Python - plotting surface around 3D plot cloud

Question

I run computational fluid dynamic simulation and I want to refine my mesh in the areas for which a quantity is superior to a threshold. I manage to extract the point locations so I obtain a list of points describing the areas that correspond to my criteria for refining.

To refine my mesh, I need to provide to the software the external boundaries of the surface (or curve if we are in 2D) that is described by the point cloud. More particularly, I need to remove all the points that are in the center of the area to get the coordinates of those which are on the boundary. Then I would like to surround the points with a curve.

I found similar post on the forum but the question was to interpolate the point cloud, so not exactly what I want: Fit Curve-Spline to 3D Point Cloud

May you help me to do that ?

Here is a 2D example of point cloud for which I would like to only keep the boundary points and plot the surrounding curve:

0.20215,0.29703,0
0.22857,0.29703,0
0.25526,0.29703,0
0.28221,0.29703,0
0.30943,0.29703,0
0.33692,0.29703,0
0.36469,0.29703,0
0.39273,0.29703,0
0.42106,0.29703,0
0.44966,0.29703,0
0.47856,0.29703,0
0.50774,0.29703,0
0.53722,0.29703,0
0.56699,0.29703,0
0.59706,0.29703,0
0.62742,0.29703,0
0.6581,0.29703,0
0.68907,0.29703,0
0.72036,0.29703,0
0.75196,0.29703,0
0.78388,0.29703,0
0.81612,0.29703,0
0.84868,0.29703,0
0.88156,0.29703,0
0.91478,0.29703,0
0.94832,0.29703,0
0.9822,0.29703,0
1.0164,0.29703,0
1.051,0.29703,0
1.0859,0.29703,0
1.1211,0.29703,0
1.1568,0.29703,0
1.1927,0.29703,0
1.229,0.29703,0
1.2657,0.29703,0
1.3028,0.29703,0
1.3402,0.29703,0
1.378,0.29703,0
1.4162,0.29703,0
1.4548,0.29703,0
1.4937,0.29703,0
1.533,0.29703,0
1.5728,0.29703,0
1.6129,0.29703,0
1.6534,0.29703,0
1.6944,0.29703,0
1.7357,0.29703,0
1.7774,0.29703,0
1.8196,0.29703,0
1.8622,0.29703,0
1.9052,0.29703,0
1.9487,0.29703,0
1.9926,0.29703,0
2.0369,0.29703,0
2.0817,0.29703,0
2.1269,0.29703,0
2.1725,0.29703,0
2.2187,0.29703,0
2.2652,0.29703,0
2.3123,0.29703,0
2.3598,0.29703,0
2.4078,0.29703,0
2.4563,0.29703,0
2.5053,0.29703,0
2.5547,0.29703,0
2.6046,0.29703,0
2.6551,0.29703,0
2.706,0.29703,0
2.7575,0.29703,0
2.8095,0.29703,0
2.862,0.29703,0
2.915,0.29703,0
2.9685,0.29703,0
3.0226,0.29703,0
3.0772,0.29703,0
3.1324,0.29703,0
3.1881,0.29703,0
3.2444,0.29703,0
3.3013,0.29703,0
3.3587,0.29703,0
3.4166,0.29703,0
3.4752,0.29703,0
3.5344,0.29703,0
3.5941,0.29703,0
3.6544,0.29703,0
3.7154,0.29703,0
3.7769,0.29703,0
3.8391,0.29703,0
3.9019,0.29703,0
3.9653,0.29703,0
4.0294,0.29703,0
4.094,0.29703,0
4.1594,0.29703,0
4.2254,0.29703,0
4.292,0.29703,0
4.3593,0.29703,0
4.4273,0.29703,0
4.496,0.29703,0
4.5654,0.29703,0
4.6354,0.29703,0
4.7062,0.29703,0
4.7776,0.29703,0
4.8498,0.29703,0
4.9227,0.29703,0
0.28221,0.28425,0
0.30943,0.28425,0
0.33692,0.28425,0
0.36469,0.28425,0
0.39273,0.28425,0
0.42106,0.28425,0
0.44966,0.28425,0
0.47856,0.28425,0
0.50774,0.28425,0
0.53722,0.28425,0
0.56699,0.28425,0
0.59706,0.28425,0
0.62742,0.28425,0
0.6581,0.28425,0
0.68907,0.28425,0
0.72036,0.28425,0
0.75196,0.28425,0
0.78388,0.28425,0
0.81612,0.28425,0
0.84868,0.28425,0
0.88156,0.28425,0
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0.9822,0.28425,0
1.0164,0.28425,0
1.051,0.28425,0
1.0859,0.28425,0
1.1211,0.28425,0
1.1568,0.28425,0
1.1927,0.28425,0
1.229,0.28425,0
1.2657,0.28425,0
1.3028,0.28425,0
1.3402,0.28425,0
1.378,0.28425,0
1.4162,0.28425,0
1.4548,0.28425,0
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1.8622,0.28425,0
1.9052,0.28425,0
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3.8391,0.28425,0
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3.9653,0.28425,0
4.0294,0.28425,0
4.094,0.28425,0
4.1594,0.28425,0
4.2254,0.28425,0
4.292,0.28425,0
4.3593,0.28425,0
4.4273,0.28425,0
4.496,0.28425,0
4.5654,0.28425,0
0.39273,0.27117,0
0.42106,0.27117,0
0.44966,0.27117,0
0.47856,0.27117,0
0.50774,0.27117,0
0.53722,0.27117,0
0.56699,0.27117,0
0.59706,0.27117,0
0.62742,0.27117,0
0.6581,0.27117,0
0.68907,0.27117,0
0.72036,0.27117,0
0.75196,0.27117,0
0.78388,0.27117,0
0.81612,0.27117,0
0.84868,0.27117,0
0.88156,0.27117,0
0.91478,0.27117,0
0.94832,0.27117,0
0.9822,0.27117,0
1.0164,0.27117,0
1.051,0.27117,0
1.0859,0.27117,0
1.1211,0.27117,0
1.1568,0.27117,0
1.1927,0.27117,0
1.229,0.27117,0
1.2657,0.27117,0
1.3028,0.27117,0
1.3402,0.27117,0
1.378,0.27117,0
1.4162,0.27117,0
1.4548,0.27117,0
1.4937,0.27117,0
1.533,0.27117,0
1.5728,0.27117,0
1.6129,0.27117,0
1.6534,0.27117,0
1.6944,0.27117,0
1.7357,0.27117,0
1.7774,0.27117,0
1.8196,0.27117,0
1.8622,0.27117,0
1.9052,0.27117,0
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2.6551,0.27117,0
2.706,0.27117,0
2.7575,0.27117,0
2.8095,0.27117,0
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2.915,0.27117,0
2.9685,0.27117,0
3.0226,0.27117,0
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3.6544,0.27117,0
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0.47856,0.25781,0
0.50774,0.25781,0
0.53722,0.25781,0
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0.59706,0.25781,0
0.62742,0.25781,0
0.6581,0.25781,0
0.68907,0.25781,0
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0.75196,0.25781,0
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0.81612,0.25781,0
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0.88156,0.25781,0
0.91478,0.25781,0
0.94832,0.25781,0
0.9822,0.25781,0
1.0164,0.25781,0
1.051,0.25781,0
1.0859,0.25781,0
1.1211,0.25781,0
1.1568,0.25781,0
1.1927,0.25781,0
1.229,0.25781,0
1.2657,0.25781,0
1.3028,0.25781,0
1.3402,0.25781,0
1.378,0.25781,0
1.4162,0.25781,0
1.4548,0.25781,0
1.4937,0.25781,0
1.533,0.25781,0
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1.6129,0.25781,0
1.6534,0.25781,0
1.6944,0.25781,0
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1.8622,0.1881,0
1.9052,0.1881,0
1.9487,0.1881,0
1.9926,0.1881,0
2.0369,0.1881,0

Thanks for your help,

Sincerely

Answer 1

It's possible to do with ConvexHull from SciPy and this function together with convex_hull_plot_2d yield this result for the provided dataset. Below is the code to reproduce the pictures. hull.points at the end of the code contain the resulting outlining set of points that you are looking for.

import matplotlib.pyplot as plt
import pandas as pd
import numpy as np
from scipy.spatial import ConvexHull, convex_hull_plot_2d

df = pd.DataFrame([{'x': 0.20215, 'y': 0.29703, 'z': 0},
 {'x': 0.22857, 'y': 0.29703, 'z': 0},
 {'x': 0.25526, 'y': 0.29703, 'z': 0},
 {'x': 0.28221, 'y': 0.29703, 'z': 0},
 {'x': 0.30943, 'y': 0.29703, 'z': 0},
 {'x': 0.33692, 'y': 0.29703, 'z': 0},
 {'x': 0.36469, 'y': 0.29703, 'z': 0},
 {'x': 0.39273, 'y': 0.29703, 'z': 0},
 {'x': 0.42106, 'y': 0.29703, 'z': 0},
 {'x': 0.44966, 'y': 0.29703, 'z': 0},
 {'x': 0.47856, 'y': 0.29703, 'z': 0},
 {'x': 0.50774, 'y': 0.29703, 'z': 0},
 {'x': 0.53722, 'y': 0.29703, 'z': 0},
 {'x': 0.56699, 'y': 0.29703, 'z': 0},
 {'x': 0.59706, 'y': 0.29703, 'z': 0},
 {'x': 0.62742, 'y': 0.29703, 'z': 0},
 {'x': 0.6581, 'y': 0.29703, 'z': 0},
 {'x': 0.68907, 'y': 0.29703, 'z': 0},
 {'x': 0.72036, 'y': 0.29703, 'z': 0},
 {'x': 0.75196, 'y': 0.29703, 'z': 0},
 {'x': 0.78388, 'y': 0.29703, 'z': 0},
 {'x': 0.81612, 'y': 0.29703, 'z': 0},
 {'x': 0.84868, 'y': 0.29703, 'z': 0},
 {'x': 0.88156, 'y': 0.29703, 'z': 0},
 {'x': 0.91478, 'y': 0.29703, 'z': 0},
 {'x': 0.94832, 'y': 0.29703, 'z': 0},
 {'x': 0.9822, 'y': 0.29703, 'z': 0},
 {'x': 1.0164, 'y': 0.29703, 'z': 0},
 {'x': 1.051, 'y': 0.29703, 'z': 0},
 {'x': 1.0859, 'y': 0.29703, 'z': 0},
 {'x': 1.1211, 'y': 0.29703, 'z': 0},
 {'x': 1.1568, 'y': 0.29703, 'z': 0},
 {'x': 1.1927, 'y': 0.29703, 'z': 0},
 {'x': 1.229, 'y': 0.29703, 'z': 0},
 {'x': 1.2657, 'y': 0.29703, 'z': 0},
 {'x': 1.3028, 'y': 0.29703, 'z': 0},
 {'x': 1.3402, 'y': 0.29703, 'z': 0},
 {'x': 1.378, 'y': 0.29703, 'z': 0},
 {'x': 1.4162, 'y': 0.29703, 'z': 0},
 {'x': 1.4548, 'y': 0.29703, 'z': 0},
 {'x': 1.4937, 'y': 0.29703, 'z': 0},
 {'x': 1.533, 'y': 0.29703, 'z': 0},
 {'x': 1.5728, 'y': 0.29703, 'z': 0},
 {'x': 1.6129, 'y': 0.29703, 'z': 0},
 {'x': 1.6534, 'y': 0.29703, 'z': 0},
 {'x': 1.6944, 'y': 0.29703, 'z': 0},
 {'x': 1.7357, 'y': 0.29703, 'z': 0},
 {'x': 1.7774, 'y': 0.29703, 'z': 0},
 {'x': 1.8196, 'y': 0.29703, 'z': 0},
 {'x': 1.8622, 'y': 0.29703, 'z': 0},
 {'x': 1.9052, 'y': 0.29703, 'z': 0},
 {'x': 1.9487, 'y': 0.29703, 'z': 0},
 {'x': 1.9926, 'y': 0.29703, 'z': 0},
 {'x': 2.0369, 'y': 0.29703, 'z': 0},
 {'x': 2.0817, 'y': 0.29703, 'z': 0},
 {'x': 2.1269, 'y': 0.29703, 'z': 0},
 {'x': 2.1725, 'y': 0.29703, 'z': 0},
 {'x': 2.2187, 'y': 0.29703, 'z': 0},
 {'x': 2.2652, 'y': 0.29703, 'z': 0},
 {'x': 2.3123, 'y': 0.29703, 'z': 0},
 {'x': 2.3598, 'y': 0.29703, 'z': 0},
 {'x': 2.4078, 'y': 0.29703, 'z': 0},
 {'x': 2.4563, 'y': 0.29703, 'z': 0},
 {'x': 2.5053, 'y': 0.29703, 'z': 0},
 {'x': 2.5547, 'y': 0.29703, 'z': 0},
 {'x': 2.6046, 'y': 0.29703, 'z': 0},
 {'x': 2.6551, 'y': 0.29703, 'z': 0},
 {'x': 2.706, 'y': 0.29703, 'z': 0},
 {'x': 2.7575, 'y': 0.29703, 'z': 0},
 {'x': 2.8095, 'y': 0.29703, 'z': 0},
 {'x': 2.862, 'y': 0.29703, 'z': 0},
 {'x': 2.915, 'y': 0.29703, 'z': 0},
 {'x': 2.9685, 'y': 0.29703, 'z': 0},
 {'x': 3.0226, 'y': 0.29703, 'z': 0},
 {'x': 3.0772, 'y': 0.29703, 'z': 0},
 {'x': 3.1324, 'y': 0.29703, 'z': 0},
 {'x': 3.1881, 'y': 0.29703, 'z': 0},
 {'x': 3.2444, 'y': 0.29703, 'z': 0},
 {'x': 3.3013, 'y': 0.29703, 'z': 0},
 {'x': 3.3587, 'y': 0.29703, 'z': 0},
 {'x': 3.4166, 'y': 0.29703, 'z': 0},
 {'x': 3.4752, 'y': 0.29703, 'z': 0},
 {'x': 3.5344, 'y': 0.29703, 'z': 0},
 {'x': 3.5941, 'y': 0.29703, 'z': 0},
 {'x': 3.6544, 'y': 0.29703, 'z': 0},
 {'x': 3.7154, 'y': 0.29703, 'z': 0},
 {'x': 3.7769, 'y': 0.29703, 'z': 0},
 {'x': 3.8391, 'y': 0.29703, 'z': 0},
 {'x': 3.9019, 'y': 0.29703, 'z': 0},
 {'x': 3.9653, 'y': 0.29703, 'z': 0},
 {'x': 4.0294, 'y': 0.29703, 'z': 0},
 {'x': 4.094, 'y': 0.29703, 'z': 0},
 {'x': 4.1594, 'y': 0.29703, 'z': 0},
 {'x': 4.2254, 'y': 0.29703, 'z': 0},
 {'x': 4.292, 'y': 0.29703, 'z': 0},
 {'x': 4.3593, 'y': 0.29703, 'z': 0},
 {'x': 4.4273, 'y': 0.29703, 'z': 0},
 {'x': 4.496, 'y': 0.29703, 'z': 0},
 {'x': 4.5654, 'y': 0.29703, 'z': 0},
 {'x': 4.6354, 'y': 0.29703, 'z': 0},
 {'x': 4.7062, 'y': 0.29703, 'z': 0},
 {'x': 4.7776, 'y': 0.29703, 'z': 0},
 {'x': 4.8498, 'y': 0.29703, 'z': 0},
 {'x': 4.9227, 'y': 0.29703, 'z': 0},
 {'x': 0.28221, 'y': 0.28425, 'z': 0},
 {'x': 0.30943, 'y': 0.28425, 'z': 0},
 {'x': 0.33692, 'y': 0.28425, 'z': 0},
 {'x': 0.36469, 'y': 0.28425, 'z': 0},
 {'x': 0.39273, 'y': 0.28425, 'z': 0},
 {'x': 0.42106, 'y': 0.28425, 'z': 0},
 {'x': 0.44966, 'y': 0.28425, 'z': 0},
 {'x': 0.47856, 'y': 0.28425, 'z': 0},
 {'x': 0.50774, 'y': 0.28425, 'z': 0},
 {'x': 0.53722, 'y': 0.28425, 'z': 0},
 {'x': 0.56699, 'y': 0.28425, 'z': 0},
 {'x': 0.59706, 'y': 0.28425, 'z': 0},
 {'x': 0.62742, 'y': 0.28425, 'z': 0},
 {'x': 0.6581, 'y': 0.28425, 'z': 0},
 {'x': 0.68907, 'y': 0.28425, 'z': 0},
 {'x': 0.72036, 'y': 0.28425, 'z': 0},
 {'x': 0.75196, 'y': 0.28425, 'z': 0},
 {'x': 0.78388, 'y': 0.28425, 'z': 0},
 {'x': 0.81612, 'y': 0.28425, 'z': 0},
 {'x': 0.84868, 'y': 0.28425, 'z': 0},
 {'x': 0.88156, 'y': 0.28425, 'z': 0},
 {'x': 0.91478, 'y': 0.28425, 'z': 0},
 {'x': 0.94832, 'y': 0.28425, 'z': 0},
 {'x': 0.9822, 'y': 0.28425, 'z': 0},
 {'x': 1.0164, 'y': 0.28425, 'z': 0},
 {'x': 1.051, 'y': 0.28425, 'z': 0},
 {'x': 1.0859, 'y': 0.28425, 'z': 0},
 {'x': 1.1211, 'y': 0.28425, 'z': 0},
 {'x': 1.1568, 'y': 0.28425, 'z': 0},
 {'x': 1.1927, 'y': 0.28425, 'z': 0},
 {'x': 1.229, 'y': 0.28425, 'z': 0},
 {'x': 1.2657, 'y': 0.28425, 'z': 0},
 {'x': 1.3028, 'y': 0.28425, 'z': 0},
 {'x': 1.3402, 'y': 0.28425, 'z': 0},
 {'x': 1.378, 'y': 0.28425, 'z': 0},
 {'x': 1.4162, 'y': 0.28425, 'z': 0},
 {'x': 1.4548, 'y': 0.28425, 'z': 0},
 {'x': 1.4937, 'y': 0.28425, 'z': 0},
 {'x': 1.533, 'y': 0.28425, 'z': 0},
 {'x': 1.5728, 'y': 0.28425, 'z': 0},
 {'x': 1.6129, 'y': 0.28425, 'z': 0},
 {'x': 1.6534, 'y': 0.28425, 'z': 0},
 {'x': 1.6944, 'y': 0.28425, 'z': 0},
 {'x': 1.7357, 'y': 0.28425, 'z': 0},
 {'x': 1.7774, 'y': 0.28425, 'z': 0},
 {'x': 1.8196, 'y': 0.28425, 'z': 0},
 {'x': 1.8622, 'y': 0.28425, 'z': 0},
 {'x': 1.9052, 'y': 0.28425, 'z': 0},
 {'x': 1.9487, 'y': 0.28425, 'z': 0},
 {'x': 1.9926, 'y': 0.28425, 'z': 0},
 {'x': 2.0369, 'y': 0.28425, 'z': 0},
 {'x': 2.0817, 'y': 0.28425, 'z': 0},
 {'x': 2.1269, 'y': 0.28425, 'z': 0},
 {'x': 2.1725, 'y': 0.28425, 'z': 0},
 {'x': 2.2187, 'y': 0.28425, 'z': 0},
 {'x': 2.2652, 'y': 0.28425, 'z': 0},
 {'x': 2.3123, 'y': 0.28425, 'z': 0},
 {'x': 2.3598, 'y': 0.28425, 'z': 0},
 {'x': 2.4078, 'y': 0.28425, 'z': 0},
 {'x': 2.4563, 'y': 0.28425, 'z': 0},
 {'x': 2.5053, 'y': 0.28425, 'z': 0},
 {'x': 2.5547, 'y': 0.28425, 'z': 0},
 {'x': 2.6046, 'y': 0.28425, 'z': 0},
 {'x': 2.6551, 'y': 0.28425, 'z': 0},
 {'x': 2.706, 'y': 0.28425, 'z': 0},
 {'x': 2.7575, 'y': 0.28425, 'z': 0},
 {'x': 2.8095, 'y': 0.28425, 'z': 0},
 {'x': 2.862, 'y': 0.28425, 'z': 0},
 {'x': 2.915, 'y': 0.28425, 'z': 0},
 {'x': 2.9685, 'y': 0.28425, 'z': 0},
 {'x': 3.0226, 'y': 0.28425, 'z': 0},
 {'x': 3.0772, 'y': 0.28425, 'z': 0},
 {'x': 3.1324, 'y': 0.28425, 'z': 0},
 {'x': 3.1881, 'y': 0.28425, 'z': 0},
 {'x': 3.2444, 'y': 0.28425, 'z': 0},
 {'x': 3.3013, 'y': 0.28425, 'z': 0},
 {'x': 3.3587, 'y': 0.28425, 'z': 0},
 {'x': 3.4166, 'y': 0.28425, 'z': 0},
 {'x': 3.4752, 'y': 0.28425, 'z': 0},
 {'x': 3.5344, 'y': 0.28425, 'z': 0},
 {'x': 3.5941, 'y': 0.28425, 'z': 0},
 {'x': 3.6544, 'y': 0.28425, 'z': 0},
 {'x': 3.7154, 'y': 0.28425, 'z': 0},
 {'x': 3.7769, 'y': 0.28425, 'z': 0},
 {'x': 3.8391, 'y': 0.28425, 'z': 0},
 {'x': 3.9019, 'y': 0.28425, 'z': 0},
 {'x': 3.9653, 'y': 0.28425, 'z': 0},
 {'x': 4.0294, 'y': 0.28425, 'z': 0},
 {'x': 4.094, 'y': 0.28425, 'z': 0},
 {'x': 4.1594, 'y': 0.28425, 'z': 0},
 {'x': 4.2254, 'y': 0.28425, 'z': 0},
 {'x': 4.292, 'y': 0.28425, 'z': 0},
 {'x': 4.3593, 'y': 0.28425, 'z': 0},
 {'x': 4.4273, 'y': 0.28425, 'z': 0},
 {'x': 4.496, 'y': 0.28425, 'z': 0},
 {'x': 4.5654, 'y': 0.28425, 'z': 0},
 {'x': 0.39273, 'y': 0.27117, 'z': 0},
 {'x': 0.42106, 'y': 0.27117, 'z': 0},
 {'x': 0.44966, 'y': 0.27117, 'z': 0},
 {'x': 0.47856, 'y': 0.27117, 'z': 0},
 {'x': 0.50774, 'y': 0.27117, 'z': 0},
 {'x': 0.53722, 'y': 0.27117, 'z': 0},
 {'x': 0.56699, 'y': 0.27117, 'z': 0},
 {'x': 0.59706, 'y': 0.27117, 'z': 0},
 {'x': 0.62742, 'y': 0.27117, 'z': 0},
 {'x': 0.6581, 'y': 0.27117, 'z': 0},
 {'x': 0.68907, 'y': 0.27117, 'z': 0},
 {'x': 0.72036, 'y': 0.27117, 'z': 0},
 {'x': 0.75196, 'y': 0.27117, 'z': 0},
 {'x': 0.78388, 'y': 0.27117, 'z': 0},
 {'x': 0.81612, 'y': 0.27117, 'z': 0},
 {'x': 0.84868, 'y': 0.27117, 'z': 0},
 {'x': 0.88156, 'y': 0.27117, 'z': 0},
 {'x': 0.91478, 'y': 0.27117, 'z': 0},
 {'x': 0.94832, 'y': 0.27117, 'z': 0},
 {'x': 0.9822, 'y': 0.27117, 'z': 0},
 {'x': 1.0164, 'y': 0.27117, 'z': 0},
 {'x': 1.051, 'y': 0.27117, 'z': 0},
 {'x': 1.0859, 'y': 0.27117, 'z': 0},
 {'x': 1.1211, 'y': 0.27117, 'z': 0},
 {'x': 1.1568, 'y': 0.27117, 'z': 0},
 {'x': 1.1927, 'y': 0.27117, 'z': 0},
 {'x': 1.229, 'y': 0.27117, 'z': 0},
 {'x': 1.2657, 'y': 0.27117, 'z': 0},
 {'x': 1.3028, 'y': 0.27117, 'z': 0},
 {'x': 1.3402, 'y': 0.27117, 'z': 0},
 {'x': 1.378, 'y': 0.27117, 'z': 0},
 {'x': 1.4162, 'y': 0.27117, 'z': 0},
 {'x': 1.4548, 'y': 0.27117, 'z': 0},
 {'x': 1.4937, 'y': 0.27117, 'z': 0},
 {'x': 1.533, 'y': 0.27117, 'z': 0},
 {'x': 1.5728, 'y': 0.27117, 'z': 0},
 {'x': 1.6129, 'y': 0.27117, 'z': 0},
 {'x': 1.6534, 'y': 0.27117, 'z': 0},
 {'x': 1.6944, 'y': 0.27117, 'z': 0},
 {'x': 1.7357, 'y': 0.27117, 'z': 0},
 {'x': 1.7774, 'y': 0.27117, 'z': 0},
 {'x': 1.8196, 'y': 0.27117, 'z': 0},
 {'x': 1.8622, 'y': 0.27117, 'z': 0},
 {'x': 1.9052, 'y': 0.27117, 'z': 0},
 {'x': 1.9487, 'y': 0.27117, 'z': 0},
 {'x': 1.9926, 'y': 0.27117, 'z': 0},
 {'x': 2.0369, 'y': 0.27117, 'z': 0},
 {'x': 2.0817, 'y': 0.27117, 'z': 0},
 {'x': 2.1269, 'y': 0.27117, 'z': 0},
 {'x': 2.1725, 'y': 0.27117, 'z': 0},
 {'x': 2.2187, 'y': 0.27117, 'z': 0},
 {'x': 2.2652, 'y': 0.27117, 'z': 0},
 {'x': 2.3123, 'y': 0.27117, 'z': 0},
 {'x': 2.3598, 'y': 0.27117, 'z': 0},
 {'x': 2.4078, 'y': 0.27117, 'z': 0},
 {'x': 2.4563, 'y': 0.27117, 'z': 0},
 {'x': 2.5053, 'y': 0.27117, 'z': 0},
 {'x': 2.5547, 'y': 0.27117, 'z': 0},
 {'x': 2.6046, 'y': 0.27117, 'z': 0},
 {'x': 2.6551, 'y': 0.27117, 'z': 0},
 {'x': 2.706, 'y': 0.27117, 'z': 0},
 {'x': 2.7575, 'y': 0.27117, 'z': 0},
 {'x': 2.8095, 'y': 0.27117, 'z': 0},
 {'x': 2.862, 'y': 0.27117, 'z': 0},
 {'x': 2.915, 'y': 0.27117, 'z': 0},
 {'x': 2.9685, 'y': 0.27117, 'z': 0},
 {'x': 3.0226, 'y': 0.27117, 'z': 0},
 {'x': 3.0772, 'y': 0.27117, 'z': 0},
 {'x': 3.1324, 'y': 0.27117, 'z': 0},
 {'x': 3.1881, 'y': 0.27117, 'z': 0},
 {'x': 3.2444, 'y': 0.27117, 'z': 0},
 {'x': 3.3013, 'y': 0.27117, 'z': 0},
 {'x': 3.3587, 'y': 0.27117, 'z': 0},
 {'x': 3.4166, 'y': 0.27117, 'z': 0},
 {'x': 3.4752, 'y': 0.27117, 'z': 0},
 {'x': 3.5344, 'y': 0.27117, 'z': 0},
 {'x': 3.5941, 'y': 0.27117, 'z': 0},
 {'x': 3.6544, 'y': 0.27117, 'z': 0},
 {'x': 3.7154, 'y': 0.27117, 'z': 0},
 {'x': 3.7769, 'y': 0.27117, 'z': 0},
 {'x': 3.8391, 'y': 0.27117, 'z': 0},
 {'x': 3.9019, 'y': 0.27117, 'z': 0},
 {'x': 3.9653, 'y': 0.27117, 'z': 0},
 {'x': 4.0294, 'y': 0.27117, 'z': 0},
 {'x': 4.094, 'y': 0.27117, 'z': 0},
 {'x': 4.1594, 'y': 0.27117, 'z': 0},
 {'x': 0.47856, 'y': 0.25781, 'z': 0},
 {'x': 0.50774, 'y': 0.25781, 'z': 0},
 {'x': 0.53722, 'y': 0.25781, 'z': 0},
 {'x': 0.56699, 'y': 0.25781, 'z': 0},
 {'x': 0.59706, 'y': 0.25781, 'z': 0},
 {'x': 0.62742, 'y': 0.25781, 'z': 0},
 {'x': 0.6581, 'y': 0.25781, 'z': 0},
 {'x': 0.68907, 'y': 0.25781, 'z': 0},
 {'x': 0.72036, 'y': 0.25781, 'z': 0},
 {'x': 0.75196, 'y': 0.25781, 'z': 0},
 {'x': 0.78388, 'y': 0.25781, 'z': 0},
 {'x': 0.81612, 'y': 0.25781, 'z': 0},
 {'x': 0.84868, 'y': 0.25781, 'z': 0},
 {'x': 0.88156, 'y': 0.25781, 'z': 0},
 {'x': 0.91478, 'y': 0.25781, 'z': 0},
 {'x': 0.94832, 'y': 0.25781, 'z': 0},
 {'x': 0.9822, 'y': 0.25781, 'z': 0},
 {'x': 1.0164, 'y': 0.25781, 'z': 0},
 {'x': 1.051, 'y': 0.25781, 'z': 0},
 {'x': 1.0859, 'y': 0.25781, 'z': 0},
 {'x': 1.1211, 'y': 0.25781, 'z': 0},
 {'x': 1.1568, 'y': 0.25781, 'z': 0},
 {'x': 1.1927, 'y': 0.25781, 'z': 0},
 {'x': 1.229, 'y': 0.25781, 'z': 0},
 {'x': 1.2657, 'y': 0.25781, 'z': 0},
 {'x': 1.3028, 'y': 0.25781, 'z': 0},
 {'x': 1.3402, 'y': 0.25781, 'z': 0},
 {'x': 1.378, 'y': 0.25781, 'z': 0},
 {'x': 1.4162, 'y': 0.25781, 'z': 0},
 {'x': 1.4548, 'y': 0.25781, 'z': 0},
 {'x': 1.4937, 'y': 0.25781, 'z': 0},
 {'x': 1.533, 'y': 0.25781, 'z': 0},
 {'x': 1.5728, 'y': 0.25781, 'z': 0},
 {'x': 1.6129, 'y': 0.25781, 'z': 0},
 {'x': 1.6534, 'y': 0.25781, 'z': 0},
 {'x': 1.6944, 'y': 0.25781, 'z': 0},
 {'x': 1.7357, 'y': 0.25781, 'z': 0},
 {'x': 1.7774, 'y': 0.25781, 'z': 0},
 {'x': 1.8196, 'y': 0.25781, 'z': 0},
 {'x': 1.8622, 'y': 0.25781, 'z': 0},
 {'x': 1.9052, 'y': 0.25781, 'z': 0},
 {'x': 1.9487, 'y': 0.25781, 'z': 0},
 {'x': 1.9926, 'y': 0.25781, 'z': 0},
 {'x': 2.0369, 'y': 0.25781, 'z': 0},
 {'x': 2.0817, 'y': 0.25781, 'z': 0},
 {'x': 2.1269, 'y': 0.25781, 'z': 0},
 {'x': 2.1725, 'y': 0.25781, 'z': 0},
 {'x': 2.2187, 'y': 0.25781, 'z': 0},
 {'x': 2.2652, 'y': 0.25781, 'z': 0},
 {'x': 2.3123, 'y': 0.25781, 'z': 0},
 {'x': 2.3598, 'y': 0.25781, 'z': 0},
 {'x': 2.4078, 'y': 0.25781, 'z': 0},
 {'x': 2.4563, 'y': 0.25781, 'z': 0},
 {'x': 2.5053, 'y': 0.25781, 'z': 0},
 {'x': 2.5547, 'y': 0.25781, 'z': 0},
 {'x': 2.6046, 'y': 0.25781, 'z': 0},
 {'x': 2.6551, 'y': 0.25781, 'z': 0},
 {'x': 2.706, 'y': 0.25781, 'z': 0},
 {'x': 2.7575, 'y': 0.25781, 'z': 0},
 {'x': 2.8095, 'y': 0.25781, 'z': 0},
 {'x': 2.862, 'y': 0.25781, 'z': 0},
 {'x': 2.915, 'y': 0.25781, 'z': 0},
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 {'x': 3.0226, 'y': 0.23041, 'z': 0},
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 {'x': 2.3123, 'y': 0.20231, 'z': 0},
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 {'x': 2.4078, 'y': 0.20231, 'z': 0},
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 {'x': 1.051, 'y': 0.1881, 'z': 0},
 {'x': 1.0859, 'y': 0.1881, 'z': 0},
 {'x': 1.1211, 'y': 0.1881, 'z': 0},
 {'x': 1.1568, 'y': 0.1881, 'z': 0},
 {'x': 1.1927, 'y': 0.1881, 'z': 0},
 {'x': 1.229, 'y': 0.1881, 'z': 0},
 {'x': 1.2657, 'y': 0.1881, 'z': 0},
 {'x': 1.3028, 'y': 0.1881, 'z': 0},
 {'x': 1.3402, 'y': 0.1881, 'z': 0},
 {'x': 1.378, 'y': 0.1881, 'z': 0},
 {'x': 1.4162, 'y': 0.1881, 'z': 0},
 {'x': 1.4548, 'y': 0.1881, 'z': 0},
 {'x': 1.4937, 'y': 0.1881, 'z': 0},
 {'x': 1.533, 'y': 0.1881, 'z': 0},
 {'x': 1.5728, 'y': 0.1881, 'z': 0},
 {'x': 1.6129, 'y': 0.1881, 'z': 0},
 {'x': 1.6534, 'y': 0.1881, 'z': 0},
 {'x': 1.6944, 'y': 0.1881, 'z': 0},
 {'x': 1.7357, 'y': 0.1881, 'z': 0},
 {'x': 1.7774, 'y': 0.1881, 'z': 0},
 {'x': 1.8196, 'y': 0.1881, 'z': 0},
 {'x': 1.8622, 'y': 0.1881, 'z': 0},
 {'x': 1.9052, 'y': 0.1881, 'z': 0},
 {'x': 1.9487, 'y': 0.1881, 'z': 0},
 {'x': 1.9926, 'y': 0.1881, 'z': 0},
 {'x': 2.0369, 'y': 0.1881, 'z': 0}])


plt.scatter(data=df, x='x', y='y', label='original_data')
plt.legend()
plt.title('original data')
plt.show()

hull = ConvexHull(df[['x', 'y']])
fig = plt.figure()
ax = fig.add_subplot(1,1,1)
convex_hull_plot_2d(hull, ax=ax)
fig.tight_layout()
plt.title('convex hull with points')
plt.show()

hull.points
array([[0.20215, 0.29703],
   [0.22857, 0.29703],
   [0.25526, 0.29703],
   ...,
   [1.9487 , 0.1881 ],
   [1.9926 , 0.1881 ],
   [2.0369 , 0.1881 ]])