=== Piecewise linear area function ===
position_cm  area_cm2  perimeter_cm  articulator
0  2.29712  5.4334  N
0.157896  2.03454  5.13063  N
0.318736  1.7986  4.8218  N
0.479625  1.57909  4.52783  N
0.640589  1.43062  4.33328  N
0.80165  1.23711  4.03489  N
0.962788  1.05853  3.74258  N
1.12141  0.94248  3.55162  N
1.27592  0.800125  3.29129  N
1.42501  0.67579  3.0171  N
1.56957  0.598974  2.86643  N
1.71099  0.483767  2.58271  N
1.85026  0.375702  2.28174  N
1.98697  0.442772  2.54212  N
2.12125  1.17144  4.82016  N
2.25327  2.41274  6.91886  N
2.38345  3.65162  7.8245  N
2.51291  4.8149  8.44583  N
2.64196  5.74047  8.87893  N
2.7714  5.77805  8.88562  N
2.90393  5.59873  8.79259  N
3.0428  5.46726  8.73068  N
3.19023  5.62412  8.98336  N
3.34707  6.13993  10.0797  N
3.50711  6.71352  11.7307  N
3.66709  6.60747  11.8023  N
3.82489  6.45474  11.5961  N
3.97818  6.2799  11.4161  N
4.13028  6.11621  11.2649  N
4.28245  5.97257  11.1317  N
4.43482  5.82722  10.9932  N
4.58739  5.76734  10.7496  N
4.74013  5.87046  10.723  N
4.89299  5.88584  10.577  N
5.04588  6.43473  9.42775  T
5.19876  6.39794  9.37565  T
5.35141  6.36315  9.32136  T
5.50377  6.44475  9.43802  T
5.65658  6.44765  9.44835  T
5.81369  6.37501  9.40301  T
5.97418  6.25318  9.34348  T
6.1346  6.1513  9.35813  T
6.29501  5.9825  9.27104  T
6.45555  5.79326  9.14944  T
6.61623  5.50105  9.01425  T
6.777  5.11188  8.66828  T
6.93778  4.72655  8.46197  T
7.0985  4.35679  8.25295  T
7.25908  4.02497  7.99384  T
7.4194  3.73909  7.73778  T
7.57946  3.50638  7.62434  T
7.73928  3.29069  7.34785  T
7.899  3.15619  7.28479  T
8.05881  3.04184  7.22652  T
8.21877  2.97094  7.29228  T
8.37815  2.96859  7.37656  T
8.53442  2.9878  7.40684  T
8.68411  3.05048  7.52935  T
8.83015  2.93262  8.58722  T
8.97621  2.84994  8.60766  T
9.12321  2.67483  8.29882  T
9.27072  2.07874  6.95684  T
9.41864  1.62835  5.84981  T
9.56738  1.38851  5.44614  T
9.71691  1.3479  5.26487  T
9.86787  1.35739  5.29868  T
10.0211  1.23584  5.24101  T
10.1766  1.08353  5.0597  T
10.3332  0.955201  4.80898  T
10.4899  0.768143  4.28677  T
10.6465  0.645985  4.12712  T
10.803  0.559041  3.99643  T
10.9605  0.445732  3.61357  T
11.1189  0.388974  3.37598  T
11.2778  0.343311  3.24748  T
11.4371  0.334461  3.24377  T
11.5968  0.317205  3.03777  T
11.7568  0.301335  3.02084  T
11.9171  0.31204  3.03303  T
12.0776  0.332306  3.14896  T
12.2382  0.399365  3.51627  T
12.3988  0.552661  4.01641  T
12.5594  0.802313  5.00384  T
12.7199  1.04883  5.40048  T
12.8802  1.33701  5.8266  T
13.0404  1.68275  6.38611  T
13.2003  1.99605  6.7311  T
13.3598  2.2805  7.05773  T
13.519  2.54205  7.20459  T
13.678  2.85441  7.55373  T
13.8365  3.14833  7.7366  T
13.9901  3.37278  7.86891  T
14.1383  3.56279  8.13593  T
14.2825  3.75875  8.25082  T
14.4239  3.89521  8.31301  T
14.5638  3.97144  8.48936  T
14.7038  4.02338  8.50138  T
14.8449  4.05485  8.51647  T
14.9872  4.00727  8.3412  T
15.1293  3.90433  8.16212  T
15.2664  3.82557  8.12875  T
15.3984  3.74338  7.97176  T
15.5259  4.22516  11.3494  T
15.6512  4.31682  11.2729  T
15.7775  8.18516  13.0653  N
15.9052  9.22584  13.5316  N
16.0345  9.42814  12.852  N
16.1683  8.00509  11.5459  N
16.3055  6.74001  10.5971  N
16.4462  5.41604  9.39362  N
16.5854  4.56575  8.58015  I
16.72  3.92705  7.91084  I
16.853  3.1151  7.32314  I
16.9803  2.48466  7.12397  I
17.1037  1.86743  6.63843  I
17.2269  1.45937  6.08665  I
17.3501  1.7298  6.89748  I
17.4734  1.2352  6.9208  L
17.5979  1.5089  5.37677  L
17.7239  0.965914  4.65067  L
17.855  0.722888  4.19238  L
17.9924  0.504974  3.37797  L
18.1334  0.406934  2.7155  L
18.2806  0.392431  2.69258  L
18.4323  0.354268  2.49092  L
18.587  0.333784  2.45916  L
18.7465  0.349877  2.83875  L
18.9073  0.376809  2.89605  L
19.0684  0.406575  2.93141  L

=== Piecewise constant (stepwise changing) area function ===
position_cm  area_cm2  perimeter_cm  articulator
0  1.49666  4.41982  N
0.568988  1.49666  4.41982  N
0.568988  0.92722  3.52372  N
1.13798  0.92722  3.52372  N
1.13798  0.487046  2.59078  N
1.70696  0.487046  2.59078  N
1.70696  0.375702  2.28174  N
2.27595  0.375702  2.28174  N
2.27595  2.62861  7.07667  N
2.84494  2.62861  7.07667  N
2.84494  5.46726  8.73068  N
3.41393  5.46726  8.73068  N
3.41393  6.2748  10.7694  N
3.98292  6.2748  10.7694  N
3.98292  5.78127  10.8063  N
4.5519  5.78127  10.8063  N
4.5519  5.76734  9.40219  N
5.12089  5.76734  9.40219  N
5.12089  6.36315  9.32136  T
5.68988  6.36315  9.32136  T
5.68988  6.02053  9.29066  T
6.25887  6.02053  9.29066  T
6.25887  4.99  8.60302  T
6.82786  4.99  8.60302  T
6.82786  3.77931  7.77381  T
7.39684  3.77931  7.77381  T
7.39684  3.10837  7.26042  T
7.96583  3.10837  7.26042  T
7.96583  2.96859  7.22652  T
8.53482  2.96859  7.22652  T
8.53482  2.69794  7.40716  T
9.10381  2.69794  7.40716  T
9.10381  1.34874  5.26864  T
9.7138  1.34874  5.26864  T
9.7138  0.983269  4.86382  T
10.2989  0.983269  4.86382  T
10.2989  0.517858  3.85728  T
10.8603  0.517858  3.85728  T
10.8603  0.336583  3.24466  T
11.3989  0.336583  3.24466  T
11.3989  0.301335  3.02084  T
11.9159  0.301335  3.02084  T
11.9159  0.311959  3.03294  T
12.4124  0.311959  3.03294  T
12.4124  0.573744  4.09979  T
12.8894  0.573744  4.09979  T
12.8894  1.35679  5.85861  T
13.348  1.35679  5.85861  T
13.348  2.25937  7.03347  T
13.7893  2.25937  7.03347  T
13.7893  3.06082  7.68215  T
14.2144  3.06082  7.68215  T
14.2144  3.66621  8.19656  T
14.6244  3.66621  8.19656  T
14.6244  3.9833  8.2995  T
15.0203  3.9833  8.2995  T
15.0203  3.74338  7.97176  T
15.4032  3.74338  7.97176  T
15.4032  3.76167  8.09997  T
15.7743  3.76167  8.09997  T
15.7743  8.0865  11.8754  N
16.1345  8.0865  11.8754  N
16.1345  5.179  9.16685  N
16.485  5.179  9.16685  N
16.485  3.27476  7.43871  I
16.8269  3.27476  7.43871  I
16.8269  1.67715  6.38113  I
17.1611  1.67715  6.38113  I
17.1611  1.2352  6.08665  L
17.4889  1.2352  6.08665  L
17.4889  0.803885  4.34512  L
17.8113  0.803885  4.34512  L
17.8113  0.409714  2.73429  L
18.1294  0.409714  2.73429  L
18.1294  0.35269  2.48847  L
18.4442  0.35269  2.48847  L
18.4442  0.333784  2.45916  L
18.7569  0.333784  2.45916  L
18.7569  0.351611  2.84244  L
19.0684  0.351611  2.84244  L

