=== Piecewise linear area function ===
position_cm  area_cm2  perimeter_cm  articulator
0  2.29712  5.4334  N
0.12934  2.00242  5.09926  N
0.270192  1.79402  4.82661  N
0.41118  1.65617  4.65056  N
0.552371  1.47262  4.39474  N
0.693833  1.34641  4.21585  N
0.835632  1.1853  3.97545  N
0.977835  1.03106  3.70503  N
1.12  0.931229  3.551  N
1.26004  0.801903  3.29306  N
1.39666  0.721034  3.14737  N
1.53059  0.615457  2.91007  N
1.66311  0.512531  2.65889  N
1.79473  0.444563  2.51112  N
1.92553  0.352866  2.23376  N
2.05557  0.335856  2.23805  N
2.18488  0.740064  4.33353  N
2.31349  1.4452  6.19142  N
2.44147  2.17492  7.09953  N
2.56891  2.83697  7.46245  N
2.69587  3.36699  7.66818  N
2.82237  3.52868  7.70726  N
2.94852  3.31281  7.60556  N
3.07611  3.10146  7.50037  N
3.2076  3.94277  9.45376  N
3.34352  3.88194  9.3902  N
3.48327  3.63254  9.24645  N
3.62525  3.24173  8.90194  N
3.76693  2.88607  8.63615  N
3.90538  2.63758  8.4318  N
4.03972  2.41217  8.29067  N
4.17363  2.182  8.0607  N
4.30768  1.94374  7.75588  N
4.44197  1.78186  7.49227  N
4.57657  1.72186  7.24242  N
4.71152  1.71711  7.17337  N
4.84689  1.74393  7.10513  N
4.98272  2.21807  6.33554  T
5.11908  2.2465  6.33645  T
5.25605  2.30016  6.34082  T
5.39333  2.36171  6.36556  T
5.53069  2.44224  6.49886  T
5.6681  2.48073  6.52355  T
5.80715  2.53099  6.63058  T
5.94894  2.56374  6.64017  T
6.09117  2.6105  6.7566  T
6.23338  2.70727  6.89159  T
6.37558  2.82291  7.04996  T
6.51781  2.95755  7.18139  T
6.66008  3.15856  7.45987  T
6.80239  3.36712  7.72893  T
6.94476  3.58103  7.83407  T
7.08717  3.82806  8.12381  T
7.22931  4.06384  8.24699  T
7.37006  4.33346  8.54109  T
7.50673  4.58737  8.66795  T
7.64014  4.86713  8.81924  T
7.77174  5.10086  8.82477  T
7.90346  5.11137  10.0361  T
8.03547  5.17705  10.3278  T
8.16747  4.98398  10.3201  T
8.29942  4.47573  9.24061  T
8.43156  4.15308  8.44558  T
8.56397  4.05653  8.19181  T
8.69707  4.14801  8.22179  T
8.83143  4.1919  8.25081  T
8.96764  4.08922  8.19267  T
9.10539  4.00316  8.14427  T
9.24376  3.86835  8.08066  T
9.38217  3.70686  8.00711  T
9.52018  3.58959  7.94789  T
9.65781  3.50593  7.90207  T
9.79638  3.42085  8.06325  T
9.93614  3.3485  8.04082  T
10.0766  3.34454  8.02818  T
10.2176  3.25381  7.79792  T
10.359  3.13181  7.56789  T
10.5005  3.05721  7.37469  T
10.6422  2.99651  7.27066  T
10.7841  2.94904  7.17045  T
10.9261  2.96644  7.17122  T
11.0681  3.11456  7.40118  T
11.2102  3.31596  7.50196  T
11.3524  3.55951  7.78445  T
11.4947  3.78538  7.89004  T
11.6369  4.02963  8.17462  T
11.7791  4.25431  8.28321  T
11.9211  4.42131  8.37047  T
12.0628  4.52509  8.42453  T
12.2042  4.61526  8.40789  T
12.3453  4.7121  8.46649  T
12.4863  4.79579  8.45759  T
12.6271  4.88685  8.52544  T
12.7672  4.92021  8.56018  T
12.9066  4.879  8.53994  T
13.0455  4.84399  8.53936  T
13.184  4.82541  8.54887  T
13.3225  4.73585  8.49829  T
13.4611  4.51856  8.22183  T
13.5998  4.29281  8.02549  T
13.7389  4.09038  7.85101  T
13.878  3.8989  7.60914  T
14.0167  3.76997  7.54466  T
14.1547  3.60195  7.3377  T
14.2922  3.44719  7.30911  T
14.4289  3.24788  7.04404  T
14.5656  3.12771  6.98736  T
14.7015  3.05948  8.20605  T
14.8365  2.7618  6.61333  T
14.9689  2.71242  8.06104  T
15.0918  2.6081  7.50925  T
15.2046  2.66094  7.36921  T
15.3049  2.79389  7.41737  T
15.3927  3.13193  7.36193  N
15.4721  2.81228  7.33472  I
15.5514  2.35471  6.94479  I
15.6302  1.94394  6.5635  I
15.7104  1.79383  6.73333  I
15.7939  2.36008  7.36872  I
15.8774  1.46746  5.88585  L
15.9618  1.21701  6.6854  L
16.0508  1.20014  6.37233  L
16.1472  1.81865  6.04049  L
16.2509  1.29001  5.19932  L
16.3574  1.11395  5.27761  L
16.4668  1.09225  5.28209  L
16.5824  1.09478  5.30117  L
16.7062  1.13723  5.33961  L
16.8374  1.1239  5.311  L

=== Piecewise constant (stepwise changing) area function ===
position_cm  area_cm2  perimeter_cm  articulator
0  1.53217  4.47773  N
0.506566  1.53217  4.47773  N
0.506566  1.00627  3.66679  N
1.01313  1.00627  3.66679  N
1.01313  0.624041  2.92936  N
1.5197  0.624041  2.92936  N
1.5197  0.33969  2.23376  N
2.02627  0.33969  2.23376  N
2.02627  0.335856  2.23709  N
2.53283  0.335856  2.23709  N
2.53283  2.64955  7.35971  N
3.0394  2.64955  7.35971  N
3.0394  3.10146  7.50037  N
3.54597  3.10146  7.50037  N
3.54597  2.39015  8.26866  N
4.05253  2.39015  8.26866  N
4.05253  1.72964  7.27484  N
4.5591  1.72964  7.27484  N
4.5591  1.71711  6.33554  N
5.06566  1.71711  6.33554  N
5.06566  2.23536  6.3361  T
5.57223  2.23536  6.3361  T
5.57223  2.45388  6.50632  T
6.0788  2.45388  6.50632  T
6.0788  2.60643  6.74647  T
6.58536  2.60643  6.74647  T
6.58536  3.05299  7.31362  T
7.09193  3.05299  7.31362  T
7.09193  3.83596  8.12794  T
7.5985  3.83596  8.12794  T
7.5985  4.77981  8.77201  T
8.10506  4.77981  8.77201  T
8.10506  4.05653  8.19181  T
8.63962  4.05653  8.19181  T
8.63962  3.95737  8.12266  T
9.15239  3.95737  8.12266  T
9.15239  3.51413  7.90656  T
9.64431  3.51413  7.90656  T
9.64431  3.31899  7.90207  T
10.1163  3.31899  7.90207  T
10.1163  3.02771  7.32413  T
10.5694  3.02771  7.32413  T
10.5694  2.94904  7.17045  T
11.0045  2.94904  7.17045  T
11.0045  3.04819  7.29815  T
11.4225  3.04819  7.29815  T
11.4225  3.67076  7.83645  T
11.8244  3.67076  7.83645  T
11.8244  4.30761  8.31106  T
12.2111  4.30761  8.31106  T
12.2111  4.62001  8.41077  T
12.5837  4.62001  8.41077  T
12.5837  4.85879  8.50453  T
12.9429  4.85879  8.50453  T
12.9429  4.75695  8.5102  T
13.2899  4.75695  8.5102  T
13.2899  4.25547  7.99331  T
13.6255  4.25547  7.99331  T
13.6255  3.83138  7.57537  T
13.9506  3.83138  7.57537  T
13.9506  3.47636  7.3145  T
14.2663  3.47636  7.3145  T
14.2663  3.12374  6.98736  T
14.5735  3.12374  6.98736  T
14.5735  2.74817  6.61333  T
14.873  2.74817  6.61333  T
14.873  2.6081  7.01295  T
15.166  2.6081  7.01295  T
15.166  2.64284  7.34118  T
15.4532  2.64284  7.34118  T
15.4532  1.79383  6.5635  I
15.7358  1.79383  6.5635  I
15.7358  1.20702  5.88585  L
16.0145  1.20702  5.88585  L
16.0145  1.20014  5.19932  L
16.2904  1.20014  5.19932  L
16.2904  1.09225  5.22833  L
16.5644  1.09225  5.22833  L
16.5644  1.09439  5.29819  L
16.8374  1.09439  5.29819  L

