=== Piecewise linear area function ===
position_cm  area_cm2  perimeter_cm  articulator
0  2.29712  5.4334  N
0.138334  2.02988  5.12817  N
0.283234  1.81265  4.84476  N
0.428217  1.66719  4.66006  N
0.573322  1.47643  4.3957  N
0.718592  1.29562  4.12638  N
0.864066  1.17565  3.95408  N
1.00978  1.01755  3.69068  N
1.15368  0.912905  3.50137  N
1.29342  0.786683  3.27053  N
1.42957  0.669664  3.00921  N
1.56266  0.601107  2.88326  N
1.69343  0.49599  2.60966  N
1.82257  0.426721  2.45938  N
1.95024  0.354483  2.23169  N
2.07653  0.554671  3.2933  N
2.20149  1.2908  5.40441  N
2.32531  2.24429  7.035  N
2.44871  3.10596  7.59659  N
2.57225  3.87058  7.9742  N
2.69593  4.5005  8.25451  N
2.81979  4.87107  8.39509  N
2.94571  5.57877  10.6922  N
3.07503  5.43371  10.4864  N
3.20823  5.13824  10.4162  N
3.34624  4.85968  10.3382  N
3.48844  4.44942  10.0708  N
3.62688  4.04024  9.82052  N
3.76294  3.56557  9.38499  N
3.89905  3.08366  8.80018  N
4.03524  2.72957  8.32202  N
4.17146  2.55261  8.10054  N
4.30818  2.4133  7.91833  N
4.44567  2.27606  7.69437  N
4.58371  2.62077  6.69882  T
4.72244  2.51937  6.55865  T
4.86194  2.43169  6.40895  T
5.00203  2.36633  6.36167  T
5.14225  2.30637  6.32113  T
5.28253  2.22326  6.19907  T
5.42367  2.159  6.16823  T
5.5679  2.10917  6.14345  T
5.713  2.05248  6.04195  T
5.85812  2.08158  6.21459  T
6.00327  2.12605  6.32823  T
6.14849  2.17892  6.44327  T
6.29383  2.28916  6.60627  T
6.43928  2.40357  6.74623  T
6.58483  2.5573  7.00909  T
6.7305  2.72253  7.19484  T
6.87599  2.8997  7.36833  T
7.02013  3.11662  7.65611  T
7.16025  3.35107  7.94796  T
7.29645  3.58787  8.07073  T
7.43018  3.67069  9.17031  T
7.56396  3.79489  9.59307  T
7.69809  3.71484  9.40033  T
7.8321  3.35499  8.98295  T
7.96621  2.89129  7.94669  T
8.10063  2.57361  7.15144  T
8.23568  2.53808  7.21666  T
8.37192  2.59985  7.09347  T
8.50992  2.5875  7.08506  T
8.65019  2.47679  7.02973  T
8.79229  2.43829  7.10137  T
8.93482  2.31832  6.96155  T
9.07756  2.21808  6.91206  T
9.22037  2.16469  7.06543  T
9.36348  2.10164  7.02997  T
9.50772  2.00474  6.80799  T
9.65295  1.94757  6.95822  T
9.79839  1.8938  7.03814  T
9.94401  1.77632  6.68591  T
10.0897  1.63316  6.22722  T
10.2354  1.46679  5.75855  T
10.381  1.30074  5.31699  T
10.5267  1.17251  5.17015  T
10.6724  1.03334  4.79021  T
10.818  0.906317  4.34667  T
10.9636  0.882276  4.32178  T
11.1093  0.863168  4.22189  T
11.2548  0.845956  4.12293  T
11.4004  0.841416  4.11553  T
11.5458  0.832544  4.02882  T
11.6912  0.835075  4.02946  T
11.8363  0.828319  4.03634  T
11.9808  0.786895  4.00479  T
12.1246  0.742245  3.80419  T
12.2678  0.715342  3.77425  T
12.4105  0.687225  3.65761  T
12.552  0.682685  3.68824  T
12.6911  0.672569  3.56887  T
12.8282  0.612661  3.31591  T
12.9619  0.537796  2.9432  T
13.0908  0.505976  2.8918  T
13.2162  0.476412  2.78354  T
13.34  0.462396  2.70115  T
13.4641  0.382285  2.5877  T
13.5893  0.294179  2.32198  T
13.7143  0.22979  2.14565  T
13.8388  0.155294  1.68629  T
13.9641  0.15  1.53126  T
14.091  0.15  1.37294  T
14.2203  0.15  1.37294  T
14.3511  0.15  1.37294  T
14.4825  0.15  2.06093  T
14.6104  0.328268  3.4748  N
14.7315  1.22119  5.78367  N
14.8481  2.12244  6.58081  N
14.9587  2.52858  6.85778  N
15.0631  3.36277  9.9176  N
15.1645  3.93184  9.95054  N
15.2667  4.21152  10.032  N
15.3704  4.2907  9.69479  N
15.474  4.76923  9.48249  N
15.5748  4.00411  8.52757  N
15.6783  2.62902  7.04365  I
15.7879  1.83984  6.19943  I
15.9048  1.20035  6.08426  I
16.0289  0.602516  5.62636  I
16.1545  0.450674  6.53843  I
16.2801  1.28068  5.50543  L
16.4058  1.08807  6.19653  L
16.5325  2.10094  5.74774  L
16.6606  2.19561  6.36985  L
16.7905  2.38129  6.8117  L
16.9257  2.62632  7.26321  L
17.0663  2.89466  7.55953  L
17.2084  3.04533  7.65193  L

=== Piecewise constant (stepwise changing) area function ===
position_cm  area_cm2  perimeter_cm  articulator
0  1.59518  4.56026  N
0.482993  1.59518  4.56026  N
0.482993  1.06507  3.76985  N
0.965986  1.06507  3.76985  N
0.965986  0.659668  2.99085  N
1.44898  0.659668  2.99085  N
1.44898  0.364822  2.26428  N
1.93197  0.364822  2.26428  N
1.93197  0.354483  2.23169  N
2.41496  0.354483  2.23169  N
2.41496  2.87035  7.44303  N
2.89796  2.87035  7.44303  N
2.89796  4.75954  9.82102  N
3.38095  4.75954  9.82102  N
3.38095  3.20797  8.95102  N
3.86394  3.20797  8.95102  N
3.86394  2.37462  7.8552  N
4.34694  2.37462  7.8552  N
4.34694  2.27606  6.4433  N
4.82993  2.27606  6.4433  N
4.82993  2.20943  6.19243  T
5.31292  2.20943  6.19243  T
5.31292  2.05248  6.04195  T
5.79591  2.05248  6.04195  T
5.79591  2.06911  6.14059  T
6.27891  2.06911  6.14059  T
6.27891  2.27784  6.58954  T
6.7619  2.27784  6.58954  T
6.7619  2.76077  7.23229  T
7.24489  2.76077  7.23229  T
7.24489  3.49824  8.02426  T
7.72789  3.49824  8.02426  T
7.72789  2.53808  7.15105  T
8.30825  2.53808  7.15105  T
8.30825  2.37713  7.02973  T
8.86494  2.37713  7.02973  T
8.86494  2.07777  6.91206  T
9.39901  2.07777  6.91206  T
9.39901  1.80257  6.76461  T
9.91148  1.80257  6.76461  T
9.91148  1.28109  5.29449  T
10.4034  1.28109  5.29449  T
10.4034  0.896793  4.33681  T
10.8757  0.896793  4.33681  T
10.8757  0.843625  4.11913  T
11.3295  0.843625  4.11913  T
11.3295  0.831598  4.02882  T
11.7659  0.831598  4.02882  T
11.7659  0.730754  3.7914  T
12.1858  0.730754  3.7914  T
12.1858  0.679904  3.65542  T
12.5902  0.679904  3.65542  T
12.5902  0.53327  2.93589  T
12.9803  0.53327  2.93589  T
12.9803  0.45144  2.68564  T
13.3569  0.45144  2.68564  T
13.3569  0.225592  2.11976  T
13.7213  0.225592  2.11976  T
13.7213  0.15  1.39376  T
14.0743  0.15  1.39376  T
14.0743  0.15  1.37294  T
14.417  0.15  1.37294  T
14.417  0.15  1.71817  T
14.7505  0.15  1.71817  T
14.7505  1.36772  5.91328  N
15.0757  1.36772  5.91328  N
15.0757  3.43346  9.647  N
15.3938  3.43346  9.647  N
15.3938  2.43243  6.83335  I
15.7056  2.43243  6.83335  I
15.7056  0.682305  5.68748  I
16.0124  0.682305  5.68748  I
16.0124  0.450674  5.50543  I
16.315  0.450674  5.50543  I
16.315  1.08807  5.69704  L
16.6145  1.08807  5.69704  L
16.6145  2.16154  6.146  L
16.912  2.16154  6.146  L
16.912  2.60139  7.21728  L
17.2084  2.60139  7.21728  L

