(*  The following are examples of curvature analysis  in seeds of  Vitis*)






	(*******************************  Forcallat tinta*)

Needs["Splines`"]

Forctinta[1]={{0.95735,4.74324},{0.97911,4.88467},{1.00087,5.36334},{1.02262,5.48301},{1.04438,5.55916},{1.06614,5.66795},{1.0879,5.76586},{1.10966,5.8529},{1.13141,5.92905},{1.15317,5.99432},{1.17493,6.07048},{1.19669,6.13575},{1.21845,6.20102},{1.2402,6.25542},{1.26196,6.28805},{1.28372,6.35333},{1.30548,6.4186},{1.32724,6.473},{1.34899,6.53827},{1.37075,6.59267},{1.39251,6.6253},{1.41427,6.69058},{1.43603,6.75585},{1.45778,6.77761},{1.47954,6.81025},{1.5013,6.84288},{1.52306,6.87552},{1.54482,6.91904},{1.56657,6.95167},{1.58833,6.99519},{1.61009,7.02783},{1.63185,7.04958},{1.65361,7.08222},{1.67536,7.10398},{1.69712,7.12574},{1.71888,7.13662},{1.74064,7.1475},{1.7624,7.16925},{1.78415,7.19101},{1.80591,7.22365},{1.82767,7.24541},{1.84943,7.25629},{1.87119,7.26716},{1.89294,7.27804},{1.9147,7.2998},{1.93646,7.32156},{1.95822,7.34332},{1.97998,7.3542},{2.00173,7.36508},{2.02349,7.38683},{2.04525,7.39771},{2.06701,7.40859},{2.08877,7.41947},{2.11052,7.43035},{2.13228,7.45211},{2.15404,7.46299},{2.1758,7.46299},{2.19756,7.46299},{2.21931,7.47387},{2.24107,7.48474},{2.26283,7.49562},{2.28459,7.5065},{2.30635,7.5065},{2.3281,7.5065},{2.34986,7.51738},{2.37162,7.52826},{2.39338,7.52826},{2.41514,7.52826},{2.43689,7.53914},{2.45865,7.55002},{2.48041,7.55002},{2.50217,7.55002},{2.52393,7.55002},{2.54568,7.55002},{2.56744,7.55002},{2.5892,7.55002},{2.61096,7.5609},{2.63272,7.57178},{2.65447,7.5609},{2.67623,7.55002},{2.69799,7.55002},{2.71975,7.55002},{2.7415,7.53914},{2.76326,7.52826},{2.78502,7.52826},{2.80678,7.52826},{2.82854,7.52826},{2.85029,7.52826},{2.87205,7.52826},{2.89381,7.51738},{2.91557,7.5065},{2.93733,7.5065},{2.95908,7.51738},{2.98084,7.51738},{3.0026,7.49562},{3.02436,7.48474},{3.04612,7.48474},{3.06787,7.48474},{3.08963,7.49562},{3.11139,7.51738},{3.13315,7.51738},{3.15491,7.5065},{3.17666,7.5065},{3.19842,7.5065},{3.22018,7.5065},{3.24194,7.5065},{3.2637,7.5065},{3.28545,7.5065},{3.30721,7.5065},{3.32897,7.5065},{3.35073,7.5065},{3.37249,7.5065},{3.39424,7.49562},{3.416,7.48474},{3.43776,7.47387},{3.45952,7.46299},{3.48128,7.46299},{3.50303,7.46299},{3.52479,7.46299},{3.54655,7.47387},{3.56831,7.47387},{3.59007,7.46299},{3.61182,7.46299},{3.63358,7.46299},{3.65534,7.46299},{3.6771,7.46299},{3.69886,7.45211},{3.72061,7.45211},{3.74237,7.46299},{3.76413,7.46299},{3.78589,7.45211},{3.80765,7.44123},{3.8294,7.45211},{3.85116,7.45211},{3.87292,7.44123},{3.89468,7.45211},{3.91644,7.46299},{3.93819,7.45211},{3.95995,7.44123},{3.98171,7.44123},{4.00347,7.43035},{4.02523,7.41947},{4.04698,7.41947},{4.06874,7.41947},{4.0905,7.41947},{4.11226,7.41947},{4.13402,7.41947},{4.15577,7.40859},{4.17753,7.39771},{4.19929,7.39771},{4.22105,7.38683},{4.24281,7.37595},{4.26456,7.37595},{4.28632,7.36508},{4.30808,7.3542},{4.32984,7.34332},{4.3516,7.32156},{4.37335,7.31068},{4.39511,7.2998},{4.41687,7.28892},{4.43863,7.27804},{4.46039,7.26716},{4.48214,7.26716},{4.5039,7.25629},{4.52566,7.23453},{4.54742,7.21277},{4.56918,7.19101},{4.59093,7.18013},{4.61269,7.16925},{4.63445,7.1475},{4.65621,7.12574},{4.67796,7.11486},{4.69972,7.10398},{4.72148,7.0931},{4.74324,7.07134},{4.765,7.03871},{4.78675,7.01695},{4.80851,7.00607},{4.83027,6.97343},{4.85203,6.96255},{4.87379,6.90816},{4.89554,6.87552},{4.9173,6.85376},{4.93906,6.81025},{4.96082,6.77761},{4.98258,6.75585},{5.00433,6.74497},{5.02609,6.72321},{5.04785,6.6797},{5.06961,6.6253},{5.09137,6.59267},{5.11312,6.51651},{5.13488,6.45124},{5.15664,6.36421},{5.1784,6.25542},{5.20016,6.15751},{5.22191,5.63532},{5.24367,5.15664},{5.26543,5.13488},{5.24367,5.11312},{5.22191,5.09137},{5.20016,4.99346},{5.1784,4.87379},{5.15664,4.78675},{5.13488,4.72148},{5.11312,4.65621},{5.09137,4.53654},{5.06961,4.44951},{5.04785,4.40599},{5.02609,4.3516},{5.00433,4.30808},{4.98258,4.26456},{4.96082,4.21017},{4.93906,4.14489},{4.9173,4.06874},{4.89554,4.01435},{4.87379,3.98171},{4.85203,3.93819},{4.83027,3.89468},{4.80851,3.85116},{4.78675,3.80765},{4.765,3.77501},{4.74324,3.73149},{4.72148,3.6771},{4.69972,3.64446},{4.67796,3.59007},{4.65621,3.54655},{4.63445,3.54655},{4.61269,3.52479},{4.59093,3.49216},{4.56918,3.44864},{4.54742,3.40512},{4.52566,3.37249},{4.5039,3.33985},{4.48214,3.30721},{4.46039,3.27458},{4.43863,3.24194},{4.41687,3.19842},{4.39511,3.15491},{4.37335,3.13315},{4.3516,3.11139},{4.32984,3.07875},{4.30808,3.04612},{4.28632,3.01348},{4.26456,2.99172},{4.24281,2.95908},{4.22105,2.91557},{4.19929,2.88293},{4.17753,2.85029},{4.15577,2.7959},{4.13402,2.77414},{4.11226,2.73063},{4.0905,2.69799},{4.06874,2.66535},{4.04698,2.62184},{4.02523,2.5892},{4.00347,2.57832},{3.98171,2.54568},{3.95995,2.50217},{3.93819,2.46953},{3.91644,2.43689},{3.89468,2.39338},{3.87292,2.33898},{3.85116,2.29547},{3.8294,2.24107},{3.80765,2.16492},{3.78589,2.08877},{3.76413,2.02349},{3.74237,1.9691},{3.72061,1.9147},{3.69886,1.86031},{3.6771,1.81679},{3.65534,1.79503},{3.63358,1.75152},{3.61182,1.69712},{3.59007,1.65361},{3.56831,1.59921},{3.54655,1.53394},{3.52479,1.46866},{3.50303,1.42515},{3.48128,1.39251},{3.45952,1.35987},{3.43776,1.33812},{3.416,1.31636},{3.39424,1.2946},{3.37249,1.26196},{3.35073,1.22933},{3.32897,1.21845},{3.30721,1.19669},{3.28545,1.16405},{3.2637,1.15317},{3.24194,1.14229},{3.22018,1.13141},{3.19842,1.13141},{3.17666,1.12054},{3.15491,1.10966},{3.13315,1.10966},{3.11139,1.10966},{3.08963,1.09878},{3.06787,1.09878},{3.04612,1.10966},{3.02436,1.10966},{3.0026,1.10966},{2.98084,1.10966},{2.95908,1.10966},{2.93733,1.10966},{2.91557,1.09878},{2.89381,1.09878},{2.87205,1.10966},{2.85029,1.12054},{2.82854,1.13141},{2.80678,1.14229},{2.78502,1.14229},{2.76326,1.15317},{2.7415,1.17493},{2.71975,1.16405},{2.69799,1.15317},{2.67623,1.16405},{2.65447,1.18581},{2.63272,1.19669},{2.61096,1.18581},{2.5892,1.18581},{2.56744,1.19669},{2.54568,1.19669},{2.52393,1.19669},{2.50217,1.19669},{2.48041,1.19669},{2.45865,1.19669},{2.43689,1.20757},{2.41514,1.21845},{2.39338,1.22933},{2.37162,1.2402},{2.34986,1.25108},{2.3281,1.26196},{2.30635,1.27284},{2.28459,1.2946},{2.26283,1.2946},{2.24107,1.28372},{2.21931,1.2946},{2.19756,1.31636},{2.1758,1.32724},{2.15404,1.33812},{2.13228,1.35987},{2.11052,1.39251},{2.08877,1.40339},{2.06701,1.41427},{2.04525,1.45778},{2.02349,1.53394},{2.00173,1.62097},{1.97998,1.67536},{1.95822,1.74064},{1.93646,1.84943},{1.9147,2.02349},{1.89294,2.14316},{1.87119,2.26283},{1.84943,2.3825},{1.82767,2.43689},{1.80591,2.50217},{1.78415,2.55656},{1.7624,2.57832},{1.74064,2.60008},{1.71888,2.62184},{1.69712,2.64359},{1.67536,2.67623},{1.65361,2.70887},{1.63185,2.76326},{1.61009,2.83942},{1.58833,2.89381},{1.56657,2.93733},{1.54482,2.95908},{1.52306,3.0026},{1.5013,3.057},{1.47954,3.07875},{1.45778,3.12227},{1.43603,3.17666},{1.41427,3.22018},{1.39251,3.25282},{1.37075,3.29633},{1.34899,3.35073},{1.32724,3.40512},{1.30548,3.45952},{1.28372,3.50303},{1.26196,3.56831},{1.2402,3.63358},{1.21845,3.6771},{1.19669,3.72061},{1.17493,3.78589},{1.15317,3.85116},{1.13141,3.89468},{1.10966,3.95995},{1.0879,4.0361},{1.06614,4.10138},{1.04438,4.15577},{1.02262,4.2972},{1.00087,4.46039},{0.97911,4.58005},{0.95735,4.9717}}
Forctinta[2]={{1.28372,5.11312},{1.30548,4.98258},{1.32724,4.78675},{1.34899,4.68884},{1.37075,4.43863},{1.39251,4.37335},{1.41427,4.28632},{1.43603,4.21017},{1.45778,4.12314},{1.47954,4.02523},{1.5013,3.97083},{1.52306,3.92731},{1.54482,3.8838},{1.56657,3.84028},{1.58833,3.77501},{1.61009,3.70973},{1.63185,3.63358},{1.65361,3.53567},{1.67536,3.4704},{1.69712,3.42688},{1.71888,3.35073},{1.74064,3.29633},{1.7624,3.2637},{1.78415,3.2093},{1.80591,3.14403},{1.82767,3.07875},{1.84943,2.82854},{1.87119,2.78502},{1.89294,2.73063},{1.9147,2.66535},{1.93646,2.5892},{1.95822,2.36074},{1.97998,2.09964},{2.00173,2.01261},{2.02349,1.97998},{2.04525,1.74064},{2.06701,1.708},{2.08877,1.68624},{2.11052,1.66449},{2.13228,1.64273},{2.15404,1.62097},{2.1758,1.59921},{2.19756,1.57745},{2.21931,1.5557},{2.24107,1.53394},{2.26283,1.52306},{2.28459,1.52306},{2.30635,1.51218},{2.3281,1.5013},{2.34986,1.49042},{2.37162,1.47954},{2.39338,1.47954},{2.41514,1.47954},{2.43689,1.47954},{2.45865,1.46866},{2.48041,1.45778},{2.50217,1.45778},{2.52393,1.44691},{2.54568,1.43603},{2.56744,1.43603},{2.5892,1.43603},{2.61096,1.43603},{2.63272,1.42515},{2.65447,1.41427},{2.67623,1.41427},{2.69799,1.40339},{2.71975,1.39251},{2.7415,1.39251},{2.76326,1.39251},{2.78502,1.39251},{2.80678,1.39251},{2.82854,1.39251},{2.85029,1.38163},{2.87205,1.37075},{2.89381,1.37075},{2.91557,1.37075},{2.93733,1.37075},{2.95908,1.37075},{2.98084,1.37075},{3.0026,1.37075},{3.02436,1.37075},{3.04612,1.37075},{3.06787,1.37075},{3.08963,1.37075},{3.11139,1.37075},{3.13315,1.38163},{3.15491,1.39251},{3.17666,1.40339},{3.19842,1.41427},{3.22018,1.42515},{3.24194,1.43603},{3.2637,1.44691},{3.28545,1.45778},{3.30721,1.46866},{3.32897,1.49042},{3.35073,1.51218},{3.37249,1.53394},{3.39424,1.56657},{3.416,1.59921},{3.43776,1.62097},{3.45952,1.64273},{3.48128,1.68624},{3.50303,1.74064},{3.52479,1.77328},{3.54655,1.79503},{3.56831,1.82767},{3.59007,1.86031},{3.61182,1.9147},{3.63358,2.1214},{3.65534,2.30635},{3.6771,2.33898},{3.69886,2.36074},{3.72061,2.3825},{3.74237,2.41514},{3.76413,2.44777},{3.78589,2.49129},{3.80765,2.54568},{3.8294,2.5892},{3.85116,2.62184},{3.87292,2.65447},{3.89468,2.68711},{3.91644,2.70887},{3.93819,2.73063},{3.95995,2.7415},{3.98171,2.76326},{4.00347,2.7959},{4.02523,2.81766},{4.04698,2.83942},{4.06874,2.86117},{4.0905,2.88293},{4.11226,2.90469},{4.13402,2.93733},{4.15577,2.99172},{4.17753,3.03524},{4.19929,3.057},{4.22105,3.08963},{4.24281,3.12227},{4.26456,3.15491},{4.28632,3.19842},{4.30808,3.23106},{4.32984,3.25282},{4.3516,3.28545},{4.37335,3.31809},{4.39511,3.36161},{4.41687,3.416},{4.43863,3.45952},{4.46039,3.50303},{4.48214,3.54655},{4.5039,3.59007},{4.52566,3.63358},{4.54742,3.6771},{4.56918,3.73149},{4.59093,3.77501},{4.61269,3.80765},{4.63445,3.85116},{4.65621,3.89468},{4.67796,3.94907},{4.69972,4.01435},{4.72148,4.05786},{4.74324,4.10138},{4.765,4.16665},{4.78675,4.21017},{4.80851,4.24281},{4.83027,4.27544},{4.85203,4.31896},{4.87379,4.42775},{4.89554,4.52566},{4.9173,4.60181},{4.93906,4.7106},{4.96082,4.81939},{4.98258,4.92818},{5.00433,5.02609},{5.02609,5.124},{5.04785,5.27631},{5.06961,5.46125},{5.09137,5.62444},{5.11312,5.77674},{5.09137,5.90729},{5.06961,5.98344},{5.04785,6.0596},{5.02609,6.15751},{5.00433,6.23366},{4.98258,6.29893},{4.96082,6.37509},{4.93906,6.48388},{4.9173,6.59267},{4.89554,6.64706},{4.87379,6.6797},{4.85203,6.74497},{4.83027,6.79937},{4.80851,6.82113},{4.78675,6.85376},{4.765,6.91904},{4.74324,6.98431},{4.72148,7.00607},{4.69972,7.02783},{4.67796,7.07134},{4.65621,7.11486},{4.63445,7.15837},{4.61269,7.19101},{4.59093,7.22365},{4.56918,7.25629},{4.54742,7.27804},{4.52566,7.2998},{4.5039,7.32156},{4.48214,7.34332},{4.46039,7.36508},{4.43863,7.38683},{4.41687,7.40859},{4.39511,7.43035},{4.37335,7.45211},{4.3516,7.47387},{4.32984,7.49562},{4.30808,7.51738},{4.28632,7.52826},{4.26456,7.53914},{4.24281,7.5609},{4.22105,7.58265},{4.19929,7.59353},{4.17753,7.60441},{4.15577,7.61529},{4.13402,7.61529},{4.11226,7.61529},{4.0905,7.62617},{4.06874,7.63705},{4.04698,7.63705},{4.02523,7.63705},{4.00347,7.63705},{3.98171,7.64793},{3.95995,7.65881},{3.93819,7.65881},{3.91644,7.65881},{3.89468,7.66969},{3.87292,7.68057},{3.85116,7.66969},{3.8294,7.66969},{3.80765,7.68057},{3.78589,7.68057},{3.76413,7.68057},{3.74237,7.68057},{3.72061,7.68057},{3.69886,7.69144},{3.6771,7.70232},{3.65534,7.69144},{3.63358,7.68057},{3.61182,7.69144},{3.59007,7.70232},{3.56831,7.70232},{3.54655,7.70232},{3.52479,7.70232},{3.50303,7.70232},{3.48128,7.70232},{3.45952,7.70232},{3.43776,7.70232},{3.416,7.70232},{3.39424,7.70232},{3.37249,7.70232},{3.35073,7.70232},{3.32897,7.70232},{3.30721,7.69144},{3.28545,7.68057},{3.2637,7.69144},{3.24194,7.70232},{3.22018,7.70232},{3.19842,7.70232},{3.17666,7.70232},{3.15491,7.70232},{3.13315,7.70232},{3.11139,7.70232},{3.08963,7.70232},{3.06787,7.7132},{3.04612,7.72408},{3.02436,7.72408},{3.0026,7.72408},{2.98084,7.72408},{2.95908,7.72408},{2.93733,7.72408},{2.91557,7.72408},{2.89381,7.72408},{2.87205,7.72408},{2.85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Mdearco[4]={{0.22036,6.1039},{0.26443,5.7954},{0.3085,5.55301},{0.35257,5.31062},{0.39664,5.15637},{0.44072,4.98008},{0.48479,4.84787},{0.52886,4.73769},{0.57293,4.62751},{0.617,4.5614},{0.66107,4.49529},{0.70514,4.42919},{0.74922,4.38512},{0.79329,4.34104},{0.83736,4.29697},{0.88143,4.23087},{0.9255,4.18679},{0.96957,4.14272},{1.01364,4.09865},{1.05772,4.07662},{1.10179,4.05458},{1.14586,4.03254},{1.18993,3.98847},{1.234,3.9444},{1.27807,3.92236},{1.32215,3.92236},{1.36622,3.92236},{1.41029,3.90033},{1.45436,3.85626},{1.49843,3.83422},{1.5425,3.83422},{1.58657,3.83422},{1.63065,3.83422},{1.67472,3.83422},{1.71879,3.83422},{1.76286,3.83422},{1.80693,3.81219},{1.851,3.79015},{1.89508,3.79015},{1.93915,3.79015},{1.98322,3.79015},{2.02729,3.79015},{2.07136,3.79015},{2.11543,3.79015},{2.1595,3.79015},{2.20358,3.81219},{2.24765,3.83422},{2.29172,3.83422},{2.33579,3.83422},{2.37986,3.81219},{2.42393,3.79015},{2.468,3.79015},{2.51208,3.79015},{2.55615,3.79015},{2.60022,3.79015},{2.64429,3.79015},{2.68836,3.79015},{2.73243,3.79015},{2.77651,3.79015},{2.82058,3.79015},{2.86465,3.79015},{2.90872,3.79015},{2.95279,3.79015},{2.99686,3.79015},{3.04093,3.79015},{3.08501,3.79015},{3.12908,3.79015},{3.17315,3.81219},{3.21722,3.83422},{3.26129,3.83422},{3.30536,3.85626},{3.34944,3.87829},{3.39351,3.87829},{3.43758,3.90033},{3.48165,3.92236},{3.52572,3.92236},{3.56979,3.9444},{3.61386,3.96644},{3.65794,3.98847},{3.70201,4.01051},{3.74608,4.03254},{3.79015,4.05458},{3.83422,4.07662},{3.87829,4.12069},{3.92236,4.16476},{3.96644,4.20883},{4.01051,4.2529},{4.05458,4.29697},{4.09865,4.36308},{4.14272,4.42919},{4.18679,4.49529},{4.23087,4.58344},{4.27494,4.67158},{4.31901,4.78176},{4.36308,4.89194},{4.40715,4.98008},{4.45122,5.1123},{4.49529,5.33265},{4.53937,5.70726},{4.49529,6.14798},{4.45122,6.45648},{4.40715,6.69887},{4.36308,6.89719},{4.31901,6.98534},{4.27494,7.05144},{4.23087,7.13959},{4.18679,7.22773},{4.14272,7.35994},{4.09865,7.49216},{4.05458,7.55826},{4.01051,7.62437},{3.96644,7.71252},{3.92236,7.80066},{3.87829,7.91084},{3.83422,7.99898},{3.79015,8.06509},{3.74608,8.13119},{3.70201,8.1973},{3.65794,8.26341},{3.61386,8.32952},{3.56979,8.39562},{3.52572,8.4397},{3.48165,8.48377},{3.43758,8.54987},{3.39351,8.61598},{3.34944,8.68209},{3.30536,8.79227},{3.26129,8.90245},{3.21722,9.01262},{3.17315,9.1228},{3.12908,9.25502},{3.08501,9.40927},{3.04093,9.51945},{2.99686,9.62963},{2.95279,9.71777},{2.90872,9.76184},{2.86465,9.80591},{2.82058,9.89406},{2.77651,10.02627},{2.73243,10.11441},{2.68836,10.15848},{2.64429,10.20256},{2.60022,10.24663},{2.55615,10.26866},{2.51208,10.2907},{2.468,10.31273},{2.42393,10.31273},{2.37986,10.31273},{2.33579,10.31273},{2.29172,10.31273},{2.24765,10.31273},{2.20358,10.31273},{2.1595,10.31273},{2.11543,10.26866},{2.07136,10.22459},{2.02729,10.20256},{1.98322,10.18052},{1.93915,10.18052},{1.89508,10.15848},{1.851,10.13645},{1.80693,10.09238},{1.76286,9.9822},{1.71879,9.84998},{1.67472,9.69573},{1.63065,9.51945},{1.58657,9.38723},{1.5425,9.27705},{1.49843,9.14484},{1.45436,9.03466},{1.41029,8.94652},{1.36622,8.88041},{1.32215,8.83634},{1.27807,8.77023},{1.234,8.68209},{1.18993,8.59395},{1.14586,8.52784},{1.10179,8.46173},{1.05772,8.39562},{1.01364,8.32952},{0.96957,8.28545},{0.9255,8.24137},{0.88143,8.17527},{0.83736,8.10916},{0.79329,8.04305},{0.74922,7.99898},{0.70514,7.93287},{0.66107,7.84473},{0.617,7.77862},{0.57293,7.71252},{0.52886,7.62437},{0.48479,7.53623},{0.44072,7.44809},{0.39664,7.33791},{0.35257,7.18366},{0.3085,6.98534},{0.26443,6.61073}}
Mdearco[5]={{0.17629,5.75133},{0.22036,5.44283},{0.26443,5.31062},{0.3085,5.1784},{0.35257,5.04619},{0.39664,4.93601},{0.44072,4.82583},{0.48479,4.71565},{0.52886,4.62751},{0.57293,4.5614},{0.617,4.49529},{0.66107,4.42919},{0.70514,4.36308},{0.74922,4.29697},{0.79329,4.23087},{0.83736,4.16476},{0.88143,4.14272},{0.9255,4.12069},{0.96957,4.07662},{1.01364,4.05458},{1.05772,4.03254},{1.10179,3.98847},{1.14586,3.96644},{1.18993,3.9444},{1.234,3.92236},{1.27807,3.90033},{1.32215,3.87829},{1.36622,3.87829},{1.41029,3.87829},{1.45436,3.87829},{1.49843,3.87829},{1.5425,3.87829},{1.58657,3.85626},{1.63065,3.83422},{1.67472,3.83422},{1.71879,3.83422},{1.76286,3.83422},{1.80693,3.81219},{1.851,3.79015},{1.89508,3.79015},{1.93915,3.79015},{1.98322,3.76811},{2.02729,3.74608},{2.07136,3.74608},{2.11543,3.76811},{2.1595,3.79015},{2.20358,3.79015},{2.24765,3.81219},{2.29172,3.83422},{2.33579,3.85626},{2.37986,3.85626},{2.42393,3.83422},{2.468,3.83422},{2.51208,3.83422},{2.55615,3.81219},{2.60022,3.76811},{2.64429,3.74608},{2.68836,3.74608},{2.73243,3.72404},{2.77651,3.70201},{2.82058,3.70201},{2.86465,3.70201},{2.90872,3.70201},{2.95279,3.70201},{2.99686,3.70201},{3.04093,3.70201},{3.08501,3.70201},{3.12908,3.70201},{3.17315,3.72404},{3.21722,3.74608},{3.26129,3.76811},{3.30536,3.81219},{3.34944,3.83422},{3.39351,3.83422},{3.43758,3.85626},{3.48165,3.90033},{3.52572,3.9444},{3.56979,3.96644},{3.61386,3.98847},{3.65794,4.01051},{3.70201,4.03254},{3.74608,4.07662},{3.79015,4.12069},{3.83422,4.16476},{3.87829,4.23087},{3.92236,4.29697},{3.96644,4.36308},{4.01051,4.45122},{4.05458,4.51733},{4.09865,4.60547},{4.14272,4.71565},{4.18679,4.82583},{4.23087,4.93601},{4.27494,5.02415},{4.31901,5.15637},{4.36308,5.35469},{4.40715,5.77337},{4.36308,6.3463},{4.31901,6.72091},{4.27494,6.87516},{4.23087,6.9633},{4.18679,7.07348},{4.14272,7.18366},{4.09865,7.2718},{4.05458,7.35994},{4.01051,7.44809},{3.96644,7.51419},{3.92236,7.5803},{3.87829,7.64641},{3.83422,7.71252},{3.79015,7.77862},{3.74608,7.82269},{3.70201,7.8888},{3.65794,7.95491},{3.61386,7.99898},{3.56979,8.04305},{3.52572,8.08712},{3.48165,8.13119},{3.43758,8.1973},{3.39351,8.26341},{3.34944,8.30748},{3.30536,8.35155},{3.26129,8.39562},{3.21722,8.4397},{3.17315,8.54987},{3.12908,8.68209},{3.08501,8.7482},{3.04093,8.83634},{2.99686,8.96855},{2.95279,9.10077},{2.90872,9.21095},{2.86465,9.32113},{2.82058,9.45334},{2.77651,9.58555},{2.73243,9.6737},{2.68836,9.73981},{2.64429,9.82795},{2.60022,9.89406},{2.55615,9.93813},{2.51208,9.96016},{2.468,9.96016},{2.42393,9.9822},{2.37986,10.00423},{2.33579,9.9822},{2.29172,9.96016},{2.24765,9.96016},{2.20358,9.96016},{2.1595,9.9822},{2.11543,10.00423},{2.07136,10.00423},{2.02729,9.9822},{1.98322,9.96016},{1.93915,9.96016},{1.89508,9.96016},{1.851,9.96016},{1.80693,9.93813},{1.76286,9.89406},{1.71879,9.82795},{1.67472,9.71777},{1.63065,9.62963},{1.58657,9.56352},{1.5425,9.45334},{1.49843,9.34316},{1.45436,9.16687},{1.41029,8.96855},{1.36622,8.83634},{1.32215,8.7482},{1.27807,8.68209},{1.234,8.57191},{1.18993,8.46173},{1.14586,8.39562},{1.10179,8.35155},{1.05772,8.30748},{1.01364,8.26341},{0.96957,8.21934},{0.9255,8.17527},{0.88143,8.13119},{0.83736,8.06509},{0.79329,7.97694},{0.74922,7.8888},{0.70514,7.77862},{0.66107,7.66844},{0.617,7.5803},{0.57293,7.49216},{0.52886,7.42605},{0.48479,7.33791},{0.44072,7.22773},{0.39664,7.11755},{0.35257,6.98534},{0.3085,6.80905},{0.26443,6.58869},{0.22036,6.23612}}
Mdearco[6]={{0.22036,5.53098},{0.26443,5.09026},{0.3085,4.91397},{0.35257,4.8038},{0.39664,4.69362},{0.44072,4.58344},{0.48479,4.49529},{0.52886,4.38512},{0.57293,4.29697},{0.617,4.23087},{0.66107,4.16476},{0.70514,4.09865},{0.74922,4.01051},{0.79329,3.96644},{0.83736,3.9444},{0.88143,3.90033},{0.9255,3.85626},{0.96957,3.83422},{1.01364,3.81219},{1.05772,3.76811},{1.10179,3.74608},{1.14586,3.72404},{1.18993,3.70201},{1.234,3.67997},{1.27807,3.65794},{1.32215,3.65794},{1.36622,3.6359},{1.41029,3.61386},{1.45436,3.61386},{1.49843,3.61386},{1.5425,3.61386},{1.58657,3.61386},{1.63065,3.61386},{1.67472,3.61386},{1.71879,3.61386},{1.76286,3.61386},{1.80693,3.61386},{1.851,3.6359},{1.89508,3.65794},{1.93915,3.65794},{1.98322,3.65794},{2.02729,3.67997},{2.07136,3.70201},{2.11543,3.67997},{2.1595,3.65794},{2.20358,3.65794},{2.24765,3.6359},{2.29172,3.61386},{2.33579,3.61386},{2.37986,3.61386},{2.42393,3.61386},{2.468,3.6359},{2.51208,3.65794},{2.55615,3.65794},{2.60022,3.65794},{2.64429,3.67997},{2.68836,3.70201},{2.73243,3.70201},{2.77651,3.70201},{2.82058,3.67997},{2.86465,3.65794},{2.90872,3.65794},{2.95279,3.65794},{2.99686,3.65794},{3.04093,3.65794},{3.08501,3.65794},{3.12908,3.65794},{3.17315,3.65794},{3.21722,3.67997},{3.26129,3.70201},{3.30536,3.72404},{3.34944,3.76811},{3.39351,3.79015},{3.43758,3.81219},{3.48165,3.83422},{3.52572,3.87829},{3.56979,3.92236},{3.61386,3.9444},{3.65794,3.98847},{3.70201,4.03254},{3.74608,4.07662},{3.79015,4.16476},{3.83422,4.2529},{3.87829,4.34104},{3.92236,4.45122},{3.96644,4.53937},{4.01051,4.64954},{4.05458,4.78176},{4.09865,4.89194},{4.14272,5.02415},{4.18679,5.57505},{4.14272,6.23612},{4.09865,6.54462},{4.05458,6.74294},{4.01051,6.89719},{3.96644,7.00737},{3.92236,7.09551},{3.87829,7.18366},{3.83422,7.2718},{3.79015,7.35994},{3.74608,7.44809},{3.70201,7.53623},{3.65794,7.62437},{3.61386,7.71252},{3.56979,7.77862},{3.52572,7.84473},{3.48165,7.91084},{3.43758,7.95491},{3.39351,8.02102},{3.34944,8.08712},{3.30536,8.13119},{3.26129,8.17527},{3.21722,8.21934},{3.17315,8.26341},{3.12908,8.30748},{3.08501,8.37359},{3.04093,8.46173},{2.99686,8.54987},{2.95279,8.66005},{2.90872,8.79227},{2.86465,8.88041},{2.82058,8.94652},{2.77651,9.0567},{2.73243,9.16687},{2.68836,9.23298},{2.64429,9.29909},{2.60022,9.40927},{2.55615,9.51945},{2.51208,9.56352},{2.468,9.58555},{2.42393,9.62963},{2.37986,9.6737},{2.33579,9.69573},{2.29172,9.69573},{2.24765,9.69573},{2.20358,9.69573},{2.1595,9.6737},{2.11543,9.69573},{2.07136,9.73981},{2.02729,9.76184},{1.98322,9.78388},{1.93915,9.78388},{1.89508,9.76184},{1.851,9.73981},{1.80693,9.73981},{1.76286,9.71777},{1.71879,9.6737},{1.67472,9.62963},{1.63065,9.58555},{1.58657,9.54148},{1.5425,9.47538},{1.49843,9.3652},{1.45436,9.25502},{1.41029,9.16687},{1.36622,8.83634},{1.32215,8.7482},{1.27807,8.63802},{1.234,8.48377},{1.18993,8.35155},{1.14586,8.24137},{1.10179,8.17527},{1.05772,8.13119},{1.01364,8.06509},{0.96957,7.99898},{0.9255,7.95491},{0.88143,7.91084},{0.83736,7.86677},{0.79329,7.82269},{0.74922,7.77862},{0.70514,7.69048},{0.66107,7.55826},{0.617,7.44809},{0.57293,7.35994},{0.52886,7.2718},{0.48479,7.16162},{0.44072,7.02941},{0.39664,6.87516},{0.35257,6.69887},{0.3085,6.52258},{0.26443,6.14798}}

(*Poner aqui la familia*)
var=Forctinta
(* el número de curvas estudiadas/semillas de la familia*)
m=3;
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[SetPrecision[{curbe[j,t],0.1<t<1},50],t,WorkingPrecision->8]];
vmed[j]=Abs[NIntegrate[curbe[j,t],{t,0.2,0.8}]];
dibcurbe[j]=Plot[{curbe[j,t],vmed[j]},{t,0,1},PlotRange->{-4,4},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,1,3}]];
Print["Valores medios de curvatura de cada ", var ," en [0.1,0.9]:  ", Table[vmed[j],{j,1,3}]];