,152729.335,213198.258,628.759
156,152733.621,213200.345,628.489
157,152738.154,213202.717,628.415
158,152744.284,213206.303,628.709
159,152748.297,213209.516,628.499
160,152752.498,213212.363,628.883
161,152754.904,213213.741,629.372
162,152757.685,213211.582,629.352
163,152758.353,213208.933,629.254
164,152760.346,213209.123,629.314
165,152760.941,213206.380,629.142
166,152760.128,213202.271,629.014
167,152757.335,213198.594,628.844
168,152755.759,213197.339,628.822
169,152763.289,213200.301,629.009
170,152759.572,213197.326,628.975
171,152756.591,213199.072,628.574
172,152759.201,213202.392,628.390
173,152759.462,213204.784,628.457
174,152756.864,213206.414,628.606
175,152757.359,213208.721,628.897
176,152756.466,213210.988,629.069
177,152751.499,213204.059,628.700
178,152746.819,213201.102,628.749
179,152741.889,213198.339,628.611
180,152739.042,213196.746,628.669
181,152735.780,213194.626,628.932
182,152731.677,213192.081,628.950
183,152735.933,213187.082,628.857
184,152740.588,213190.671,628.946
185,152745.251,213194.414,628.803
186,152749.876,213197.718,628.695
187,152753.870,213200.839,628.717
188,152754.703,213194.185,628.870
189,152748.420,213189.568,628.785
190,152740.765,213183.848,628.788
Thank you all.
7
The first trick was reading your text file into a dataframe with x, y, and z columns (not a necessary step for finding volume). Since it’s not a csv or a regularly delimited file, it doesn’t read easily with pd.read_csv(). You could either clean up the raw file first to make it more easily readable or clean it up after reading it in. I chose the latter.
import numpy as np, pandas as pd
from scipy.spatial import ConvexHull
df = pd.read_csv('PS.txt', sep=' ', header=None).stack().str.split(',', expand=True)
df = pd.concat([df[[1,2,3]].rename(columns={1:'x', 2:'y', 3:'z'}),
df[[4,5,6]].dropna().rename(columns={4:'x', 5:'y', 6:'z'})], ignore_index=True)
>>> df
x y z
0 152691.129 213258.428 631.716
1 152691.316 213256.857 631.827
2 152692.729 213255.315 631.945
3 152695.035 213250.459 631.882
4 152696.787 213246.130 632.107
... ... ... ...
375 152753.870 213200.839 628.717
376 152754.703 213194.185 628.870
377 152748.420 213189.568 628.785
378 152740.765 213183.848 628.788
379 152691.129 213258.428 631.716
380 rows × 3 columns
For finding the volume of convex polyhedrons you can use scipy.spatial.ConvexHull.
volume = ConvexHull(df.values).volume
>>> volume
13977.540571063422
Alternatively, you could just extract the points to find the volume without using a dataframe.
raw_string = '1,152691.129,213258.428,631.716 2,152691.316,213256.857,631.827 3,152692.729,213255.315,631.945 4,152695.035,213250.459,631.882 5,152696.787,213246.130,632.107 6,152698.298,213242.364,631.578 7,152699.839,213239.028,631.723 8,152700.217,213237.356,631.350 9,152701.883,213233.297,631.206 10,152702.981,213229.478,631.392 11,152705.247,213224.878,631.609 12,152706.485,213222.668,632.294 13,152708.542,213219.988,632.765 14,152708.552,213220.002,632.750 15,152711.060,213215.836,632.809 16,152713.617,213211.422,632.346 17,152718.564,213202.802,631.409 18,152722.731,213197.100,631.362 19,152726.272,213192.046,631.498 20,152730.236,213186.253,631.371 21,152734.179,213180.031,631.452 22,152737.690,213175.369,631.344 23,152741.310,213177.118,631.309 24,152748.978,213182.575,631.163 25,152756.270,213188.301,631.247 26,152759.305,213190.724,631.267 27,152762.942,213192.492,631.256 28,152765.987,213194.916,631.162 29,152769.216,213197.108,631.358 30,152771.065,213200.136,631.245 31,152769.791,213202.537,631.736 32,152767.962,213205.946,631.614 33,152764.967,213211.123,631.717 34,152762.501,213215.213,631.571 35,152758.903,213221.344,631.816 36,152757.514,213225.138,632.015 37,152754.682,213229.676,631.975 38,152751.918,213234.024,631.889 39,152748.804,213239.425,632.106 40,152745.263,213245.349,631.928 41,152741.336,213251.451,631.912 42,152737.827,213256.240,632.071 43,152733.422,213263.828,632.060 44,152729.597,213269.791,632.211 45,152727.207,213273.974,632.440 46,152725.795,213276.797,632.435 47,152725.042,213277.064,632.554 48,152723.422,213276.584,632.513 49,152715.066,213272.147,632.442 50,152709.221,213268.936,632.387 51,152702.480,213264.648,632.467 52,152697.043,213261.739,632.231 53,152693.678,213259.727,632.141 54,152718.231,213206.304,629.044 55,152720.573,213203.068,628.925 56,152723.331,213199.193,628.898 57,152723.927,213196.993,628.870 58,152728.193,213190.552,628.813 59,152731.767,213185.322,628.960 60,152735.617,213179.673,629.032 61,152737.550,213176.409,629.168 62,152740.349,213177.727,629.093 63,152747.789,213183.248,628.736 64,152755.001,213188.781,628.874 65,152758.970,213192.543,629.045 66,152761.357,213193.329,629.181 67,152766.041,213196.920,629.269 68,152767.944,213199.372,629.367 69,152768.401,213201.151,629.219 70,152764.862,213207.360,629.122 71,152761.754,213212.748,629.312 72,152757.478,213220.474,629.310 73,152753.623,213228.269,629.393 74,152748.167,213237.432,629.557 75,152742.455,213247.561,629.629 76,152737.519,213254.209,629.883 77,152733.522,213259.618,630.021 78,152732.286,213261.395,629.511 79,152728.106,213268.732,629.516 80,152726.549,213271.128,629.326 81,152723.805,213274.373,629.317 82,152721.984,213273.677,629.192 83,152716.138,213270.812,629.574 84,152710.821,213268.060,629.567 85,152706.132,213265.473,629.309 86,152701.330,213262.217,628.895 87,152697.388,213260.418,628.983 88,152694.490,213258.500,629.225 89,152693.393,213258.304,629.621 90,152694.345,213256.439,629.329 91,152696.949,213251.571,629.259 92,152698.927,213246.215,629.155 93,152700.346,213242.499,629.009 94,152702.244,213238.054,628.970 95,152703.983,213233.276,628.897 96,152705.018,213229.281,629.012 97,152706.526,213226.382,629.127 98,152707.929,213223.484,629.261 99,152711.127,213219.338,629.268 100,152713.425,213215.829,629.093 101,152716.183,213210.623,628.744 102,152699.816,213255.436,628.810 103,152703.999,213257.574,628.649 104,152708.446,213259.993,629.049 105,152715.256,213263.596,629.281 106,152719.561,213265.977,629.373 107,152724.048,213268.319,629.370 108,152726.984,213263.115,629.579 109,152724.089,213260.586,629.322 110,152718.138,213256.749,629.407 111,152713.111,213253.939,629.257 112,152709.817,213251.502,628.953 113,152707.199,213249.989,628.670 114,152702.574,213247.411,628.844 115,152705.577,213241.685,628.898 116,152710.906,213244.101,628.792 117,152715.875,213246.241,628.887 118,152717.636,213247.094,629.211 119,152725.472,213251.103,629.307 120,152728.123,213252.443,629.553 121,152731.916,213254.534,629.897 122,152736.446,213247.816,629.464 123,152732.745,213245.056,629.233 124,152727.080,213241.423,629.124 125,152721.365,213238.400,628.874 126,152714.975,213234.559,628.970 127,152708.530,213231.420,628.871 128,152712.677,213225.120,629.003 129,152716.666,213227.440,628.856 130,152722.213,213230.296,628.799 131,152726.407,213232.656,628.672 132,152731.916,213235.770,628.876 133,152736.523,213238.443,629.147 134,152740.674,213240.783,629.344 135,152744.868,213234.142,629.359 136,152740.977,213231.527,629.126 137,152735.601,213228.189,628.759 138,152730.823,213225.042,628.534 139,152726.882,213222.278,628.481 140,152722.476,213218.921,628.594 141,152718.191,213215.736,628.733 142,152722.108,213210.698,628.572 143,152727.304,213212.925,628.314 144,152732.755,213215.602,628.129 145,152738.899,213219.785,628.257 146,152741.104,213221.031,628.425 147,152745.450,213223.517,628.798 148,152749.876,213225.960,629.039 149,152753.427,213219.757,629.075 150,152748.345,213216.114,628.684 151,152743.630,213212.799,628.256 152,152737.131,213209.291,628.304 153,152730.671,213206.158,628.415 154,152726.464,213203.380,628.630 155,152729.335,213198.258,628.759 156,152733.621,213200.345,628.489 157,152738.154,213202.717,628.415 158,152744.284,213206.303,628.709 159,152748.297,213209.516,628.499 160,152752.498,213212.363,628.883 161,152754.904,213213.741,629.372 162,152757.685,213211.582,629.352 163,152758.353,213208.933,629.254 164,152760.346,213209.123,629.314 165,152760.941,213206.380,629.142 166,152760.128,213202.271,629.014 167,152757.335,213198.594,628.844 168,152755.759,213197.339,628.822 169,152763.289,213200.301,629.009 170,152759.572,213197.326,628.975 171,152756.591,213199.072,628.574 172,152759.201,213202.392,628.390 173,152759.462,213204.784,628.457 174,152756.864,213206.414,628.606 175,152757.359,213208.721,628.897 176,152756.466,213210.988,629.069 177,152751.499,213204.059,628.700 178,152746.819,213201.102,628.749 179,152741.889,213198.339,628.611 180,152739.042,213196.746,628.669 181,152735.780,213194.626,628.932 182,152731.677,213192.081,628.950 183,152735.933,213187.082,628.857 184,152740.588,213190.671,628.946 185,152745.251,213194.414,628.803 186,152749.876,213197.718,628.695 187,152753.870,213200.839,628.717 188,152754.703,213194.185,628.870 189,152748.420,213189.568,628.785 190,152740.765,213183.848,628.788'
points = []
for x in raw_string.split(' '):
current_line = [float(x) for x in x.split(',')[1:]]
if len(current_string)%3==0:
if len(current_line)!=3:
for n in range(1, int((len(current_line)/3)+1)):
points.append(current_line[3*(n-1):3*n])
else:
points.append(current_line)
else:
continue
volume = ConvexHull(points).volume
>>> volume
13977.540571063422
1