=== Piecewise linear area function ===
position_cm  area_cm2  perimeter_cm  articulator
0  2.29712  5.4334  N
0.133725  2.04484  5.14423  N
0.272638  1.83165  4.86687  N
0.411607  1.69261  4.69478  N
0.550661  1.50347  4.4288  N
0.689828  1.37349  4.2489  N
0.829137  1.20751  3.99891  N
0.968616  1.04969  3.73083  N
1.10688  0.949954  3.57301  N
1.24193  0.818744  3.31863  N
1.37335  0.738763  3.17253  N
1.50133  0.632509  2.93906  N
1.62701  0.530594  2.69022  N
1.75243  0.461394  2.53964  N
1.87645  0.365976  2.261  N
1.999  0.375552  2.32265  N
2.12013  0.870855  4.27696  N
2.23995  1.81599  6.33215  N
2.35862  2.79351  7.33344  N
2.47663  3.73116  7.89863  N
2.59417  4.55059  8.28651  N
2.71128  5.08996  8.50539  N
2.82838  4.98028  8.44497  N
2.94783  4.81513  8.35812  N
3.07122  4.91266  8.75329  N
3.20023  5.24284  9.63786  N
3.33545  5.52472  10.323  N
3.474  5.72455  11.023  N
3.61301  5.60055  10.835  N
3.75182  5.40428  10.6052  N
3.88732  5.26151  10.5202  N
4.01801  5.1951  10.5201  N
4.14685  5.10463  10.4666  N
4.2758  4.99537  10.3995  N
4.40502  4.8968  10.3331  N
4.53453  4.81141  10.2647  N
4.66436  4.86211  10.1985  N
4.79453  4.94845  10.1532  N
4.92502  5.02745  10.1138  N
5.05583  5.63372  9.03012  T
5.187  5.68998  9.05202  T
5.3184  5.73534  9.03637  T
5.44976  5.90675  9.20951  T
5.58104  5.98742  9.23452  T
5.71345  6.06624  9.26309  T
5.84974  6.09652  9.2712  T
5.98916  6.12954  9.30016  T
6.12868  6.21912  9.42558  T
6.26817  6.23258  9.45131  T
6.4076  6.25948  9.48542  T
6.54697  6.28454  9.5149  T
6.68632  6.32219  9.54347  T
6.82566  6.37252  9.5873  T
6.96502  6.52504  9.76871  T
7.10441  6.61723  9.83254  T
7.24384  6.71247  9.90575  T
7.38332  6.82089  9.9836  T
7.52283  6.96827  10.0891  T
7.66237  7.24242  10.3349  T
7.80142  7.44993  10.4669  T
7.93914  7.68536  10.6166  T
8.07296  7.99552  10.8935  T
8.2029  8.0302  12.0531  T
8.33168  8.08219  12.4624  T
8.46064  7.99703  12.5332  T
8.58974  7.63852  12.1401  T
8.71875  7.15002  11.0259  T
8.84765  6.87991  10.5175  T
8.97657  6.92846  10.6454  T
9.10575  6.87022  10.6229  T
9.23564  6.79538  10.8633  T
9.3668  6.58123  10.7751  T
9.49977  6.30081  10.6289  T
9.63455  5.96703  10.4668  T
9.76961  5.59011  10.3064  T
9.90481  5.17709  10.1506  T
10.0401  4.75295  9.9301  T
10.1757  4.32589  9.73197  T
10.3125  3.82437  8.98906  T
10.4504  3.31611  8.15466  T
10.5891  2.83847  7.3154  T
10.728  2.47135  6.78744  T
10.8672  2.11791  5.90895  T
11.0064  1.85689  5.53157  T
11.1457  1.71541  5.4602  T
11.2849  1.66908  5.44079  T
11.4242  1.65465  5.44051  T
11.5635  1.67804  5.45865  T
11.7027  1.70126  5.47384  T
11.8419  1.73945  5.49215  T
11.981  1.78403  5.51697  T
12.1197  1.80006  5.51555  T
12.2578  1.80003  5.52485  T
12.3952  1.79825  5.53558  T
12.5322  1.80105  5.54278  T
12.6688  1.82323  5.56643  T
12.8049  1.84467  5.596  T
12.9398  1.87033  5.62762  T
13.0738  1.83348  5.61155  T
13.2071  1.77939  5.4879  T
13.3399  1.74174  5.47329  T
13.4728  1.72455  5.3705  T
13.6061  1.68797  5.34093  T
13.7399  1.55801  5.24709  T
13.8747  1.41621  5.15914  T
14.0105  1.30528  4.98602  T
14.1469  1.2053  4.83394  T
14.284  1.12353  4.67135  T
14.4218  1.06129  4.63052  T
14.5598  0.996205  4.6861  T
14.697  0.923812  4.55171  T
14.8329  0.888122  4.55038  T
14.9678  0.912833  4.83661  T
15.1017  0.884884  4.76708  T
15.2318  0.815125  4.70395  T
15.3492  0.740804  4.56276  T
15.4537  0.668414  4.25677  T
15.5521  0.632944  4.24245  T
15.6479  0.647039  4.26044  T
15.743  0.659312  4.27568  T
15.8382  0.702603  4.51752  T
15.9333  1.17158  5.89329  N
16.0276  1.51096  6.93334  I
16.1215  1.75238  7.79811  I
16.2185  1.5035  7.33334  L
16.321  1.4957  8.45056  L
16.4302  2.51641  7.61267  L
16.547  2.54439  7.62082  L
16.6687  2.4394  7.45771  L

=== Piecewise constant (stepwise changing) area function ===
position_cm  area_cm2  perimeter_cm  articulator
0  1.53305  4.4704  N
0.528917  1.53305  4.4704  N
0.528917  0.985333  3.62899  N
1.05783  0.985333  3.62899  N
1.05783  0.563241  2.76993  N
1.58675  0.563241  2.76993  N
1.58675  0.365976  2.261  N
2.11567  0.365976  2.261  N
2.11567  0.852587  4.20488  N
2.64458  0.852587  4.20488  N
2.64458  4.78276  8.35812  N
3.1735  4.78276  8.35812  N
3.1735  5.17444  9.4546  N
3.70242  5.17444  9.4546  N
3.70242  5.03305  10.4227  N
4.23133  5.03305  10.4227  N
4.23133  4.81141  10.1651  N
4.76025  4.81141  10.1651  N
4.76025  4.92572  9.03012  N
5.28917  4.92572  9.03012  N
5.28917  5.72525  9.03637  T
5.81808  5.72525  9.03637  T
5.81808  6.08949  9.26932  T
6.347  6.08949  9.26932  T
6.347  6.24779  9.4706  T
6.87592  6.24779  9.4706  T
6.87592  6.42752  9.65273  T
7.40483  6.42752  9.65273  T
7.40483  6.84362  9.99987  T
7.93375  6.84362  9.99987  T
7.93375  7.67615  10.6107  T
8.46267  7.67615  10.6107  T
8.46267  6.87991  10.5175  T
8.96501  6.87991  10.5175  T
8.96501  6.41237  10.6229  T
9.44687  6.41237  10.6229  T
9.44687  5.1635  10.1435  T
9.90915  5.1635  10.1435  T
9.90915  3.67604  8.74555  T
10.3527  3.67604  8.74555  T
10.3527  2.34321  6.46895  T
10.7785  2.34321  6.46895  T
10.7785  1.70154  5.4544  T
11.1873  1.70154  5.4544  T
11.1873  1.65465  5.44051  T
11.5802  1.65465  5.44051  T
11.5802  1.68082  5.46047  T
11.9578  1.68082  5.46047  T
11.9578  1.77662  5.51284  T
12.3213  1.77662  5.51284  T
12.3213  1.79825  5.52981  T
12.6714  1.79825  5.52981  T
12.6714  1.82364  5.56699  T
13.009  1.82364  5.56699  T
13.009  1.74314  5.47383  T
13.335  1.74314  5.47383  T
13.335  1.64499  5.30989  T
13.6504  1.64499  5.30989  T
13.6504  1.34984  5.05556  T
13.9559  1.34984  5.05556  T
13.9559  1.14227  4.70862  T
14.2526  1.14227  4.70862  T
14.2526  1.00498  4.63052  T
14.5412  1.00498  4.63052  T
14.5412  0.89079  4.55048  T
14.8228  0.89079  4.55048  T
14.8228  0.885645  4.55038  T
15.098  0.885645  4.55038  T
15.098  0.727796  4.50777  T
15.368  0.727796  4.50777  T
15.368  0.632944  4.24245  T
15.6335  0.632944  4.24245  T
15.6335  0.644921  4.25773  T
15.8954  0.644921  4.25773  T
15.8954  0.984735  5.34518  N
16.1547  0.984735  5.34518  N
16.1547  1.4957  7.33334  L
16.4121  1.4957  7.33334  L
16.4121  2.34774  7.45771  L
16.6687  2.34774  7.45771  L

