=== Piecewise linear area function ===
position_cm  area_cm2  perimeter_cm  articulator
0  2.29712  5.4334  N
0.125171  2.05484  5.15394  N
0.255361  1.90639  4.96674  N
0.385595  1.72063  4.73457  N
0.515897  1.53562  4.47123  N
0.64629  1.41599  4.31292  N
0.776795  1.25231  4.06049  N
0.907436  1.14195  3.88807  N
1.03812  0.999621  3.66302  N
1.16624  0.864682  3.39294  N
1.29101  0.788611  3.27339  N
1.41253  0.679362  3.02854  N
1.53116  0.616964  2.91531  N
1.648  0.520019  2.66233  N
1.76458  0.456196  2.52809  N
1.87984  0.364672  2.25798  N
1.99377  0.377175  2.32527  N
2.10643  0.793688  4.04289  N
2.21789  1.66539  6.10066  N
2.32825  2.58166  7.197  N
2.43791  3.47191  7.76752  N
2.54715  4.28874  8.16643  N
2.656  4.94351  8.45763  N
2.76449  5.11888  8.52008  N
2.87399  4.9704  8.44054  N
2.98672  4.8179  8.36106  N
3.10363  5.03456  8.90334  N
3.22573  5.31648  9.70558  N
3.35328  5.58929  10.3666  N
3.4833  5.78839  11.0855  N
3.61353  5.62007  10.787  N
3.74358  5.33833  10.4249  N
3.87203  5.18373  10.2998  N
3.9995  5.00889  10.1114  N
4.12697  4.79386  9.86281  N
4.25446  4.62013  9.66976  N
4.38202  4.45836  9.4443  N
4.50966  4.37302  9.26473  N
4.63741  4.4268  9.26949  N
4.76527  4.45797  9.22028  N
4.89326  4.47336  9.09063  N
5.02138  4.92831  8.57873  T
5.14965  4.93126  8.53897  T
5.27812  4.95857  8.56187  T
5.40668  4.98875  8.56993  T
5.53523  5.06083  8.77908  T
5.66378  5.05155  8.75642  T
5.793  5.06342  8.76715  T
5.92336  5.05897  8.76641  T
6.05371  5.05877  8.76957  T
6.18401  5.12014  8.95912  T
6.31424  5.18465  8.98891  T
6.44404  5.26397  9.03122  T
6.57059  5.33445  8.96579  T
6.69381  5.30533  10.045  T
6.81435  5.28428  10.3556  T
6.9334  5.2055  10.3688  T
7.05285  4.81098  9.96598  T
7.17274  4.26217  8.89646  T
7.29314  3.86974  8.0689  T
7.41385  3.70146  7.78059  T
7.53494  3.64965  7.58027  T
7.65652  3.59134  7.56213  T
7.77876  3.40237  7.37982  T
7.90191  3.25914  7.40536  T
8.0264  3.07888  7.13386  T
8.15243  2.87239  6.86997  T
8.28015  2.68417  6.67716  T
8.40866  2.50243  6.49033  T
8.53727  2.32228  6.21078  T
8.66592  2.1412  5.95668  T
8.79461  2.00567  5.87941  T
8.9238  1.88196  5.72919  T
9.05366  1.77672  5.6718  T
9.18389  1.66204  5.52949  T
9.31441  1.5327  5.35723  T
9.44504  1.38781  5.22532  T
9.57571  1.2393  4.98517  T
9.7064  1.0852  4.37976  T
9.83709  0.977817  4.29722  T
9.96779  0.860032  4.04925  T
10.0984  0.815128  4.01958  T
10.229  0.777188  3.98857  T
10.3594  0.740495  3.9645  T
10.4897  0.709663  3.94665  T
10.6198  0.679306  3.92559  T
10.7497  0.661923  3.92567  T
10.8794  0.684026  4.16267  T
11.0086  0.637088  3.92693  T
11.1369  0.619167  3.92631  T
11.2645  0.610388  3.92394  T
11.3915  0.595054  3.80527  T
11.5182  0.617103  3.83019  T
11.6447  0.648305  3.98343  T
11.7705  0.676106  4.01545  T
11.8955  0.715788  4.16243  T
12.02  0.682472  4.03919  T
12.144  0.668022  4.03643  T
12.2677  0.681033  4.04597  T
12.3915  0.697715  4.0609  T
12.5156  0.700261  4.05695  T
12.6402  0.652006  4.11125  T
12.7656  0.56651  3.94151  T
12.8919  0.501057  3.69158  T
13.0186  0.46098  3.55115  T
13.1459  0.417728  3.32119  T
13.2738  0.448755  3.64348  T
13.4025  0.463846  3.75369  T
13.5321  0.478345  3.87471  T
13.6622  0.546209  4.47866  T
13.7919  0.597326  4.56661  T
13.9181  0.727402  5.13581  T
14.0427  0.852219  5.2413  T
14.1668  0.930315  5.28173  T
14.2871  0.971281  5.31347  T
14.3956  1.01906  5.34393  T
14.4951  1.08132  5.38103  T
14.5912  1.18025  5.60983  T
14.6862  1.36348  6.32999  T
14.7811  1.42573  6.20464  T
14.8764  1.68207  6.19297  N
14.9724  1.09032  5.50053  I
15.0692  1.01233  6.906  I
15.1674  1.59709  8.09336  I
15.2675  1.31975  8.56257  L
15.3696  2.51466  7.65069  L
15.4724  2.53509  7.79531  L
15.5766  2.57725  7.80439  L
15.6859  2.47919  7.6349  L

=== Piecewise constant (stepwise changing) area function ===
position_cm  area_cm2  perimeter_cm  articulator
0  1.64972  4.63363  N
0.43554  1.64972  4.63363  N
0.43554  1.17266  3.93605  N
0.87108  1.17266  3.93605  N
0.87108  0.774576  3.24194  N
1.30662  0.774576  3.24194  N
1.30662  0.46847  2.55391  N
1.74216  0.46847  2.55391  N
1.74216  0.364672  2.25798  N
2.1777  0.364672  2.25798  N
2.1777  1.35107  5.35866  N
2.61324  1.35107  5.35866  N
2.61324  4.68629  8.34324  N
3.04878  4.68629  8.34324  N
3.04878  4.93291  8.64891  N
3.48432  4.93291  8.64891  N
3.48432  5.11812  10.2291  N
3.91986  5.11812  10.2291  N
3.91986  4.49211  9.49135  N
4.3554  4.49211  9.49135  N
4.3554  4.37302  9.19428  N
4.79094  4.37302  9.19428  N
4.79094  4.46106  8.53897  N
5.22648  4.46106  8.53897  N
5.22648  4.94759  8.55267  T
5.66202  4.94759  8.55267  T
5.66202  5.05155  8.75642  T
6.09756  5.05155  8.75642  T
6.09756  5.07942  8.83336  T
6.5331  5.07942  8.83336  T
6.5331  5.0891  8.96579  T
6.96864  5.0891  8.96579  T
6.96864  3.66362  7.6343  T
7.50228  3.66362  7.6343  T
7.50228  3.0966  7.16056  T
8.01416  3.0966  7.16056  T
8.01416  2.36717  6.28043  T
8.50523  2.36717  6.28043  T
8.50523  1.83931  5.70593  T
8.97643  1.83931  5.70593  T
8.97643  1.4059  5.2418  T
9.42872  1.4059  5.2418  T
9.42872  0.95443  4.24798  T
9.86304  0.95443  4.24798  T
9.86304  0.762736  3.97909  T
10.2803  0.762736  3.97909  T
10.2803  0.671046  3.92559  T
10.6815  0.671046  3.92559  T
10.6815  0.628845  3.92563  T
11.0676  0.628845  3.92563  T
11.0676  0.595054  3.80527  T
11.4395  0.595054  3.80527  T
11.4395  0.603403  3.81471  T
11.7982  0.603403  3.81471  T
11.7982  0.668022  4.03643  T
12.1445  0.668022  4.03643  T
12.1445  0.668075  4.03647  T
12.4795  0.668075  4.03647  T
12.4795  0.546563  3.86534  T
12.8041  0.546563  3.86534  T
12.8041  0.426777  3.3693  T
13.1192  0.426777  3.3693  T
13.1192  0.417728  3.32119  T
13.4259  0.417728  3.32119  T
13.4259  0.46646  3.77551  T
13.7249  0.46646  3.77551  T
13.7249  0.570918  4.52118  T
14.0174  0.570918  4.52118  T
14.0174  0.826784  5.21981  T
14.3041  0.826784  5.21981  T
14.3041  0.978767  5.31824  T
14.5861  0.978767  5.31824  T
14.5861  1.17501  5.5977  T
14.8644  1.17501  5.5977  T
14.8644  1.01233  5.50053  I
15.1398  1.01233  5.50053  I
15.1398  1.31975  7.65069  L
15.4133  1.31975  7.65069  L
15.4133  2.47919  7.6349  L
15.6859  2.47919  7.6349  L

