(*  The following are examples of curvature analysis  on  individual tubercles in seeds of Euphorbiaceae*)






	(*******************************  VerdejoSal*)

Needs["Splines`"]

VerdejoSal[1]={{1.41944,2.6588},{1.44063,2.54228},{1.46181,2.43635},{1.483,2.34102},{1.50418,2.00205},{1.52537,1.88553},{1.54655,1.80078},{1.56774,1.74782},{1.58893,1.68426},{1.61011,1.6313},{1.6313,1.57833},{1.65248,1.52537},{1.67367,1.49359},{1.69485,1.46181},{1.71604,1.43003},{1.73723,1.38766},{1.75841,1.34529},{1.7796,1.32411},{1.80078,1.29233},{1.82197,1.26055},{1.84315,1.22877},{1.86434,1.19699},{1.88553,1.17581},{1.90671,1.15462},{1.9279,1.14403},{1.94908,1.13343},{1.97027,1.11225},{1.99145,1.10166},{2.01264,1.09106},{2.03383,1.08047},{2.05501,1.06988},{2.0762,1.04869},{2.09738,1.02751},{2.11857,1.01691},{2.13975,1.00632},{2.16094,0.98513},{2.18213,0.97454},{2.20331,0.96395},{2.2245,0.95336},{2.24568,0.94276},{2.26687,0.93217},{2.28805,0.93217},{2.30924,0.92158},{2.33042,0.91098},{2.35161,0.91098},{2.3728,0.90039},{2.39398,0.8898},{2.41517,0.8898},{2.43635,0.8898},{2.45754,0.8898},{2.47872,0.8898},{2.49991,0.8898},{2.5211,0.8898},{2.54228,0.87921},{2.56347,0.86861},{2.58465,0.86861},{2.60584,0.86861},{2.62702,0.86861},{2.64821,0.86861},{2.6694,0.87921},{2.69058,0.8898},{2.71177,0.8898},{2.73295,0.8898},{2.75414,0.8898},{2.77532,0.8898},{2.79651,0.8898},{2.8177,0.8898},{2.83888,0.8898},{2.86007,0.90039},{2.88125,0.91098},{2.90244,0.91098},{2.92362,0.91098},{2.94481,0.91098},{2.966,0.91098},{2.98718,0.91098},{3.00837,0.91098},{3.02955,0.91098},{3.05074,0.91098},{3.07192,0.91098},{3.09311,0.92158},{3.1143,0.93217},{3.13548,0.93217},{3.15667,0.93217},{3.17785,0.93217},{3.19904,0.93217},{3.22022,0.93217},{3.24141,0.93217},{3.26259,0.93217},{3.28378,0.93217},{3.30497,0.93217},{3.32615,0.93217},{3.34734,0.92158},{3.36852,0.91098},{3.38971,0.91098},{3.41089,0.91098},{3.43208,0.90039},{3.45327,0.8898},{3.47445,0.8898},{3.49564,0.87921},{3.51682,0.86861},{3.53801,0.85802},{3.55919,0.83683},{3.58038,0.82624},{3.60157,0.81565},{3.62275,0.77328},{3.64394,0.73091},{3.66512,0.72031},{3.68631,0.70972},{3.70749,0.70972},{3.72868,0.72031},{3.74987,0.70972},{3.77105,0.69913},{3.79224,0.69913},{3.81342,0.70972},{3.83461,0.72031},{3.85579,0.72031},{3.87698,0.72031},{3.89817,0.72031},{3.91935,0.72031},{3.94054,0.72031},{3.96172,0.72031},{3.98291,0.72031},{4.00409,0.72031},{4.02528,0.72031},{4.04646,0.72031},{4.06765,0.70972},{4.08884,0.69913},{4.11002,0.69913},{4.13121,0.69913},{4.15239,0.69913},{4.17358,0.69913},{4.19476,0.68853},{4.21595,0.67794},{4.23714,0.68853},{4.25832,0.69913},{4.27951,0.69913},{4.30069,0.69913},{4.32188,0.69913},{4.34306,0.69913},{4.36425,0.70972},{4.38544,0.72031},{4.40662,0.73091},{4.42781,0.7415},{4.44899,0.7415},{4.47018,0.75209},{4.49136,0.76268},{4.51255,0.77328},{4.53374,0.78387},{4.55492,0.78387},{4.57611,0.79446},{4.59729,0.80506},{4.61848,0.81565},{4.63966,0.82624},{4.66085,0.83683},{4.68204,0.84743},{4.70322,0.85802},{4.72441,0.87921},{4.74559,0.8898},{4.76678,0.90039},{4.78796,0.92158},{4.80915,0.93217},{4.83034,0.94276},{4.85152,0.96395},{4.87271,0.98513},{4.89389,1.00632},{4.91508,1.01691},{4.93626,1.02751},{4.95745,1.04869},{4.97863,1.06988},{4.99982,1.09106},{5.02101,1.12284},{5.04219,1.16521},{5.06338,1.19699},{5.08456,1.22877},{5.10575,1.26055},{5.12693,1.29233},{5.14812,1.31351},{5.16931,1.3347},{5.19049,1.37707},{5.21168,1.43003},{5.23286,1.483},{5.25405,1.52537},{5.27523,1.56774},{5.29642,1.61011},{5.31761,1.66308},{5.33879,1.71604},{5.35998,1.75841},{5.38116,1.79019},{5.40235,1.82197},{5.42353,1.86434},{5.44472,1.9173},{5.46591,1.98086},{5.48709,2.04442},{5.50828,2.09738},{5.52946,2.17153},{5.55065,2.28805},{5.57183,2.39398},{5.59302,2.46813},{5.61421,2.61643},{5.63539,2.91303},{5.61421,3.46386},{5.59302,3.48504},{5.57183,3.65453},{5.55065,3.78164},{5.52946,3.86639},{5.50828,3.94054},{5.48709,4.00409},{5.46591,4.04646},{5.44472,4.11002},{5.42353,4.20536},{5.40235,4.26891},{5.38116,4.31129},{5.35998,4.37484},{5.33879,4.42781},{5.31761,4.48077},{5.29642,4.54433},{5.27523,4.5867},{5.25405,4.61848},{5.23286,4.66085},{5.21168,4.70322},{5.19049,4.735},{5.16931,4.76678},{5.14812,4.80915},{5.12693,4.86211},{5.10575,4.91508},{5.08456,4.94686},{5.06338,4.96804},{5.04219,4.99982},{5.02101,5.02101},{4.99982,5.05278},{4.97863,5.10575},{4.95745,5.14812},{4.93626,5.16931},{4.91508,5.1799},{4.89389,5.21168},{4.87271,5.25405},{4.85152,5.28583},{4.83034,5.30701},{4.80915,5.3282},{4.78796,5.34938},{4.76678,5.37057},{4.74559,5.39176},{4.72441,5.41294},{4.70322,5.44472},{4.68204,5.4765},{4.66085,5.49768},{4.63966,5.51887},{4.61848,5.54006},{4.59729,5.56124},{4.57611,5.58243},{4.55492,5.60361},{4.53374,5.6248},{4.51255,5.65658},{4.49136,5.70954},{4.47018,5.81547},{4.44899,5.93199},{4.42781,5.99555},{4.40662,6.03792},{4.38544,6.0697},{4.36425,6.10148},{4.34306,6.14385},{4.32188,6.19681},{4.30069,6.30274},{4.27951,6.41926},{4.25832,6.52519},{4.23714,6.60993},{4.21595,6.6629},{4.19476,6.71586},{4.17358,6.74764},{4.15239,6.77942},{4.13121,6.8112},{4.11002,6.84297},{4.08884,6.87475},{4.06765,6.89594},{4.04646,6.91712},{4.02528,6.9489},{4.00409,6.98068},{3.98291,7.00187},{3.96172,7.01246},{3.94054,7.02305},{3.91935,7.04424},{3.89817,7.05483},{3.87698,7.06542},{3.85579,7.07602},{3.83461,7.08661},{3.81342,7.1078},{3.79224,7.11839},{3.77105,7.12898},{3.74987,7.13957},{3.72868,7.13957},{3.70749,7.15017},{3.68631,7.16076},{3.66512,7.17135},{3.64394,7.18195},{3.62275,7.19254},{3.60157,7.20313},{3.58038,7.21372},{3.55919,7.22432},{3.53801,7.22432},{3.51682,7.22432},{3.49564,7.22432},{3.47445,7.21372},{3.45327,7.21372},{3.43208,7.22432},{3.41089,7.21372},{3.38971,7.21372},{3.36852,7.22432},{3.34734,7.22432},{3.32615,7.22432},{3.30497,7.22432},{3.28378,7.22432},{3.26259,7.22432},{3.24141,7.21372},{3.22022,7.20313},{3.19904,7.19254},{3.17785,7.18195},{3.15667,7.17135},{3.13548,7.15017},{3.1143,7.13957},{3.09311,7.12898},{3.07192,7.1078},{3.05074,7.08661},{3.02955,7.06542},{3.00837,7.04424},{2.98718,7.01246},{2.966,6.98068},{2.94481,6.9595},{2.92362,6.92772},{2.90244,6.89594},{2.88125,6.86416},{2.86007,6.83238},{2.83888,6.8112},{2.8177,6.77942},{2.79651,6.74764},{2.77532,6.72645},{2.75414,6.69467},{2.73295,6.6523},{2.71177,6.59934},{2.69058,6.54638},{2.6694,6.504},{2.64821,6.46163},{2.62702,6.41926},{2.60584,6.37689},{2.58465,6.33452},{2.56347,6.13325},{2.54228,5.93199},{2.5211,5.88962},{2.49991,5.84725},{2.47872,5.79428},{2.45754,5.74132},{2.43635,5.69895},{2.41517,5.66717},{2.39398,5.6248},{2.3728,5.57183},{2.35161,5.52946},{2.33042,5.4765},{2.30924,5.43413},{2.28805,5.41294},{2.26687,5.39176},{2.24568,5.37057},{2.2245,5.34938},{2.20331,5.31761},{2.18213,5.28583},{2.16094,5.26464},{2.13975,5.23286},{2.11857,5.20108},{2.09738,5.1799},{2.0762,5.15871},{2.05501,5.13753},{2.03383,5.10575},{2.01264,5.07397},{1.99145,5.0316},{1.97027,4.98923},{1.94908,4.95745},{1.9279,4.92567},{1.90671,4.89389},{1.88553,4.86211},{1.86434,4.83034},{1.84315,4.79856},{1.82197,4.77737},{1.80078,4.71381},{1.7796,4.63966},{1.75841,4.60789},{1.73723,4.56551},{1.71604,4.50196},{1.69485,4.4384},{1.67367,4.36425},{1.65248,4.30069},{1.6313,4.25832},{1.61011,4.19476},{1.58893,4.11002},{1.56774,4.01469},{1.54655,3.89817},{1.52537,3.77105},{1.50418,3.56979},{1.483,3.31556},{1.46181,3.07192},{1.44063,2.86007}}
VerdejoSal[2]={{1.12284`,2.82829`},{1.14403`,2.55287`},{1.16521`,2.43635`},{1.1864`,2.3622`},{1.20758`,2.29865`},{1.22877`,2.2245`},{1.24996`,2.15035`},{1.27114`,2.08679`},{1.29233`,2.02323`},{1.31351`,1.98086`},{1.3347`,1.93849`},{1.35588`,1.89612`},{1.37707`,1.87493`},{1.39825`,1.84315`},{1.41944`,1.81138`},{1.44063`,1.7796`},{1.46181`,1.74782`},{1.483`,1.71604`},{1.50418`,1.68426`},{1.52537`,1.65248`},{1.54655`,1.61011`},{1.56774`,1.57833`},{1.58893`,1.55715`},{1.61011`,1.53596`},{1.6313`,1.51478`},{1.65248`,1.49359`},{1.67367`,1.483`},{1.69485`,1.4724`},{1.71604`,1.45122`},{1.73723`,1.43003`},{1.75841`,1.40885`},{1.7796`,1.38766`},{1.80078`,1.36648`},{1.82197`,1.34529`},{1.84315`,1.3347`},{1.86434`,1.32411`},{1.88553`,1.31351`},{1.90671`,1.30292`},{1.9279`,1.28173`},{1.94908`,1.27114`},{1.97027`,1.26055`},{1.99145`,1.23936`},{2.01264`,1.22877`},{2.03383`,1.21818`},{2.05501`,1.20758`},{2.0762`,1.20758`},{2.09738`,1.19699`},{2.11857`,1.1864`},{2.13975`,1.17581`},{2.16094`,1.15462`},{2.18213`,1.14403`},{2.20331`,1.13343`},{2.2245`,1.12284`},{2.24568`,1.11225`},{2.26687`,1.10166`},{2.28805`,1.10166`},{2.30924`,1.10166`},{2.33042`,1.10166`},{2.35161`,1.10166`},{2.3728`,1.10166`},{2.39398`,1.10166`},{2.41517`,1.10166`},{2.43635`,1.10166`},{2.45754`,1.10166`},{2.47872`,1.10166`},{2.49991`,1.09106`},{2.5211`,1.08047`},{2.54228`,1.06988`},{2.56347`,1.05928`},{2.58465`,1.05928`},{2.60584`,1.04869`},{2.62702`,1.0381`},{2.64821`,1.0381`},{2.6694`,1.0381`},{2.69058`,1.04869`},{2.71177`,1.04869`},{2.73295`,1.0381`},{2.75414`,1.02751`},{2.77532`,1.01691`},{2.79651`,1.00632`},{2.8177`,0.99573`},{2.83888`,0.99573`},{2.86007`,0.99573`},{2.88125`,0.99573`},{2.90244`,1.00632`},{2.92362`,1.0381`},{2.94481`,1.06988`},{2.966`,1.10166`},{2.98718`,1.13343`},{3.00837`,1.13343`},{3.02955`,1.11225`},{3.05074`,1.11225`},{3.07192`,1.11225`},{3.09311`,1.11225`},{3.1143`,1.12284`},{3.13548`,1.13343`},{3.15667`,1.14403`},{3.17785`,1.14403`},{3.19904`,1.14403`},{3.22022`,1.15462`},{3.24141`,1.16521`},{3.26259`,1.16521`},{3.28378`,1.17581`},{3.30497`,1.1864`},{3.32615`,1.1864`},{3.34734`,1.1864`},{3.36852`,1.1864`},{3.38971`,1.1864`},{3.41089`,1.1864`},{3.43208`,1.19699`},{3.45327`,1.20758`},{3.47445`,1.20758`},{3.49564`,1.20758`},{3.51682`,1.20758`},{3.53801`,1.20758`},{3.55919`,1.21818`},{3.58038`,1.22877`},{3.60157`,1.22877`},{3.62275`,1.22877`},{3.64394`,1.21818`},{3.66512`,1.20758`},{3.68631`,1.21818`},{3.70749`,1.22877`},{3.72868`,1.22877`},{3.74987`,1.22877`},{3.77105`,1.22877`},{3.79224`,1.23936`},{3.81342`,1.24996`},{3.83461`,1.24996`},{3.85579`,1.24996`},{3.87698`,1.26055`},{3.89817`,1.27114`},{3.91935`,1.27114`},{3.94054`,1.27114`},{3.96172`,1.28173`},{3.98291`,1.29233`},{4.00409`,1.29233`},{4.02528`,1.30292`},{4.04646`,1.31351`},{4.06765`,1.32411`},{4.08884`,1.3347`},{4.11002`,1.3347`},{4.13121`,1.34529`},{4.15239`,1.35588`},{4.17358`,1.36648`},{4.19476`,1.38766`},{4.21595`,1.39825`},{4.23714`,1.40885`},{4.25832`,1.41944`},{4.27951`,1.41944`},{4.30069`,1.43003`},{4.32188`,1.44063`},{4.34306`,1.45122`},{4.36425`,1.4724`},{4.38544`,1.483`},{4.40662`,1.49359`},{4.42781`,1.51478`},{4.44899`,1.53596`},{4.47018`,1.57833`},{4.49136`,1.6313`},{4.51255`,1.66308`},{4.53374`,1.68426`},{4.55492`,1.70545`},{4.57611`,1.73723`},{4.59729`,1.769`},{4.61848`,1.81138`},{4.63966`,1.87493`},{4.66085`,1.93849`},{4.68204`,1.99145`},{4.70322`,2.03383`},{4.72441`,2.08679`},{4.74559`,2.15035`},{4.76678`,2.19272`},{4.78796`,2.2245`},{4.80915`,2.27746`},{4.83034`,2.35161`},{4.85152`,2.40457`},{4.87271`,2.42576`},{4.89389`,2.46813`},{4.91508`,2.53169`},{4.93626`,2.57406`},{4.95745`,2.61643`},{4.97863`,2.6694`},{4.99982`,2.73295`},{5.02101`,2.83888`},{5.04219`,2.966`},{5.02101`,3.1143`},{4.99982`,3.35793`},{4.97863`,3.52742`},{4.95745`,3.56979`},{4.93626`,3.63334`},{4.91508`,3.70749`},{4.89389`,3.77105`},{4.87271`,3.82402`},{4.85152`,3.89817`},{4.83034`,3.97232`},{4.80915`,4.02528`},{4.78796`,4.06765`},{4.76678`,4.11002`},{4.74559`,4.16299`},{4.72441`,4.21595`},{4.70322`,4.25832`},{4.68204`,4.30069`},{4.66085`,4.35366`},{4.63966`,4.40662`},{4.61848`,4.4384`},{4.59729`,4.47018`},{4.57611`,4.51255`},{4.55492`,4.55492`},{4.53374`,4.59729`},{4.51255`,4.63966`},{4.49136`,4.68204`},{4.47018`,4.72441`},{4.44899`,4.75619`},{4.42781`,4.78796`},{4.40662`,4.83034`},{4.38544`,4.86211`},{4.36425`,4.89389`},{4.34306`,4.92567`},{4.32188`,4.94686`},{4.30069`,4.97863`},{4.27951`,5.01041`},{4.25832`,5.0316`},{4.23714`,5.06338`},{4.21595`,5.09516`},{4.19476`,5.11634`},{4.17358`,5.13753`},{4.15239`,5.15871`},{4.13121`,5.19049`},{4.11002`,5.23286`},{4.08884`,5.26464`},{4.06765`,5.28583`},{4.04646`,5.29642`},{4.02528`,5.31761`},{4.00409`,5.34938`},{3.98291`,5.39176`},{3.96172`,5.44472`},{3.94054`,5.46591`},{3.91935`,5.4765`},{3.89817`,5.49768`},{3.87698`,5.50828`},{3.85579`,5.51887`},{3.83461`,5.54006`},{3.81342`,5.55065`},{3.79224`,5.56124`},{3.77105`,5.59302`},{3.74987`,5.6248`},{3.72868`,5.64598`},{3.70749`,5.66717`},{3.68631`,5.69895`},{3.66512`,5.73073`},{3.64394`,5.76251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VerdejoSal[3]={{0.67794,3.1143},{0.69913,2.78592},{0.72031,2.56347},{0.7415,2.39398},{0.76268,2.30924},{0.78387,2.25627},{0.80506,2.18213},{0.82624,2.11857},{0.84743,2.05501},{0.86861,1.99145},{0.8898,1.93849},{0.91098,1.88553},{0.93217,1.83256},{0.95336,1.79019},{0.97454,1.769},{0.99573,1.73723},{1.01691,1.69485},{1.0381,1.66308},{1.05928,1.6313},{1.08047,1.59952},{1.10166,1.56774},{1.12284,1.53596},{1.14403,1.50418},{1.16521,1.4724},{1.1864,1.44063},{1.20758,1.40885},{1.22877,1.39825},{1.24996,1.38766},{1.27114,1.36648},{1.29233,1.34529},{1.31351,1.32411},{1.3347,1.30292},{1.35588,1.28173},{1.37707,1.27114},{1.39825,1.26055},{1.41944,1.23936},{1.44063,1.21818},{1.46181,1.20758},{1.483,1.19699},{1.50418,1.17581},{1.52537,1.16521},{1.54655,1.15462},{1.56774,1.14403},{1.58893,1.13343},{1.61011,1.11225},{1.6313,1.10166},{1.65248,1.09106},{1.67367,1.08047},{1.69485,1.06988},{1.71604,1.05928},{1.73723,1.04869},{1.75841,1.0381},{1.7796,1.0381},{1.80078,1.02751},{1.82197,1.01691},{1.84315,1.01691},{1.86434,1.00632},{1.88553,1.00632},{1.90671,1.01691},{1.9279,1.00632},{1.94908,0.99573},{1.97027,0.99573},{1.99145,0.99573},{2.01264,0.99573},{2.03383,0.99573},{2.05501,0.98513},{2.0762,0.97454},{2.09738,0.97454},{2.11857,0.97454},{2.13975,0.97454},{2.16094,0.98513},{2.18213,0.99573},{2.20331,0.99573},{2.2245,0.99573},{2.24568,0.99573},{2.26687,0.99573},{2.28805,0.99573},{2.30924,1.00632},{2.33042,1.01691},{2.35161,1.01691},{2.3728,1.01691},{2.39398,1.02751},{2.41517,1.0381},{2.43635,1.04869},{2.45754,1.05928},{2.47872,1.06988},{2.49991,1.08047},{2.5211,1.09106},{2.54228,1.10166},{2.56347,1.11225},{2.58465,1.12284},{2.60584,1.12284},{2.62702,1.13343},{2.64821,1.14403},{2.6694,1.15462},{2.69058,1.16521},{2.71177,1.16521},{2.73295,1.17581},{2.75414,1.1864},{2.77532,1.1864},{2.79651,1.1864},{2.8177,1.19699},{2.83888,1.20758},{2.86007,1.20758},{2.88125,1.20758},{2.90244,1.20758},{2.92362,1.20758},{2.94481,1.20758},{2.966,1.20758},{2.98718,1.20758},{3.00837,1.19699},{3.02955,1.1864},{3.05074,1.1864},{3.07192,1.17581},{3.09311,1.16521},{3.1143,1.15462},{3.13548,1.13343},{3.15667,1.12284},{3.17785,1.12284},{3.19904,1.11225},{3.22022,1.10166},{3.24141,1.10166},{3.26259,1.10166},{3.28378,1.10166},{3.30497,1.10166},{3.32615,1.10166},{3.34734,1.10166},{3.36852,1.09106},{3.38971,1.08047},{3.41089,1.08047},{3.43208,1.08047},{3.45327,1.08047},{3.47445,1.08047},{3.49564,1.08047},{3.51682,1.09106},{3.53801,1.11225},{3.55919,1.13343},{3.58038,1.14403},{3.60157,1.15462},{3.62275,1.16521},{3.64394,1.17581},{3.66512,1.1864},{3.68631,1.19699},{3.70749,1.20758},{3.72868,1.21818},{3.74987,1.22877},{3.77105,1.23936},{3.79224,1.24996},{3.81342,1.27114},{3.83461,1.29233},{3.85579,1.30292},{3.87698,1.32411},{3.89817,1.34529},{3.91935,1.36648},{3.94054,1.37707},{3.96172,1.38766},{3.98291,1.41944},{4.00409,1.44063},{4.02528,1.45122},{4.04646,1.4724},{4.06765,1.50418},{4.08884,1.52537},{4.11002,1.55715},{4.13121,1.59952},{4.15239,1.6313},{4.17358,1.67367},{4.19476,1.71604},{4.21595,1.75841},{4.23714,1.80078},{4.25832,1.84315},{4.27951,1.87493},{4.30069,1.9173},{4.32188,1.97027},{4.34306,2.01264},{4.36425,2.0762},{4.38544,2.17153},{4.40662,2.25627},{4.42781,2.31983},{4.44899,2.38339},{4.47018,2.44695},{4.49136,2.53169},{4.51255,2.62702},{4.53374,2.76473},{4.55492,2.94481},{4.57611,3.45327},{4.59729,3.37912},{4.55492,3.96172},{4.53374,4.11002},{4.51255,4.22654},{4.49136,4.27951},{4.47018,4.39603},{4.44899,4.44899},{4.42781,4.51255},{4.40662,4.59729},{4.38544,4.67144},{4.36425,4.71381},{4.34306,4.75619},{4.32188,4.83034},{4.30069,4.89389},{4.27951,4.93626},{4.25832,4.97863},{4.23714,5.01041},{4.21595,5.0316},{4.19476,5.07397},{4.17358,5.10575},{4.15239,5.10575},{4.13121,5.11634},{4.11002,5.12693},{4.08884,5.12693},{4.06765,5.15871},{4.04646,5.24346},{4.02528,5.3282},{4.00409,5.39176},{3.98291,5.50828},{3.96172,5.54006},{3.94054,5.55065},{3.91935,5.55065},{3.89817,5.56124},{3.87698,5.60361},{3.85579,5.63539},{3.83461,5.63539},{3.81342,5.65658},{3.79224,5.68835},{3.77105,5.73073},{3.74987,5.7731},{3.72868,5.79428},{3.70749,5.83665},{3.68631,5.87903},{3.66512,5.90021},{3.64394,5.93199},{3.62275,5.98495},{3.60157,6.31333},{3.58038,6.3557},{3.55919,6.39808},{3.53801,6.41926},{3.51682,6.44045},{3.49564,6.49341},{3.47445,6.55697},{3.45327,6.64171},{3.43208,6.74764},{3.41089,6.83238},{3.38971,6.92772},{3.36852,7.05483},{3.34734,7.20313},{3.32615,7.28787},{3.30497,7.30906},{3.28378,7.34084},{3.26259,7.37262},{3.24141,7.4044},{3.22022,7.43617},{3.19904,7.45736},{3.17785,7.45736},{3.15667,7.46795},{3.13548,7.47855},{3.1143,7.47855},{3.09311,7.47855},{3.07192,7.47855},{3.05074,7.48914},{3.02955,7.49973},{3.00837,7.51032},{2.98718,7.52092},{2.966,7.51032},{2.94481,7.49973},{2.92362,7.49973},{2.90244,7.49973},{2.88125,7.49973},{2.86007,7.48914},{2.83888,7.47855},{2.8177,7.47855},{2.79651,7.47855},{2.77532,7.47855},{2.75414,7.47855},{2.73295,7.47855},{2.71177,7.47855},{2.69058,7.47855},{2.6694,7.47855},{2.64821,7.47855},{2.62702,7.47855},{2.60584,7.46795},{2.58465,7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VerdejoSal[4]={{1.08047,3.43208},{1.10166,3.32615},{1.12284,3.13548},{1.14403,2.73295},{1.16521,2.59525},{1.1864,2.48932},{1.20758,2.39398},{1.22877,2.30924},{1.24996,2.25627},{1.27114,2.17153},{1.29233,2.09738},{1.31351,2.05501},{1.3347,2.01264},{1.35588,1.97027},{1.37707,1.9279},{1.39825,1.89612},{1.41944,1.85375},{1.44063,1.80078},{1.46181,1.769},{1.483,1.74782},{1.50418,1.72663},{1.52537,1.69485},{1.54655,1.66308},{1.56774,1.64189},{1.58893,1.61011},{1.61011,1.57833},{1.6313,1.56774},{1.65248,1.55715},{1.67367,1.53596},{1.69485,1.52537},{1.71604,1.51478},{1.73723,1.49359},{1.75841,1.4724},{1.7796,1.45122},{1.80078,1.44063},{1.82197,1.43003},{1.84315,1.40885},{1.86434,1.38766},{1.88553,1.37707},{1.90671,1.36648},{1.9279,1.35588},{1.94908,1.34529},{1.97027,1.3347},{1.99145,1.32411},{2.01264,1.31351},{2.03383,1.30292},{2.05501,1.29233},{2.0762,1.28173},{2.09738,1.26055},{2.11857,1.24996},{2.13975,1.23936},{2.16094,1.22877},{2.18213,1.22877},{2.20331,1.22877},{2.2245,1.22877},{2.24568,1.22877},{2.26687,1.21818},{2.28805,1.20758},{2.30924,1.20758},{2.33042,1.20758},{2.35161,1.20758},{2.3728,1.20758},{2.39398,1.20758},{2.41517,1.20758},{2.43635,1.20758},{2.45754,1.20758},{2.47872,1.20758},{2.49991,1.20758},{2.5211,1.20758},{2.54228,1.20758},{2.56347,1.20758},{2.58465,1.20758},{2.60584,1.20758},{2.62702,1.21818},{2.64821,1.22877},{2.6694,1.22877},{2.69058,1.22877},{2.71177,1.23936},{2.73295,1.24996},{2.75414,1.24996},{2.77532,1.24996},{2.79651,1.26055},{2.8177,1.27114},{2.83888,1.27114},{2.86007,1.27114},{2.88125,1.27114},{2.90244,1.28173},{2.92362,1.29233},{2.94481,1.29233},{2.966,1.29233},{2.98718,1.29233},{3.00837,1.30292},{3.02955,1.32411},{3.05074,1.3347},{3.07192,1.34529},{3.09311,1.35588},{3.1143,1.35588},{3.13548,1.35588},{3.15667,1.36648},{3.17785,1.37707},{3.19904,1.37707},{3.22022,1.37707},{3.24141,1.37707},{3.26259,1.38766},{3.28378,1.39825},{3.30497,1.39825},{3.32615,1.39825},{3.34734,1.38766},{3.36852,1.37707},{3.38971,1.37707},{3.41089,1.37707},{3.43208,1.37707},{3.45327,1.37707},{3.47445,1.37707},{3.49564,1.36648},{3.51682,1.36648},{3.53801,1.37707},{3.55919,1.36648},{3.58038,1.35588},{3.60157,1.35588},{3.62275,1.35588},{3.64394,1.34529},{3.66512,1.3347},{3.68631,1.32411},{3.70749,1.31351},{3.72868,1.31351},{3.74987,1.31351},{3.77105,1.30292},{3.79224,1.29233},{3.81342,1.28173},{3.83461,1.27114},{3.85579,1.26055},{3.87698,1.24996},{3.89817,1.24996},{3.91935,1.23936},{3.94054,1.22877},{3.96172,1.22877},{3.98291,1.22877},{4.00409,1.22877},{4.02528,1.21818},{4.04646,1.20758},{4.06765,1.20758},{4.08884,1.20758},{4.11002,1.20758},{4.13121,1.20758},{4.15239,1.20758},{4.17358,1.20758},{4.19476,1.21818},{4.21595,1.22877},{4.23714,1.22877},{4.25832,1.22877},{4.27951,1.22877},{4.30069,1.22877},{4.32188,1.23936},{4.34306,1.24996},{4.36425,1.24996},{4.38544,1.26055},{4.40662,1.27114},{4.42781,1.27114},{4.44899,1.28173},{4.47018,1.29233},{4.49136,1.29233},{4.51255,1.30292},{4.53374,1.31351},{4.55492,1.32411},{4.57611,1.34529},{4.59729,1.35588},{4.61848,1.36648},{4.63966,1.38766},{4.66085,1.40885},{4.68204,1.43003},{4.70322,1.44063},{4.72441,1.45122},{4.74559,1.46181},{4.76678,1.4724},{4.78796,1.49359},{4.80915,1.52537},{4.83034,1.55715},{4.85152,1.57833},{4.87271,1.59952},{4.89389,1.6207},{4.91508,1.65248},{4.93626,1.69485},{4.95745,1.72663},{4.97863,1.75841},{4.99982,1.80078},{5.02101,1.83256},{5.04219,1.85375},{5.06338,1.88553},{5.08456,1.94908},{5.10575,2.00205},{5.12693,2.03383},{5.14812,2.0762},{5.16931,2.11857},{5.19049,2.17153},{5.21168,2.2139},{5.23286,2.25627},{5.25405,2.29865},{5.27523,2.33042},{5.29642,2.3622},{5.31761,2.38339},{5.33879,2.42576},{5.35998,2.69058},{5.38116,2.88125},{5.40235,3.13548},{5.42353,3.30497},{5.44472,3.41089},{5.46591,3.53801},{5.48709,3.6969},{5.50828,3.83461},{5.48709,3.96172},{5.46591,4.17358},{5.44472,4.38544},{5.42353,4.47018},{5.40235,4.56551},{5.38116,4.63966},{5.35998,4.70322},{5.33879,4.77737},{5.31761,4.85152},{5.29642,4.90448},{5.27523,4.97863},{5.25405,5.04219},{5.23286,5.06338},{5.21168,5.08456},{5.19049,5.12693},{5.16931,5.16931},{5.14812,5.21168},{5.12693,5.25405},{5.10575,5.29642},{5.08456,5.33879},{5.06338,5.39176},{5.04219,5.43413},{5.02101,5.45531},{4.99982,5.50828},{4.97863,5.57183},{4.95745,5.60361},{4.93626,5.63539},{4.91508,5.67776},{4.89389,5.70954},{4.87271,5.74132},{4.85152,5.79428},{4.83034,5.85784},{4.80915,5.90021},{4.78796,5.9214},{4.76678,5.94258},{4.74559,5.97436},{4.72441,6.03792},{4.70322,6.11207},{4.68204,6.16503},{4.66085,6.218},{4.63966,6.27096},{4.61848,6.32393},{4.59729,6.60993},{4.57611,6.70527},{4.55492,6.8112},{4.53374,6.93831},{4.51255,7.07602},{4.49136,7.16076},{4.47018,7.26669},{4.44899,7.3938},{4.42781,7.44677},{4.40662,7.47855},{4.38544,7.52092},{4.36425,7.55269},{4.34306,7.57388},{4.32188,7.59507},{4.30069,7.61625},{4.27951,7.64803},{4.25832,7.67981},{4.23714,7.70099},{4.21595,7.72218},{4.19476,7.74337},{4.17358,7.75396},{4.15239,7.76455},{4.13121,7.77514},{4.11002,7.78574},{4.08884,7.79633},{4.06765,7.79633},{4.04646,7.79633},{4.02528,7.79633},{4.00409,7.79633},{3.98291,7.79633},{3.96172,7.78574},{3.94054,7.77514},{3.91935,7.78574},{3.89817,7.79633},{3.87698,7.80692},{3.85579,7.81752},{3.83461,7.81752},{3.81342,7.81752},{3.79224,7.81752},{3.77105,7.82811},{3.74987,7.8387},{3.72868,7.84929},{3.70749,7.85989},{3.68631,7.85989},{3.66512,7.87048},{3.64394,7.88107},{3.62275,7.88107},{3.60157,7.88107},{3.58038,7.88107},{3.55919,7.88107},{3.53801,7.88107},{3.51682,7.88107},{3.49564,7.87048},{3.47445,7.85989},{3.45327,7.85989},{3.43208,7.84929},{3.41089,7.82811},{3.38971,7.80692},{3.36852,7.79633},{3.34734,7.78574},{3.32615,7.76455},{3.30497,7.74337},{3.28378,7.72218},{3.26259,7.71159},{3.24141,7.70099},{3.22022,7.6904},{3.19904,7.6904},{3.17785,7.67981},{3.15667,7.65862},{3.13548,7.64803},{3.1143,7.61625},{3.09311,7.56329},{3.07192,7.53151},{3.05074,7.49973},{3.02955,7.45736},{3.00837,7.4044},{2.98718,7.35143},{2.966,7.31965},{2.94481,7.27728},{2.92362,7.22432},{2.90244,7.19254},{2.88125,7.16076},{2.86007,7.0972},{2.83888,7.03365},{2.8177,6.98068},{2.79651,6.92772},{2.77532,6.88535},{2.75414,6.85357},{2.73295,6.75823},{2.71177,6.63112},{2.69058,6.55697},{2.6694,6.504},{2.64821,6.47223},{2.62702,6.45104},{2.60584,6.41926},{2.58465,6.38748},{2.56347,6.37689},{2.54228,6.3557},{2.5211,6.32393},{2.49991,6.30274},{2.47872,6.29215},{2.45754,6.28155},{2.43635,6.26037},{2.41517,6.23918},{2.39398,6.218},{2.3728,6.19681},{2.35161,6.18622},{2.33042,6.17563},{2.30924,6.15444},{2.28805,6.13325},{2.26687,6.11207},{2.24568,6.09088},{2.2245,6.08029},{2.20331,6.0697},{2.18213,6.04851},{2.16094,6.02733},{2.13975,6.00614},{2.11857,5.98495},{2.09738,5.96377},{2.0762,5.93199},{2.05501,5.88962},{2.03383,5.84725},{2.01264,5.81547},{1.99145,5.79428},{1.97027,5.7731},{1.94908,5.74132},{1.9279,5.70954},{1.90671,5.68835},{1.88553,5.66717},{1.86434,5.63539},{1.84315,5.60361},{1.82197,5.57183},{1.80078,5.52946},{1.7796,5.49768},{1.75841,5.46591},{1.73723,5.41294},{1.71604,5.35998},{1.69485,5.31761},{1.67367,5.27523},{1.65248,5.24346},{1.6313,5.20108},{1.61011,5.15871},{1.58893,5.12693},{1.56774,5.08456},{1.54655,5.05278},{1.52537,5.02101},{1.50418,4.97863},{1.483,4.93626},{1.46181,4.89389},{1.44063,4.85152},{1.41944,4.79856},{1.39825,4.74559},{1.37707,4.70322},{1.35588,4.66085},{1.3347,4.60789},{1.31351,4.53374},{1.29233,4.45959},{1.27114,4.39603},{1.24996,4.32188},{1.22877,4.23714},{1.20758,4.1418},{1.1864,4.03587},{1.16521,3.95113},{1.14403,3.89817},{1.12284,3.77105},{1.10166,3.55919}}

(*Poner aqui la familia*)
var=VerdejoSal;
(* el número de curvas estudiadas/semillas de la familia*)
m=4;
For[j=1,j≤m,j++,
puntos=var[j];
(* pru es el spline cubico
d es el vector que contiene la información de pru 
n es el número de trozos del spline, es decir, el número de puntos menos 1
*)
pru=SplineFit[puntos,Cubic];
d=InputForm[pru];
n=IntegerPart[d[[1,2,2]]];
spli=ParametricPlot[pru[t],{t,0,n},PlotRange->All, DisplayFunction->Identity];
(* Con los coeficientes se calculan los polinomios cúbicos que dan el spline. Habrá n polinomios para la primera coordenada (X) y otros tantos para la segunda
*)
For[i=0,i<n,i++,
SX[i,t_]=d[[1,4,i+1,1,1]]+d[[1,4,i+1,1,2]]*(t-i)+d[[1,4,i+1,1,3]]*(t-i)^2+d[[1,4,i+1,1,4]]*(t-i)^3];
For[i=0,i<n,i++,SY[i,t_]=d[[1,4,i+1,2,1]]+d[[1,4,i+1,2,2]]*(t-i)+d[[1,4,i+1,2,3]]*(t-i)^2+d[[1,4,i+1,2,4]]*(t-i)^3];
(* Derivada primera y segunda de cada trozo del spline
*)
For[i=0,i<n,i++,DX[i,t_]=d[[1,4,i+1,1,2]]+2*d[[1,4,i+1,1,3]]*(t-i)+3*d[[1,4,i+1,1,4]]*(t-i)^2];
For[i=0,i<n,i++,DY[i,t_]=d[[1,4,i+1,2,2]]+2*d[[1,4,i+1,2,3]]*(t-i)+3*d[[1,4,i+1,2,4]]*(t-i)^2];
For[i=0,i<n,i++,DDX[i,t_]=2*d[[1,4,i+1,1,3]]+6*d[[1,4,i+1,1,4]]*(t-i)];
For[i=0,i<n,i++,DDY[i,t_]=2*d[[1,4,i+1,2,3]]+6*d[[1,4,i+1,2,4]]*(t-i)];
(*Cálculo de la curvatura a trozos
*)
For[i=0,i<n,i++,cur[i,t_]=(DX[i,t]DDY[i,t]-DDX[i,t]DY[i,t])/((DX[i,t])^2+(DY[i,t])^2)^(3/2)];
(* Dibujos de los trozos de curvatura 
*)
For[i=0,i<n,i++,dib[i]=Plot[cur[i,t],{t,i,i+1},DisplayFunction->Identity]];
pp=dib[0];
For[i=1,i<n,i++,pp=Show[pp,dib[i],PlotRange->All]];
(* bez es el spline de Bezier
b es el vector que contiene la información de bez
nb es el número de trozos del spline, es decir, el número de puntos menos 1 (Como nb=n, no se define nuevo)
*)
bez=SplineFit[puntos,Bezier];
b=InputForm[bez];
(*Calculo de las funciones de Bezier para la coordenada X y la Y; la curva es la imagen del intervalo[0,1]*)
For[i=1,i≤n+1,i++,BX[t_]=bez[[4,1,1]]/.#1->t];
For[i=1,i≤n+1,i++,BY[t_]=bez[[4,1,2]]/.#1->t];
dibez[j]=ParametricPlot[{BX[t],BY[t]},{t,0,1},PlotRange->All,DisplayFunction->Identity];
curbe[j,t_]=(BX'[t]BY''[t]-BX''[t]BY'[t])/((BX'[t])^2+(BY'[t])^2)^(3/2);
cur[j]=Abs[NMaxValue[{curbe[j,t],0.2<t<1},t]];
vmed[j]=Abs[NIntegrate[curbe[j,t],{t,0.2,0.8}]];
dibcurbe[j]=Plot[{curbe[j,t],vmed[j]},{t,0,1},PlotRange->{-5,5},DisplayFunction->Identity,PlotStyle->{RGBColor[0,1,0],{Dotted,Dashed}}];
total=GraphicsGrid[{
(*{spli,pp},*)
{Print[""],dibez[j],dibcurbe[j]}},Spacings->0.5];
Print[var,j, ":", "Máximo valor de la curvatura (en valor absoluto)",cur[j]];
Print[total]
]
Print["Curvaturas de cada ", var ,":  ", Table[cur[j],{j,1,4}]];
Print["Valores medios de curvatura de cada ", var ," en [0.1,0.9]:  ", Table[vmed[j],{j,1,4}]];