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






	(*******************************  ListanPrieto2024*)

Needs["Splines`"]

ListanPrieto[1]={{0.39292,7.55286},{0.43658,8.16408},{0.48024,8.49151},{0.5239,8.64432},{0.56756,8.73163},{0.61121,8.81895},{0.65487,8.90627},{0.69853,8.99358},{0.74219,9.0809},{0.78585,9.14639},{0.82951,9.21187},{0.87316,9.27736},{0.91682,9.34285},{0.96048,9.40834},{1.00414,9.45199},{1.0478,9.49565},{1.09145,9.53931},{1.13511,9.58297},{1.17877,9.64846},{1.22243,9.71394},{1.26609,9.7576},{1.30975,9.80126},{1.3534,9.82309},{1.39706,9.86675},{1.44072,9.91041},{1.48438,9.93223},{1.52804,9.99772},{1.57169,10.08504},{1.61535,10.15053},{1.65901,10.21601},{1.70267,10.30333},{1.74633,10.39065},{1.78999,10.45613},{1.83364,10.52162},{1.8773,10.63076},{1.92096,10.73991},{1.96462,10.84906},{2.00828,10.9582},{2.05193,11.00186},{2.09559,11.02369},{2.13925,11.08918},{2.18291,11.15466},{2.22657,11.22015},{2.27023,11.28564},{2.31388,11.30747},{2.35754,11.30747},{2.4012,11.30747},{2.44486,11.3293},{2.48852,11.35112},{2.53217,11.35112},{2.57583,11.35112},{2.61949,11.35112},{2.66315,11.35112},{2.70681,11.35112},{2.75046,11.35112},{2.79412,11.37295},{2.83778,11.39478},{2.88144,11.39478},{2.9251,11.39478},{2.96876,11.39478},{3.01241,11.37295},{3.05607,11.35112},{3.09973,11.35112},{3.14339,11.3293},{3.18705,11.30747},{3.2307,11.28564},{3.27436,11.22015},{3.31802,11.13283},{3.36168,11.04552},{3.40534,10.9582},{3.449,10.89271},{3.49265,10.82723},{3.53631,10.73991},{3.57997,10.65259},{3.62363,10.58711},{3.66729,10.52162},{3.71094,10.4343},{3.7546,10.36882},{3.79826,10.30333},{3.84192,10.23784},{3.88558,10.19418},{3.92924,10.1287},{3.97289,10.06321},{4.01655,9.99772},{4.06021,9.93223},{4.10387,9.86675},{4.14753,9.77943},{4.19118,9.71394},{4.23484,9.64846},{4.2785,9.58297},{4.32216,9.53931},{4.36582,9.47382},{4.40948,9.40834},{4.45313,9.36468},{4.49679,9.29919},{4.54045,9.21187},{4.58411,9.14639},{4.62777,9.10273},{4.67142,9.03724},{4.71508,8.94993},{4.75874,8.88444},{4.8024,8.81895},{4.84606,8.73163},{4.88972,8.66615},{4.93337,8.57883},{4.97703,8.4042},{5.02069,8.25139},{5.06435,8.14225},{5.10801,8.0331},{5.15166,7.77115},{5.19532,7.48738},{5.15166,7.24726},{5.10801,6.96348},{5.06435,6.78885},{5.02069,6.57055},{4.97703,6.35226},{4.93337,6.24312},{4.88972,6.1558},{4.84606,6.06849},{4.8024,5.98117},{4.75874,5.91568},{4.71508,5.85019},{4.67142,5.78471},{4.62777,5.74105},{4.58411,5.69739},{4.54045,5.65373},{4.49679,5.61007},{4.45313,5.56642},{4.40948,5.52276},{4.36582,5.4791},{4.32216,5.45727},{4.2785,5.43544},{4.23484,5.39178},{4.19118,5.3263},{4.14753,5.28264},{4.10387,5.28264},{4.06021,5.28264},{4.01655,5.26081},{3.97289,5.23898},{3.92924,5.23898},{3.88558,5.21715},{3.84192,5.19532},{3.79826,5.19532},{3.7546,5.17349},{3.71094,5.15166},{3.66729,5.15166},{3.62363,5.15166},{3.57997,5.15166},{3.53631,5.15166},{3.49265,5.15166},{3.449,5.15166},{3.40534,5.15166},{3.36168,5.17349},{3.31802,5.19532},{3.27436,5.19532},{3.2307,5.19532},{3.18705,5.19532},{3.14339,5.21715},{3.09973,5.26081},{3.05607,5.28264},{3.01241,5.28264},{2.96876,5.30447},{2.9251,5.3263},{2.88144,5.3263},{2.83778,5.30447},{2.79412,5.26081},{2.75046,5.23898},{2.70681,5.23898},{2.66315,5.23898},{2.61949,5.21715},{2.57583,5.19532},{2.53217,5.19532},{2.48852,5.21715},{2.44486,5.21715},{2.4012,5.19532},{2.35754,5.17349},{2.31388,5.15166},{2.27023,5.15166},{2.22657,5.15166},{2.18291,5.15166},{2.13925,5.12984},{2.09559,5.10801},{2.05193,5.10801},{2.00828,5.10801},{1.96462,5.10801},{1.92096,5.10801},{1.8773,5.10801},{1.83364,5.10801},{1.78999,5.10801},{1.74633,5.12984},{1.70267,5.15166},{1.65901,5.15166},{1.61535,5.17349},{1.57169,5.19532},{1.52804,5.21715},{1.48438,5.23898},{1.44072,5.23898},{1.39706,5.26081},{1.3534,5.30447},{1.30975,5.34813},{1.26609,5.39178},{1.22243,5.41361},{1.17877,5.45727},{1.13511,5.52276},{1.09145,5.56642},{1.0478,5.61007},{1.00414,5.65373},{0.96048,5.71922},{0.91682,5.78471},{0.87316,5.82837},{0.82951,5.89385},{0.78585,5.98117},{0.74219,6.06849},{0.69853,6.13397},{0.65487,6.22129},{0.61121,6.33043},{0.56756,6.41775},{0.5239,6.5269},{0.48024,6.72336},{0.43658,7.00714}}
ListanPrieto[2]={{0.26195,5.21715},{0.30561,4.73691},{0.34927,4.49679},{0.39292,4.36582},{0.43658,4.25667},{0.48024,4.14753},{0.5239,4.06021},{0.56756,3.97289},{0.61121,3.86375},{0.65487,3.77643},{0.69853,3.71094},{0.74219,3.62363},{0.78585,3.55814},{0.82951,3.51448},{0.87316,3.449},{0.91682,3.38351},{0.96048,3.33985},{1.00414,3.29619},{1.0478,3.25253},{1.09145,3.18705},{1.13511,3.12156},{1.17877,3.09973},{1.22243,3.0779},{1.26609,3.03424},{1.30975,2.99058},{1.3534,2.96876},{1.39706,2.94693},{1.44072,2.9251},{1.48438,2.90327},{1.52804,2.88144},{1.57169,2.85961},{1.61535,2.83778},{1.65901,2.83778},{1.70267,2.81595},{1.74633,2.79412},{1.78999,2.79412},{1.83364,2.77229},{1.8773,2.75046},{1.92096,2.75046},{1.96462,2.75046},{2.00828,2.72864},{2.05193,2.70681},{2.09559,2.70681},{2.13925,2.70681},{2.18291,2.70681},{2.22657,2.70681},{2.27023,2.70681},{2.31388,2.70681},{2.35754,2.70681},{2.4012,2.70681},{2.44486,2.72864},{2.48852,2.77229},{2.53217,2.79412},{2.57583,2.81595},{2.61949,2.83778},{2.66315,2.83778},{2.70681,2.85961},{2.75046,2.88144},{2.79412,2.88144},{2.83778,2.85961},{2.88144,2.83778},{2.9251,2.83778},{2.96876,2.81595},{3.01241,2.79412},{3.05607,2.79412},{3.09973,2.77229},{3.14339,2.75046},{3.18705,2.75046},{3.2307,2.75046},{3.27436,2.75046},{3.31802,2.75046},{3.36168,2.75046},{3.40534,2.75046},{3.449,2.75046},{3.49265,2.75046},{3.53631,2.77229},{3.57997,2.79412},{3.62363,2.79412},{3.66729,2.79412},{3.71094,2.81595},{3.7546,2.83778},{3.79826,2.83778},{3.84192,2.85961},{3.88558,2.90327},{3.92924,2.9251},{3.97289,2.94693},{4.01655,2.96876},{4.06021,2.99058},{4.10387,3.03424},{4.14753,3.05607},{4.19118,3.09973},{4.23484,3.14339},{4.2785,3.16522},{4.32216,3.20888},{4.36582,3.27436},{4.40948,3.36168},{4.45313,3.42717},{4.49679,3.47082},{4.54045,3.53631},{4.58411,3.62363},{4.62777,3.71094},{4.67142,3.79826},{4.71508,3.88558},{4.75874,3.95106},{4.8024,4.03838},{4.84606,4.16936},{4.88972,4.30033},{4.93337,4.45313},{4.97703,4.60594},{5.02069,4.99886},{4.97703,5.41361},{4.93337,5.61007},{4.88972,5.80654},{4.84606,5.98117},{4.8024,6.11214},{4.75874,6.19946},{4.71508,6.28678},{4.67142,6.35226},{4.62777,6.41775},{4.58411,6.50507},{4.54045,6.59238},{4.49679,6.65787},{4.45313,6.70153},{4.40948,6.76702},{4.36582,6.8325},{4.32216,6.87616},{4.2785,6.91982},{4.23484,6.96348},{4.19118,7.00714},{4.14753,7.05079},{4.10387,7.07262},{4.06021,7.09445},{4.01655,7.15994},{3.97289,7.22543},{3.92924,7.26909},{3.88558,7.29091},{3.84192,7.31274},{3.79826,7.3564},{3.7546,7.40006},{3.71094,7.44372},{3.66729,7.59652},{3.62363,7.77115},{3.57997,7.85847},{3.53631,7.92396},{3.49265,7.98945},{3.449,8.07676},{3.40534,8.38237},{3.36168,8.73163},{3.31802,8.86261},{3.27436,8.94993},{3.2307,9.01541},{3.18705,9.05907},{3.14339,9.10273},{3.09973,9.14639},{3.05607,9.16822},{3.01241,9.16822},{2.96876,9.19005},{2.9251,9.21187},{2.88144,9.21187},{2.83778,9.21187},{2.79412,9.2337},{2.75046,9.25553},{2.70681,9.27736},{2.66315,9.29919},{2.61949,9.29919},{2.57583,9.29919},{2.53217,9.27736},{2.48852,9.25553},{2.44486,9.27736},{2.4012,9.27736},{2.35754,9.25553},{2.31388,9.25553},{2.27023,9.2337},{2.22657,9.21187},{2.18291,9.19005},{2.13925,9.16822},{2.09559,9.14639},{2.05193,9.10273},{2.00828,9.05907},{1.96462,8.99358},{1.92096,8.90627},{1.8773,8.84078},{1.83364,8.77529},{1.78999,8.70981},{1.74633,8.66615},{1.70267,8.57883},{1.65901,8.36054},{1.61535,8.09859},{1.57169,7.90213},{1.52804,7.79298},{1.48438,7.7275},{1.44072,7.66201},{1.39706,7.59652},{1.3534,7.44372},{1.30975,7.29091},{1.26609,7.22543},{1.22243,7.18177},{1.17877,7.13811},{1.13511,7.09445},{1.09145,7.02897},{1.0478,6.96348},{1.00414,6.91982},{0.96048,6.87616},{0.91682,6.8325},{0.87316,6.76702},{0.82951,6.70153},{0.78585,6.65787},{0.74219,6.59238},{0.69853,6.5269},{0.65487,6.48324},{0.61121,6.41775},{0.56756,6.35226},{0.5239,6.28678},{0.48024,6.19946},{0.43658,6.11214},{0.39292,6.003},{0.34927,5.87202},{0.30561,5.67556}}
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ListanPrieto[5]={{0.48024,4.34399},{0.5239,4.88972},{0.56756,5.26081},{0.61121,5.50093},{0.65487,5.67556},{0.69853,5.87202},{0.74219,6.04666},{0.78585,6.1558},{0.82951,6.26495},{0.87316,6.37409},{0.91682,6.46141},{0.96048,6.54873},{1.00414,6.63604},{1.0478,6.72336},{1.09145,6.81067},{1.13511,6.87616},{1.17877,6.91982},{1.22243,6.98531},{1.26609,7.05079},{1.30975,7.09445},{1.3534,7.15994},{1.39706,7.24726},{1.44072,7.33457},{1.48438,7.46555},{1.52804,7.61835},{1.57169,7.70567},{1.61535,7.8803},{1.65901,8.05493},{1.70267,8.09859},{1.74633,8.27322},{1.78999,8.49151},{1.83364,8.62249},{1.8773,8.75346},{1.92096,8.84078},{1.96462,8.88444},{2.00828,8.90627},{2.05193,8.90627},{2.09559,8.9281},{2.13925,8.94993},{2.18291,8.97175},{2.22657,8.99358},{2.27023,9.01541},{2.31388,9.03724},{2.35754,9.05907},{2.4012,9.0809},{2.44486,9.10273},{2.48852,9.12456},{2.53217,9.12456},{2.57583,9.12456},{2.61949,9.12456},{2.66315,9.14639},{2.70681,9.16822},{2.75046,9.16822},{2.79412,9.16822},{2.83778,9.16822},{2.88144,9.16822},{2.9251,9.16822},{2.96876,9.16822},{3.01241,9.16822},{3.05607,9.16822},{3.09973,9.16822},{3.14339,9.14639},{3.18705,9.10273},{3.2307,9.0809},{3.27436,9.01541},{3.31802,8.90627},{3.36168,8.64432},{3.40534,8.38237},{3.449,8.25139},{3.49265,8.12042},{3.53631,8.01127},{3.57997,7.90213},{3.62363,7.81481},{3.66729,7.7275},{3.71094,7.66201},{3.7546,7.61835},{3.79826,7.57469},{3.84192,7.50921},{3.88558,7.42189},{3.92924,7.3564},{3.97289,7.31274},{4.01655,7.24726},{4.06021,7.18177},{4.10387,7.13811},{4.14753,7.09445},{4.19118,7.05079},{4.23484,6.98531},{4.2785,6.91982},{4.32216,6.87616},{4.36582,6.8325},{4.40948,6.78885},{4.45313,6.72336},{4.49679,6.65787},{4.54045,6.57055},{4.58411,6.50507},{4.62777,6.46141},{4.67142,6.39592},{4.71508,6.33043},{4.75874,6.24312},{4.8024,6.17763},{4.84606,6.11214},{4.88972,6.02483},{4.93337,5.93751},{4.97703,5.82837},{5.02069,5.67556},{5.06435,5.39178},{5.10801,5.12984},{5.15166,4.71508},{5.10801,4.23484},{5.06435,4.03838},{5.02069,3.88558},{4.97703,3.77643},{4.93337,3.68912},{4.88972,3.55814},{4.84606,3.449},{4.8024,3.38351},{4.75874,3.29619},{4.71508,3.20888},{4.67142,3.16522},{4.62777,3.12156},{4.58411,3.05607},{4.54045,2.99058},{4.49679,2.94693},{4.45313,2.9251},{4.40948,2.90327},{4.36582,2.88144},{4.32216,2.85961},{4.2785,2.81595},{4.23484,2.79412},{4.19118,2.77229},{4.14753,2.75046},{4.10387,2.75046},{4.06021,2.72864},{4.01655,2.70681},{3.97289,2.70681},{3.92924,2.70681},{3.88558,2.68498},{3.84192,2.66315},{3.79826,2.66315},{3.7546,2.66315},{3.71094,2.66315},{3.66729,2.66315},{3.62363,2.66315},{3.57997,2.66315},{3.53631,2.66315},{3.49265,2.66315},{3.449,2.66315},{3.40534,2.66315},{3.36168,2.66315},{3.31802,2.66315},{3.27436,2.66315},{3.2307,2.68498},{3.18705,2.70681},{3.14339,2.72864},{3.09973,2.75046},{3.05607,2.77229},{3.01241,2.79412},{2.96876,2.81595},{2.9251,2.83778},{2.88144,2.83778},{2.83778,2.85961},{2.79412,2.88144},{2.75046,2.88144},{2.70681,2.88144},{2.66315,2.88144},{2.61949,2.85961},{2.57583,2.83778},{2.53217,2.83778},{2.48852,2.81595},{2.44486,2.77229},{2.4012,2.75046},{2.35754,2.72864},{2.31388,2.68498},{2.27023,2.66315},{2.22657,2.64132},{2.18291,2.61949},{2.13925,2.61949},{2.09559,2.61949},{2.05193,2.61949},{2.00828,2.59766},{1.96462,2.57583},{1.92096,2.57583},{1.8773,2.554},{1.83364,2.53217},{1.78999,2.53217},{1.74633,2.53217},{1.70267,2.53217},{1.65901,2.53217},{1.61535,2.554},{1.57169,2.57583},{1.52804,2.57583},{1.48438,2.59766},{1.44072,2.61949},{1.39706,2.64132},{1.3534,2.66315},{1.30975,2.68498},{1.26609,2.72864},{1.22243,2.75046},{1.17877,2.77229},{1.13511,2.81595},{1.09145,2.85961},{1.0478,2.90327},{1.00414,2.94693},{0.96048,3.01241},{0.91682,3.0779},{0.87316,3.14339},{0.82951,3.20888},{0.78585,3.29619},{0.74219,3.40534},{0.69853,3.49265},{0.65487,3.55814},{0.61121,3.64546},{0.56756,3.77643},{0.5239,3.92924}}
ListanPrieto[6]={{0.48024,4.34399},{0.5239,4.88972},{0.56756,5.26081},{0.61121,5.50093},{0.65487,5.67556},{0.69853,5.87202},{0.74219,6.04666},{0.78585,6.1558},{0.82951,6.26495},{0.87316,6.37409},{0.91682,6.46141},{0.96048,6.54873},{1.00414,6.63604},{1.0478,6.72336},{1.09145,6.81067},{1.13511,6.87616},{1.17877,6.91982},{1.22243,6.98531},{1.26609,7.05079},{1.30975,7.09445},{1.3534,7.15994},{1.39706,7.24726},{1.44072,7.33457},{1.48438,7.46555},{1.52804,7.61835},{1.57169,7.70567},{1.61535,7.8803},{1.65901,8.05493},{1.70267,8.09859},{1.74633,8.27322},{1.78999,8.49151},{1.83364,8.62249},{1.8773,8.75346},{1.92096,8.84078},{1.96462,8.88444},{2.00828,8.90627},{2.05193,8.90627},{2.09559,8.9281},{2.13925,8.94993},{2.18291,8.97175},{2.22657,8.99358},{2.27023,9.01541},{2.31388,9.03724},{2.35754,9.05907},{2.4012,9.0809},{2.44486,9.10273},{2.48852,9.12456},{2.53217,9.12456},{2.57583,9.12456},{2.61949,9.12456},{2.66315,9.14639},{2.70681,9.16822},{2.75046,9.16822},{2.79412,9.16822},{2.83778,9.16822},{2.88144,9.16822},{2.9251,9.16822},{2.96876,9.16822},{3.01241,9.16822},{3.05607,9.16822},{3.09973,9.16822},{3.14339,9.14639},{3.18705,9.10273},{3.2307,9.0809},{3.27436,9.01541},{3.31802,8.90627},{3.36168,8.64432},{3.40534,8.38237},{3.449,8.25139},{3.49265,8.12042},{3.53631,8.01127},{3.57997,7.90213},{3.62363,7.81481},{3.66729,7.7275},{3.71094,7.66201},{3.7546,7.61835},{3.79826,7.57469},{3.84192,7.50921},{3.88558,7.42189},{3.92924,7.3564},{3.97289,7.31274},{4.01655,7.24726},{4.06021,7.18177},{4.10387,7.13811},{4.14753,7.09445},{4.19118,7.05079},{4.23484,6.98531},{4.2785,6.91982},{4.32216,6.87616},{4.36582,6.8325},{4.40948,6.78885},{4.45313,6.72336},{4.49679,6.65787},{4.54045,6.57055},{4.58411,6.50507},{4.62777,6.46141},{4.67142,6.39592},{4.71508,6.33043},{4.75874,6.24312},{4.8024,6.17763},{4.84606,6.11214},{4.88972,6.02483},{4.93337,5.93751},{4.97703,5.82837},{5.02069,5.67556},{5.06435,5.39178},{5.10801,5.12984},{5.15166,4.71508},{5.10801,4.23484},{5.06435,4.03838},{5.02069,3.88558},{4.97703,3.77643},{4.93337,3.68912},{4.88972,3.55814},{4.84606,3.449},{4.8024,3.38351},{4.75874,3.29619},{4.71508,3.20888},{4.67142,3.16522},{4.62777,3.12156},{4.58411,3.05607},{4.54045,2.99058},{4.49679,2.94693},{4.45313,2.9251},{4.40948,2.90327},{4.36582,2.88144},{4.32216,2.85961},{4.2785,2.81595},{4.23484,2.79412},{4.19118,2.77229},{4.14753,2.75046},{4.10387,2.75046},{4.06021,2.72864},{4.01655,2.70681},{3.97289,2.70681},{3.92924,2.70681},{3.88558,2.68498},{3.84192,2.66315},{3.79826,2.66315},{3.7546,2.66315},{3.71094,2.66315},{3.66729,2.66315},{3.62363,2.66315},{3.57997,2.66315},{3.53631,2.66315},{3.49265,2.66315},{3.449,2.66315},{3.40534,2.66315},{3.36168,2.66315},{3.31802,2.66315},{3.27436,2.66315},{3.2307,2.68498},{3.18705,2.70681},{3.14339,2.72864},{3.09973,2.75046},{3.05607,2.77229},{3.01241,2.79412},{2.96876,2.81595},{2.9251,2.83778},{2.88144,2.83778},{2.83778,2.85961},{2.79412,2.88144},{2.75046,2.88144},{2.70681,2.88144},{2.66315,2.88144},{2.61949,2.85961},{2.57583,2.83778},{2.53217,2.83778},{2.48852,2.81595},{2.44486,2.77229},{2.4012,2.75046},{2.35754,2.72864},{2.31388,2.68498},{2.27023,2.66315},{2.22657,2.64132},{2.18291,2.61949},{2.13925,2.61949},{2.09559,2.61949},{2.05193,2.61949},{2.00828,2.59766},{1.96462,2.57583},{1.92096,2.57583},{1.8773,2.554},{1.83364,2.53217},{1.78999,2.53217},{1.74633,2.53217},{1.70267,2.53217},{1.65901,2.53217},{1.61535,2.554},{1.57169,2.57583},{1.52804,2.57583},{1.48438,2.59766},{1.44072,2.61949},{1.39706,2.64132},{1.3534,2.66315},{1.30975,2.68498},{1.26609,2.72864},{1.22243,2.75046},{1.17877,2.77229},{1.13511,2.81595},{1.09145,2.85961},{1.0478,2.90327},{1.00414,2.94693},{0.96048,3.01241},{0.91682,3.0779},{0.87316,3.14339},{0.82951,3.20888},{0.78585,3.29619},{0.74219,3.40534},{0.69853,3.49265},{0.65487,3.55814},{0.61121,3.64546},{0.56756,3.77643},{0.5239,3.92924}}

(*Poner aqui la familia*)
var=ListanPrieto;
(* el número de curvas estudiadas/semillas de la familia*)
m=6;
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[NMinValue[{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,1,6}]];
Print["Valores medios de curvatura de cada ", var ," en [0.1,0.9]:  ", Table[vmed[j],{j,1,6}]];