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': 1.1927, 'y': 0.1881, 'z': 0},
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 {'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 ]])

Answer 2

The convex hull is a nice approach, although it wouldn't solve the case that you are showing (the donut shape with an inner boundary).

I think that the algorithm that you need is called "Marching cubes" (or Marching squares, in 2D). It is a broadly used method, so you should be able to easily find some libraries in python that implement it.

https://en.wikipedia.org/wiki/Marching_squares

Basically, considering the 2D case, the algorithm works like this:

• Discretize the space in a grid.
• Count the number of points in every cell
• Apply a threshold to the cells so you end up with either "empty" or "filled" cells
• According to the state of every cell, and its neighbors, there are some predefined cases (16 in 2D) on how the boundary curve should look like.
• Merge all the small curves

In 3D the idea is the same, but with cubes instead of squares, and with higher number of predefined cases.

Answer 3

The convex hull approaches mentioned by others do not work when the shape has holes (as in the case with your torus example).

The problem you’re trying to solve is called surface reconstruction. The final mesh will not have the internal points as you wanted.

Open3D has some algorithms implemented for this and you can them on your data in Python.

Surface reconstruction

To convert your numpy point cloud to Open3D’s use

pcd = o3d.geometry.PointCloud()
pcd.points = o3d.utility.Vector3dVector(xyz)