=== Piecewise linear area function ===
position_cm  area_cm2  perimeter_cm  articulator
0  2.29712  5.4334  N
0.146844  2.01658  5.1108  N
0.300761  1.7919  4.81837  N
0.454783  1.63583  4.61856  N
0.608965  1.44264  4.35392  N
0.763358  1.2575  4.0719  N
0.918016  1.12816  3.86833  N
1.07273  0.971839  3.61818  N
1.22371  0.827149  3.33391  N
1.37022  0.739132  3.17817  N
1.51331  0.624174  2.92507  N
1.65438  0.515885  2.65708  N
1.79393  0.442793  2.50243  N
1.93191  0.348431  2.22001  N
2.06841  0.499471  3.05364  N
2.20351  1.24867  5.37619  N
2.33734  2.24621  7.04284  N
2.47027  3.18075  7.619  N
2.60264  4.00865  8.01674  N
2.73449  4.55692  8.22114  N
2.86613  4.43041  8.1527  N
3.00103  4.2336  8.05  N
3.14112  4.92488  10.3447  N
3.28692  5.11832  10.4599  N
3.43837  5.03108  10.3769  N
3.59281  4.77022  10.0696  N
3.74682  4.43874  9.7435  N
3.89792  4.22183  9.59763  N
4.04738  4.00179  9.38248  N
4.19685  3.76086  9.12189  N
4.34637  3.55259  8.91606  N
4.49601  3.43522  8.69433  N
4.64574  3.41063  8.53306  N
4.79551  3.42448  8.47726  N
4.94529  3.79247  7.78298  T
5.09505  3.78573  7.82401  T
5.24476  3.76754  7.79562  T
5.39433  3.68055  7.73589  T
5.54376  3.56978  7.68095  T
5.69348  3.37761  7.58699  T
5.84643  3.13915  7.30357  T
6.00114  2.92896  7.19296  T
6.15593  2.68651  6.90871  T
6.31076  2.4713  6.81162  T
6.46555  2.23733  6.5996  T
6.62025  2.01114  6.38483  T
6.7748  1.79972  6.10821  T
6.92915  1.59883  5.8321  T
7.08332  1.45523  5.59416  T
7.23731  1.34789  5.53138  T
7.39115  1.27261  5.41996  T
7.54492  1.24479  5.4956  T
7.69769  1.22784  5.49491  T
7.84536  1.26152  5.52591  T
7.98795  1.32733  5.7368  T
8.12718  1.25282  6.93569  T
8.26597  1.22165  7.3401  T
8.40568  1.24039  7.3277  T
8.54622  1.11242  7.10596  T
8.6873  0.731334  5.89159  T
8.82917  0.442529  3.85409  T
8.97198  0.295797  3.01649  T
9.11601  0.354595  3.35578  T
9.26192  0.475917  4.07015  T
9.41035  0.462404  3.73473  T
9.56104  0.433187  3.6143  T
9.71139  0.41918  3.50206  T
9.86119  0.377472  3.27536  T
10.0103  0.339076  3.05654  T
10.1596  0.327555  3.04652  T
10.3101  0.359718  3.37106  T
10.4614  0.367684  3.3775  T
10.6133  0.442144  3.84538  T
10.7657  0.504233  3.98155  T
10.9186  0.657105  4.7076  T
11.0719  0.763751  4.9436  T
11.2256  0.894131  5.20596  T
11.3797  1.03574  5.47514  T
11.5339  1.19835  5.75719  T
11.6881  1.38514  6.23448  T
11.842  1.71819  6.58989  T
11.9951  2.14832  7.35013  T
12.1456  2.58186  7.56741  T
12.2893  3.11997  8.17397  T
12.4271  3.64175  8.60446  T
12.5602  4.14901  8.87685  T
12.69  4.77875  9.26195  T
12.8187  5.39258  9.75663  T
12.9482  5.98817  10.0852  T
13.0802  6.3657  10.2392  T
13.2118  6.54694  10.2852  T
13.3406  6.56102  10.2829  T
13.466  6.60539  10.1664  T
13.5875  6.71988  10.2252  T
13.706  7.25221  13.3746  T
13.8222  7.7303  13.5566  T
13.9387  8.72059  13.8717  N
14.0574  13.683  15.3079  N
14.1805  14.6189  16.499  N
14.3086  15.8214  16.9799  N
14.4428  15.544  16.8927  N
14.5847  14.9525  16.5386  N
14.7353  13.8393  15.794  N
14.8886  13.2911  15.4294  N
15.0418  12.3395  14.6583  N
15.1953  11.3593  14.062  N
15.3486  10.1621  13.121  N
15.5001  9.2258  12.2221  N
15.647  8.28772  11.4129  N
15.7863  6.80269  10.2271  N
15.9162  6.23549  9.85428  I
16.0393  5.66201  9.32758  I
16.1612  5.48671  9.74226  I
16.2818  4.63263  8.95467  I
16.3987  3.61369  8.00207  I
16.5094  2.98323  7.26399  I
16.6153  2.7072  7.46736  I
16.7204  2.6499  8.44407  I
16.8255  1.87597  6.53438  L
16.9309  1.49878  6.25832  L
17.0382  1.42712  5.12399  L
17.1509  0.928514  4.36031  L
17.2712  0.66942  3.97399  L
17.4007  0.532154  3.55977  L
17.5386  0.474399  3.34074  L
17.679  0.412354  3.12771  L
17.821  0.400551  3.5044  L
17.9647  0.411408  3.54214  L
18.1135  0.41842  3.52634  L

=== Piecewise constant (stepwise changing) area function ===
position_cm  area_cm2  perimeter_cm  articulator
0  1.54408  4.49288  N
0.528005  1.54408  4.49288  N
0.528005  0.988734  3.64521  N
1.05601  0.988734  3.64521  N
1.05601  0.569902  2.79076  N
1.58401  0.569902  2.79076  N
1.58401  0.348431  2.22001  N
2.11202  0.348431  2.22001  N
2.11202  0.741323  3.8034  N
2.64002  0.741323  3.8034  N
2.64002  4.1641  8.05  N
3.16803  4.1641  8.05  N
3.16803  4.54806  9.85103  N
3.69603  4.54806  9.85103  N
3.69603  3.72298  9.08446  N
4.22404  3.72298  9.08446  N
4.22404  3.41063  8.49346  N
4.75204  3.41063  8.49346  N
4.75204  3.42046  7.78153  N
5.28005  3.42046  7.78153  N
5.28005  3.19899  7.37469  T
5.80805  3.19899  7.37469  T
5.80805  2.43306  6.77697  T
6.33605  2.43306  6.77697  T
6.33605  1.68355  5.94854  T
6.86406  1.68355  5.94854  T
6.86406  1.27244  5.41996  T
7.39206  1.27244  5.41996  T
7.39206  1.22784  5.42041  T
7.92007  1.22784  5.42041  T
7.92007  1.20179  5.6364  T
8.44807  1.20179  5.6364  T
8.44807  0.295797  3.01649  T
9.03975  0.295797  3.01649  T
9.03975  0.323464  3.17614  T
9.6073  0.323464  3.17614  T
9.6073  0.328159  3.04704  T
10.1518  0.328159  3.04704  T
10.1518  0.327555  3.04652  T
10.6742  0.327555  3.04652  T
10.6742  0.466986  3.89986  T
11.1757  0.466986  3.89986  T
11.1757  0.851796  5.12077  T
11.6573  0.851796  5.12077  T
11.6573  1.3478  6.13907  T
12.12  1.3478  6.13907  T
12.12  2.50806  7.53043  T
12.5648  2.50806  7.53043  T
12.5648  4.17159  8.89066  T
12.9929  4.17159  8.89066  T
12.9929  6.11594  10.1373  T
13.4052  6.11594  10.1373  T
13.4052  6.58388  10.1664  T
13.8029  6.58388  10.1664  T
13.8029  7.65066  13.5263  T
14.1869  7.65066  13.5263  T
14.1869  14.6793  16.5232  N
14.5583  14.6793  16.5232  N
14.5583  13.107  15.2802  N
14.9182  13.107  15.2802  N
14.9182  10.7941  13.6178  N
15.2676  10.7941  13.6178  N
15.2676  8.53905  11.6297  N
15.6076  8.53905  11.6297  N
15.6076  6.12822  9.75576  I
15.9392  6.12822  9.75576  I
15.9392  4.76229  9.07424  I
16.2634  4.76229  9.07424  I
16.2634  2.79556  7.26399  I
16.5814  2.79556  7.26399  I
16.5814  1.63046  6.3547  L
16.8941  1.63046  6.3547  L
16.8941  0.817151  4.19426  L
17.2026  0.817151  4.19426  L
17.2026  0.487216  3.38935  L
17.508  0.487216  3.38935  L
17.508  0.401363  3.12771  L
17.8112  0.401363  3.12771  L
17.8112  0.400551  3.47849  L
18.1135  0.400551  3.47849  L

