=== Piecewise linear area function ===
position_cm  area_cm2  perimeter_cm  articulator
0  2.29712  5.4334  N
0.135011  2.0418  5.14093  N
0.275439  1.82747  4.86191  N
0.415928  1.68675  4.68683  N
0.556509  1.49713  4.42076  N
0.697213  1.36585  4.23853  N
0.83807  1.19962  3.98728  N
0.979094  1.04182  3.72077  N
1.11878  0.940618  3.55236  N
1.25562  0.81012  3.30777  N
1.38849  0.691767  3.05662  N
1.51796  0.623845  2.9238  N
1.64598  0.519768  2.66311  N
1.77335  0.45095  2.51794  N
1.8992  0.355515  2.23905  N
2.0236  0.413626  2.49076  N
2.14661  1.035  4.72298  N
2.26832  2.00302  6.58811  N
2.38901  2.98458  7.46634  N
2.5091  3.90609  7.972  N
2.62871  4.67528  8.325  N
2.74788  5.00016  8.45458  N
2.86741  4.85709  8.37859  N
2.9892  4.69766  8.29572  N
3.1159  5.01274  9.20742  N
3.24856  5.31998  9.98502  N
3.38645  5.59585  10.6782  N
3.52693  5.5827  10.8616  N
3.66741  5.32778  10.4717  N
3.80759  5.02611  10.1285  N
3.94721  4.82302  9.9074  N
4.0868  4.58356  9.62241  N
4.2264  4.36084  9.3361  N
4.36602  4.15175  9.06465  N
4.50567  4.0241  8.78022  N
4.64536  3.96517  8.56438  N
4.78508  3.95023  8.48094  N
4.92482  4.22895  7.9623  T
5.06461  4.18579  7.92633  T
5.20444  4.15075  7.89319  T
5.34433  4.13268  7.87021  T
5.48429  4.09207  7.84958  T
5.6244  4.01698  7.74264  T
5.76474  3.95529  7.72167  T
5.90569  3.84841  7.60205  T
6.04667  3.76019  7.55227  T
6.18759  3.69267  7.51283  T
6.32843  3.61995  7.39644  T
6.4692  3.56577  7.36908  T
6.60992  3.54817  7.36257  T
6.75063  3.5341  7.35492  T
6.89132  3.53312  7.41495  T
7.03203  3.58607  7.50784  T
7.17275  3.63266  7.53409  T
7.31352  3.68212  7.5653  T
7.45435  3.81084  7.8006  T
7.59522  3.94748  7.95864  T
7.73614  4.09206  8.11508  T
7.87511  4.26719  8.28915  T
8.01083  4.48122  8.47978  T
8.1428  4.7095  8.60205  T
8.27197  4.77977  9.52412  T
8.40122  4.77267  9.64901  T
8.5309  4.73333  9.75935  T
8.66088  4.46007  9.45575  T
8.79103  4.02599  8.52843  T
8.92144  3.7394  7.79533  T
9.0518  3.68353  7.57766  T
9.18245  3.75405  7.60917  T
9.31392  3.79053  7.65052  T
9.44676  3.6942  7.59844  T
9.58155  3.60067  7.47796  T
9.71773  3.41915  7.29456  T
9.8536  3.18162  7.07101  T
9.98911  3.00138  7.06582  T
10.1241  2.83104  6.7873  T
10.2598  2.68262  6.71401  T
10.3968  2.55489  6.66742  T
10.5352  2.47068  6.70515  T
10.6744  2.33629  6.35887  T
10.8144  2.18169  6.09928  T
10.9547  2.01847  5.8521  T
11.0952  1.91272  5.71499  T
11.2358  1.81821  5.656  T
11.3766  1.73952  5.52595  T
11.5174  1.77042  5.54694  T
11.6582  1.8952  5.77441  T
11.7991  2.03736  5.86709  T
11.94  2.24814  6.29518  T
12.0809  2.44822  6.57584  T
12.2218  2.64633  6.6786  T
12.3627  2.85482  6.96186  T
12.5033  2.96496  7.00855  T
12.6435  3.07189  7.07128  T
12.7835  3.17418  7.13711  T
12.9234  3.27409  7.20372  T
13.0632  3.36914  7.27268  T
13.2024  3.46005  7.34359  T
13.3408  3.45417  7.33952  T
13.4785  3.42237  7.32846  T
13.6159  3.39561  7.31823  T
13.753  3.38142  7.32719  T
13.8902  3.28977  7.26  T
14.0275  3.09962  7.07024  T
14.1651  2.90097  6.95611  T
14.3034  2.70758  6.76572  T
14.4422  2.5434  6.67662  T
14.5814  2.39256  6.59905  T
14.7209  2.22604  6.34195  T
14.8608  2.08285  6.3029  T
15.0001  1.92464  6.09276  T
15.1375  1.84517  6.02984  T
15.273  1.70374  5.78932  T
15.4071  1.53714  5.67069  T
15.5346  1.32989  5.37423  T
15.6506  1.16456  5.27168  T
15.7557  1.02034  5.08771  T
15.8557  0.870365  4.54618  T
15.954  0.826008  4.53571  T
16.0508  0.805297  4.5296  T
16.1465  0.919055  5.72279  T
16.2417  1.24041  5.88783  N
16.3361  1.48939  5.90237  I
16.4297  1.94176  8.5369  I
16.524  1.94374  8.06918  L
16.6234  2.44871  7.45267  L
16.7291  2.48673  7.60018  L
16.8422  2.50049  7.47099  L
16.9621  2.46413  7.58372  L

=== Piecewise constant (stepwise changing) area function ===
position_cm  area_cm2  perimeter_cm  articulator
0  1.52627  4.46165  N
0.534903  1.52627  4.46165  N
0.534903  0.976101  3.6114  N
1.06981  0.976101  3.6114  N
1.06981  0.55332  2.74715  N
1.60471  0.55332  2.74715  N
1.60471  0.355515  2.23905  N
2.13961  0.355515  2.23905  N
2.13961  0.999624  4.5959  N
2.67451  0.999624  4.5959  N
2.67451  4.69766  8.29572  N
3.20942  4.69766  8.29572  N
3.20942  5.16227  9.75558  N
3.74432  5.16227  9.75558  N
3.74432  4.28174  9.23341  N
4.27922  4.28174  9.23341  N
4.27922  3.95023  8.37313  N
4.81412  3.95023  8.37313  N
4.81412  4.00817  7.86952  T
5.34903  4.00817  7.86952  T
5.34903  3.86491  7.62052  T
5.88393  3.86491  7.62052  T
5.88393  3.58516  7.37887  T
6.41883  3.58516  7.37887  T
6.41883  3.53312  7.35492  T
6.95373  3.53312  7.35492  T
6.95373  3.55661  7.45615  T
7.48864  3.55661  7.45615  T
7.48864  3.8441  7.83907  T
8.02354  3.8441  7.83907  T
8.02354  4.50321  8.49156  T
8.55844  4.50321  8.49156  T
8.55844  3.68353  7.57766  T
9.07288  3.68353  7.57766  T
9.07288  3.61122  7.49156  T
9.56634  3.61122  7.49156  T
9.56634  2.9375  6.96137  T
10.0397  2.9375  6.96137  T
10.0397  2.49577  6.66742  T
10.494  2.49577  6.66742  T
10.494  2.0472  5.89561  T
10.93  2.0472  5.89561  T
10.93  1.7551  5.55169  T
11.3487  1.7551  5.55169  T
11.3487  1.73952  5.52595  T
11.751  1.73952  5.52595  T
11.751  1.98882  5.83544  T
12.1378  1.98882  5.83544  T
12.1378  2.52811  6.61727  T
12.5099  2.52811  6.61727  T
12.5099  2.97005  7.01154  T
12.8685  2.97005  7.01154  T
12.8685  3.23483  7.17755  T
13.2142  3.23483  7.17755  T
13.2142  3.40881  7.32328  T
13.5481  3.40881  7.32328  T
13.5481  3.30255  7.26936  T
13.871  3.30255  7.26936  T
13.871  2.87464  6.93019  T
14.1839  2.87464  6.93019  T
14.1839  2.49407  6.65125  T
14.4877  2.49407  6.65125  T
14.4877  2.16216  6.32453  T
14.7833  2.16216  6.32453  T
14.7833  1.88325  6.05998  T
15.0716  1.88325  6.05998  T
15.0716  1.60367  5.71806  T
15.3535  1.60367  5.71806  T
15.3535  1.19393  5.2899  T
15.63  1.19393  5.2899  T
15.63  0.849522  4.54126  T
15.9019  0.849522  4.54126  T
15.9019  0.805297  4.5296  T
16.1701  0.805297  4.5296  T
16.1701  0.998717  5.7637  N
16.4356  0.998717  5.7637  N
16.4356  1.94188  7.45267  L
16.6993  1.94188  7.45267  L
16.6993  2.46413  7.47099  L
16.9621  2.46413  7.47099  L

