=== Piecewise linear area function ===
position_cm  area_cm2  perimeter_cm  articulator
0  2.29712  5.4334  N
0.135059  1.98891  5.08217  N
0.282557  1.77629  4.80525  N
0.430224  1.63062  4.6164  N
0.578144  1.44589  4.36122  N
0.726401  1.26841  4.09092  N
0.875078  1.15137  3.91778  N
1.02423  0.997621  3.66126  N
1.17228  0.852881  3.38125  N
1.3178  0.768138  3.2431  N
1.46012  0.651178  2.97908  N
1.59968  0.578823  2.84647  N
1.73858  0.473545  2.56722  N
1.87702  0.405689  2.42028  N
2.0147  0.338244  2.23906  N
2.15164  0.544118  3.6136  N
2.28789  1.22378  5.90449  N
2.42342  1.95588  6.97499  N
2.55802  2.60975  7.26134  N
2.69167  3.17576  7.46444  N
2.82445  3.29512  7.48377  N
2.9568  3.0592  7.37447  N
3.09079  2.8384  7.25708  N
3.22849  3.42329  8.85959  N
3.37159  3.67354  9.25981  N
3.51946  3.54598  9.20431  N
3.66824  3.31675  9.07034  N
3.81664  3.02238  8.86713  N
3.96267  2.87943  8.86969  N
4.10235  2.7848  8.89375  N
4.23704  2.69002  8.96534  N
4.37122  2.56208  8.90461  N
4.50586  2.4587  8.93911  N
4.64105  2.41802  8.89253  N
4.77688  2.54669  8.965  N
4.91344  2.66136  8.91602  N
5.05077  3.61416  7.63433  T
5.18892  3.73024  7.77575  T
5.32788  3.81511  7.80485  T
5.46734  3.98882  7.93633  T
5.60679  4.18234  8.04084  T
5.74647  4.38277  8.12124  T
5.88909  4.65695  8.35465  T
6.03593  4.88387  8.55414  T
6.18514  5.0676  8.65446  T
6.33436  5.21977  8.82126  T
6.48358  5.35873  8.9335  T
6.63281  5.49228  9.00185  T
6.78205  5.62994  9.07939  T
6.93129  5.81433  9.31058  T
7.08053  5.96518  9.38403  T
7.22978  6.1245  9.47531  T
7.37904  6.34662  9.73512  T
7.52825  6.53366  9.84759  T
7.67628  6.69375  9.95142  T
7.81972  6.7077  11.1018  T
7.95899  6.65155  11.4009  T
8.09547  6.47231  11.3901  T
8.232  5.86747  10.4606  T
8.36852  5.36463  9.39812  T
8.50497  5.11025  8.94569  T
8.64148  5.05926  9.01963  T
8.77842  4.93703  8.96506  T
8.91627  4.70633  8.78  T
9.05558  4.47135  8.6845  T
9.19681  4.19098  8.49363  T
9.34023  3.90402  8.18508  T
9.48578  3.6084  7.96037  T
9.63219  3.24503  7.52012  T
9.77881  2.91292  7.26771  T
9.92557  2.63621  7.16353  T
10.0731  2.32257  6.41407  T
10.2217  2.01724  5.82105  T
10.3706  1.719  5.41743  T
10.5196  1.45498  5.22981  T
10.6686  1.20712  4.92819  T
10.8177  0.969333  4.1324  T
10.9667  0.816893  3.94187  T
11.1156  0.752654  3.88561  T
11.2642  0.7073  3.84685  T
11.4127  0.695467  3.83717  T
11.561  0.684294  3.82892  T
11.709  0.715072  3.95808  T
11.8567  0.769149  4.19734  T
12.0038  0.760645  3.99281  T
12.1499  0.786992  4.01141  T
12.2954  0.811929  4.02654  T
12.4403  0.864895  4.15198  T
12.585  0.93127  4.19891  T
12.7293  0.996752  4.25136  T
12.8726  1.06349  4.38637  T
13.0154  1.06796  4.38328  T
13.1579  1.06901  4.30875  T
13.3004  1.11358  4.34245  T
13.4433  1.19037  4.81754  T
13.5869  1.13419  4.75244  T
13.7313  1.09981  5.07276  T
13.8767  1.02867  4.76012  T
14.0225  0.974187  4.50064  T
14.1688  0.939956  4.28433  T
14.3156  0.923608  4.27084  T
14.4629  0.929464  4.5859  T
14.6103  0.929292  4.65842  T
14.7575  0.942972  4.66987  T
14.9032  1.05206  4.99643  T
15.0468  1.09957  4.89092  T
15.1905  1.14162  5.06872  T
15.3268  1.16356  5.07885  T
15.4473  1.21738  5.30997  T
15.5541  1.27696  5.3638  T
15.6531  1.57251  6.7366  T
15.7483  1.81061  6.7877  T
15.8419  2.02955  6.81859  T
15.9342  2.27198  6.87414  N
16.0257  2.81079  7.18737  I
16.1196  2.17142  6.67463  I
16.2176  2.35967  8.29537  I
16.3203  1.47275  6.95101  L
16.4249  1.21387  6.00189  L
16.5348  1.26258  4.8154  L
16.6512  0.870903  4.307  L
16.7738  0.647591  3.68595  L
16.9027  0.547494  3.19247  L
17.0359  0.507025  3.014  L
17.1704  0.485186  2.98979  L
17.306  0.47046  3.1154  L
17.4457  0.474055  3.34809  L
17.5914  0.503265  3.40591  L
17.74  0.55039  3.57969  L

=== Piecewise constant (stepwise changing) area function ===
position_cm  area_cm2  perimeter_cm  articulator
0  1.53795  4.48839  N
0.504426  1.53795  4.48839  N
0.504426  1.01347  3.68772  N
1.00885  1.01347  3.68772  N
1.00885  0.623617  2.92856  N
1.51328  0.623617  2.92856  N
1.51328  0.338244  2.23906  N
2.0177  0.338244  2.23906  N
2.0177  0.342763  2.26923  N
2.52213  0.342763  2.26923  N
2.52213  2.43542  7.18499  N
3.02656  2.43542  7.18499  N
3.02656  2.8384  7.25708  N
3.53098  2.8384  7.25708  N
3.53098  2.83015  8.86713  N
4.03541  2.83015  8.86713  N
4.03541  2.44848  8.88222  N
4.53984  2.44848  8.88222  N
4.53984  2.41802  7.69507  N
5.04426  2.41802  7.69507  N
5.04426  3.56901  7.63433  T
5.54869  3.56901  7.63433  T
5.54869  4.10171  7.99729  T
6.05311  4.10171  7.99729  T
6.05311  4.90503  8.56569  T
6.55754  4.90503  8.56569  T
6.55754  5.42492  8.96737  T
7.06197  5.42492  8.96737  T
7.06197  5.94641  9.37489  T
7.56639  5.94641  9.37489  T
7.56639  6.50468  9.87434  T
8.07082  6.50468  9.87434  T
8.07082  5.0403  8.94569  T
8.66273  5.0403  8.94569  T
8.66273  4.12356  8.42114  T
9.23051  4.12356  8.42114  T
9.23051  2.92108  7.27392  T
9.7752  2.92108  7.27392  T
9.7752  1.86465  5.61454  T
10.2979  1.86465  5.61454  T
10.2979  0.998256  4.2292  T
10.7995  0.998256  4.2292  T
10.7995  0.705941  3.84574  T
11.2813  0.705941  3.84574  T
11.2813  0.684294  3.82892  T
11.7442  0.684294  3.82892  T
11.7442  0.727933  3.99281  T
12.1892  0.727933  3.99281  T
12.1892  0.79372  4.01549  T
12.6174  0.79372  4.01549  T
12.6174  0.945968  4.21068  T
13.0299  0.945968  4.21068  T
13.0299  1.06807  4.30875  T
13.4277  1.06807  4.30875  T
13.4277  1.06037  4.75244  T
13.8119  1.06037  4.75244  T
13.8119  0.938322  4.28299  T
14.1835  0.938322  4.28299  T
14.1835  0.923608  4.27084  T
14.5435  0.923608  4.27084  T
14.5435  0.929292  4.62555  T
14.8931  0.929292  4.62555  T
14.8931  1.0445  4.89092  T
15.2332  1.0445  4.89092  T
15.2332  1.14849  5.07189  T
15.5649  1.14849  5.07189  T
15.5649  1.30907  5.51295  T
15.8893  1.30907  5.51295  T
15.8893  2.15388  6.67463  I
16.2073  2.15388  6.67463  I
16.2073  1.21387  4.97325  L
16.5202  1.21387  4.97325  L
16.5202  0.604895  3.47545  L
16.8288  0.604895  3.47545  L
16.8288  0.491045  2.99628  L
17.1343  0.491045  2.99628  L
17.1343  0.47046  2.98979  L
17.4377  0.47046  2.98979  L
17.4377  0.473848  3.3347  L
17.74  0.473848  3.3347  L

