This is my set of data, where I would like to fit a closed curve to, just like this post
JavaScript
x
185
185
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array([[ 0.3 , -0.05],2
[ 0.35, -0.05],3
[ 0.4 , -0.05],4
[ 0.45, -0.05],5
[ 0.5 , -0.05],6
[ 0.55, -0.05],7
[ 0.6 , -0.05],8
[ 0.65, -0.05],9
[ 0.7 , -0.05],10
[ 0.75, -0.05],11
[ 0.8 , -0.05],12
[ 0.85, -0.05],13
[ 0.9 , -0.05],14
[ 0.95, -0.05],15
[ 1. , -0.05],16
[ 1.05, -0.05],17
[ 1.1 , -0.05],18
[ 1.15, -0.05],19
[ 1.2 , -0.05],20
[ 1.25, -0.05],21
[ 1.3 , -0.05],22
[ 1.35, -0.05],23
[ 1.4 , -0.05],24
[ 1.45, -0.05],25
[ 1.5 , -0.05],26
[ 1.55, -0.05],27
[ 1.6 , -0.05],28
[ 1.65, -0.05],29
[ 1.7 , -0.05],30
[ 1.75, -0.05],31
[ 1.8 , -0.05],32
[ 0. , -0.1 ],33
[ 0.05, -0.1 ],34
[ 0. , -0.15],35
[ 2.1 , -0.15],36
[ 2.15, -0.15],37
[ 0. , -0.2 ],38
[ 2.1 , -0.2 ],39
[ 2.15, -0.2 ],40
[ 2.2 , -0.2 ],41
[ 2.2 , -0.25],42
[ 2.35, -0.35],43
[-0.15, -0.4 ],44
[ 2.35, -0.4 ],45
[-0.15, -0.45],46
[ 2.35, -0.45],47
[ 2.4 , -0.45],48
[ 2.35, -0.5 ],49
[ 2.4 , -0.5 ],50
[ 2.4 , -0.55],51
[-0.25, -0.6 ],52
[-0.2 , -0.6 ],53
[ 2.4 , -0.6 ],54
[ 2.45, -0.6 ],55
[-0.4 , -0.65],56
[ 2.45, -0.65],57
[-0.4 , -0.7 ],58
[ 2.45, -0.7 ],59
[ 2.5 , -0.7 ],60
[ 2.45, -0.75],61
[ 2.45, -0.8 ],62
[-0.5 , -0.85],63
[ 2.45, -0.85],64
[ 2.5 , -0.85],65
[-0.5 , -0.9 ],66
[ 2.45, -0.9 ],67
[ 2.5 , -0.9 ],68
[-0.5 , -0.95],69
[ 2.5 , -0.95],70
[-0.5 , -1. ],71
[ 2.5 , -1. ],72
[-0.5 , -1.05],73
[-0.45, -1.05],74
[ 2.5 , -1.05],75
[-0.5 , -1.1 ],76
[-0.45, -1.1 ],77
[ 2.5 , -1.1 ],78
[ 2.55, -1.1 ],79
[-0.5 , -1.15],80
[-0.45, -1.15],81
[ 2.5 , -1.15],82
[ 2.55, -1.15],83
[-0.5 , -1.2 ],84
[-0.45, -1.2 ],85
[ 2.5 , -1.2 ],86
[ 2.55, -1.2 ],87
[-0.45, -1.25],88
[ 2.55, -1.25],89
[-0.45, -1.3 ],90
[ 2.55, -1.3 ],91
[-0.45, -1.35],92
[ 2.55, -1.35],93
[-0.45, -1.4 ],94
[ 2.55, -1.4 ],95
[-0.45, -1.45],96
[-0.4 , -1.45],97
[ 2.55, -1.45],98
[-0.45, -1.5 ],99
[-0.4 , -1.5 ],100
[ 2.6 , -1.5 ],101
[-0.45, -1.55],102
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[ 2.6 , -1.55],104
[-0.45, -1.6 ],105
[-0.4 , -1.6 ],106
[ 2.6 , -1.6 ],107
[-0.45, -1.65],108
[-0.4 , -1.65],109
[ 2.6 , -1.65],110
[-0.45, -1.7 ],111
[-0.4 , -1.7 ],112
[ 2.6 , -1.7 ],113
[-0.4 , -1.75],114
[ 2.55, -1.75],115
[-0.4 , -1.8 ],116
[ 2.55, -1.8 ],117
[-0.45, -1.85],118
[-0.4 , -1.85],119
[ 2.55, -1.85],120
[-0.45, -1.9 ],121
[-0.4 , -1.9 ],122
[-0.4 , -1.95],123
[-0.4 , -2. ],124
[-0.35, -2. ],125
[-0.4 , -2.05],126
[-0.35, -2.05],127
[ 2.5 , -2.05],128
[ 2.55, -2.05],129
[-0.35, -2.1 ],130
[ 2.5 , -2.1 ],131
[ 2.55, -2.1 ],132
[-0.35, -2.15],133
[ 2.5 , -2.15],134
[ 2.55, -2.15],135
[-0.4 , -2.2 ],136
[-0.35, -2.2 ],137
[ 2.5 , -2.2 ],138
[-0.4 , -2.25],139
[-0.35, -2.25],140
[-0.35, -2.3 ],141
[ 2.45, -2.3 ],142
[-0.3 , -2.35],143
[ 2.45, -2.35],144
[-0.3 , -2.4 ],145
[-0.3 , -2.45],146
[-0.2 , -2.6 ],147
[ 2.05, -2.6 ],148
[ 2.2 , -2.6 ],149
[ 2.25, -2.6 ],150
[ 2.1 , -2.65],151
[-0.15, -2.7 ],152
[-0.05, -2.75],153
[ 0. , -2.75],154
[ 0.05, -2.75],155
[ 0.1 , -2.75],156
[ 0.15, -2.75],157
[-0.05, -2.8 ],158
[ 0. , -2.8 ],159
[ 0.05, -2.8 ],160
[ 0.1 , -2.8 ],161
[ 1.1 , -2.8 ],162
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[ 1.2 , -2.8 ],164
[ 1.25, -2.8 ],165
[ 1.3 , -2.8 ],166
[ 1.35, -2.8 ],167
[ 1.4 , -2.8 ],168
[ 1.45, -2.8 ],169
[ 1.5 , -2.8 ],170
[ 1.55, -2.8 ],171
[ 1.6 , -2.8 ],172
[ 1.65, -2.8 ],173
[ 1.7 , -2.8 ],174
[ 1.75, -2.8 ],175
[ 1.8 , -2.8 ],176
[ 0.7 , -2.85],177
[ 0.75, -2.85],178
[ 0.8 , -2.85],179
[ 0.85, -2.85],180
[ 0.9 , -2.85],181
[ 0.95, -2.85],182
[ 1. , -2.85],183
[ 1.05, -2.85]])184
185
here is the visualized dataset:
However, these are the results I got no matter how I sort my array.
I pinned a few problems about my dataset but don’t know how to deal with them:
- Many x and y values are not one to one
- Points are not sorted in a neighboring order
So if my assumptions are correct, the main question would be how can I sort the array in such an order that the splprep method works? If not, I would really appreciate any solution that helps me solve the problem!
[Update] Thanks to @michael-szczesny ‘s reply I got a satisfying result
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Answer
You can translate your data to the origin an sort by the complex angle.
Setup the data
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import numpy as np2
import matplotlib.pyplot as plt3
from scipy.interpolate import splprep, splev4
5
x = np.array(6
[[-0.50, -1.20],7
[-0.50, -1.15],8
[-0.50, -1.10],9
[-0.50, -1.05],10
[-0.50, -1.00],11
[-0.50, -0.95],12
[-0.50, -0.90],13
[-0.50, -0.85],14
[-0.45, -1.90],15
[-0.45, -1.85],16
[-0.45, -1.70],17
[-0.45, -1.65],18
[-0.45, -1.60],19
[-0.45, -1.55],20
[-0.45, -1.50],21
[-0.45, -1.45],22
[-0.45, -1.40],23
[-0.45, -1.35],24
[-0.45, -1.30],25
[-0.45, -1.25],26
[-0.45, -1.20],27
[-0.45, -1.15],28
[-0.45, -1.10],29
[-0.45, -1.05],30
[-0.40, -2.25],31
[-0.40, -2.20],32
[-0.40, -2.05],33
[-0.40, -2.00],34
[-0.40, -1.95],35
[-0.40, -1.90],36
[-0.40, -1.85],37
[-0.40, -1.80],38
[-0.40, -1.75],39
[-0.40, -1.70],40
[-0.40, -1.65],41
[-0.40, -1.60],42
[-0.40, -1.55],43
[-0.40, -1.50],44
[-0.40, -1.45],45
[-0.40, -0.70],46
[-0.40, -0.65],47
[-0.35, -2.30],48
[-0.35, -2.25],49
[-0.35, -2.20],50
[-0.35, -2.15],51
[-0.35, -2.10],52
[-0.35, -2.05],53
[-0.35, -2.00],54
[-0.30, -2.45],55
[-0.30, -2.40],56
[-0.30, -2.35],57
[-0.25, -0.60],58
[-0.20, -2.60],59
[-0.20, -0.60],60
[-0.15, -2.70],61
[-0.15, -0.45],62
[-0.15, -0.40],63
[-0.05, -2.80],64
[-0.05, -2.75],65
[0.00, -2.80],66
[0.00, -2.75],67
[0.00, -0.20],68
[0.00, -0.15],69
[0.00, -0.10],70
[0.05, -2.80],71
[0.05, -2.75],72
[0.05, -0.10],73
[0.10, -2.80],74
[0.10, -2.75],75
[0.15, -2.75],76
[0.30, -0.05],77
[0.35, -0.05],78
[0.40, -0.05],79
[0.45, -0.05],80
[0.50, -0.05],81
[0.55, -0.05],82
[0.60, -0.05],83
[0.65, -0.05],84
[0.70, -2.85],85
[0.70, -0.05],86
[0.75, -2.85],87
[0.75, -0.05],88
[0.80, -2.85],89
[0.80, -0.05],90
[0.85, -2.85],91
[0.85, -0.05],92
[0.90, -2.85],93
[0.90, -0.05],94
[0.95, -2.85],95
[0.95, -0.05],96
[1.00, -2.85],97
[1.00, -0.05],98
[1.05, -2.85],99
[1.05, -0.05],100
[1.10, -2.80],101
[1.10, -0.05],102
[1.15, -2.80],103
[1.15, -0.05],104
[1.20, -2.80],105
[1.20, -0.05],106
[1.25, -2.80],107
[1.25, -0.05],108
[1.30, -2.80],109
[1.30, -0.05],110
[1.35, -2.80],111
[1.35, -0.05],112
[1.40, -2.80],113
[1.40, -0.05],114
[1.45, -2.80],115
[1.45, -0.05],116
[1.50, -2.80],117
[1.50, -0.05],118
[1.55, -2.80],119
[1.55, -0.05],120
[1.60, -2.80],121
[1.60, -0.05],122
[1.65, -2.80],123
[1.65, -0.05],124
[1.70, -2.80],125
[1.70, -0.05],126
[1.75, -2.80],127
[1.75, -0.05],128
[1.80, -2.80],129
[1.80, -0.05],130
[2.05, -2.60],131
[2.10, -2.65],132
[2.10, -0.20],133
[2.10, -0.15],134
[2.15, -0.20],135
[2.15, -0.15],136
[2.20, -2.60],137
[2.20, -0.25],138
[2.20, -0.20],139
[2.25, -2.60],140
[2.35, -0.50],141
[2.35, -0.45],142
[2.35, -0.40],143
[2.35, -0.35],144
[2.40, -0.60],145
[2.40, -0.55],146
[2.40, -0.50],147
[2.40, -0.45],148
[2.45, -2.35],149
[2.45, -2.30],150
[2.45, -0.90],151
[2.45, -0.85],152
[2.45, -0.80],153
[2.45, -0.75],154
[2.45, -0.70],155
[2.45, -0.65],156
[2.45, -0.60],157
[2.50, -2.20],158
[2.50, -2.15],159
[2.50, -2.10],160
[2.50, -2.05],161
[2.50, -1.20],162
[2.50, -1.15],163
[2.50, -1.10],164
[2.50, -1.05],165
[2.50, -1.00],166
[2.50, -0.95],167
[2.50, -0.90],168
[2.50, -0.85],169
[2.50, -0.70],170
[2.55, -2.15],171
[2.55, -2.10],172
[2.55, -2.05],173
[2.55, -1.85],174
[2.55, -1.80],175
[2.55, -1.75],176
[2.55, -1.45],177
[2.55, -1.40],178
[2.55, -1.35],179
[2.55, -1.30],180
[2.55, -1.25],181
[2.55, -1.20],182
[2.55, -1.15],183
[2.55, -1.10],184
[2.60, -1.70],185
[2.60, -1.65],186
[2.60, -1.60],187
[2.60, -1.55],188
[2.60, -1.50]])189
Convert your data to complex coordinates with np.angle((xs[:,0] + 1j*xs[:,1])) and use it to sort your data.
JavaScript
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xs = (x - x.mean(0))2
x_sort = xs[np.angle((xs[:,0] + 1j*xs[:,1])).argsort()]3
Now you can plot(code by @rth) your data in the right order.
JavaScript
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# plot from https://stackoverflow.com/a/31466013/14277722 as mentioned in the question2
tck, u = splprep(x_sort.T, u=None, s=0.0, per=1) 3
u_new = np.linspace(u.min(), u.max(), 1000)4
x_new, y_new = splev(u_new, tck, der=0)5
6
plt.figure(figsize=(10,10))7
plt.plot(x_sort[:,0], x_sort[:,1], 'ro')8
plt.plot(x_new, y_new, 'b--');9
Out:
