bezierfunction.php

<?php

//Documentation on:
// http://en.wikipedia.org/wiki/B%C3%A9zier_curve
//Implemented by: jfajardo.

//NOTES: This program fails with a length of array > 1020 elements.

//Binomial coefficient
function binomial_coeff($n, $k){
	$j = $res = 1;
	if($k < 0 || $k > $n)
		return 0;
    if(($n - $k) < $k)
        $k = $n - $k;
    while($j <= $k) {
        $res *= $n--;
        $res /= $j++;
      }
    return $res;
}

//$p = array(2, 4, 3, 5);
$p = array(32.588349636161,30.467955694874,31.632679127412,31.991055568193,31.184708576436,31.244437983233,31.871596754599,32.110514381786,28.556614677377,32.991523132039,31.871596754599,30.378361584679,33.006455483738,29.124044041946,32.812334911649,32.319567305575,29.213638152142,25.346159062049,32.40916141577,24.674203235585,32.752605504852,31.319099741729,30.288767474484,32.543552581063,31.901461457998,31.259370334932,29.840796923508,24.778729697479,31.528152665518,32.080649678388,31.244437983233,28.511817622279,16.416612745927,31.199640928135,33.379764276218,28.765667601166,29.975188088801,31.498287962119,29.676541054817,32.633146691258,28.795532304564,33.514155441511,32.946726076942,31.752137941006,32.573417284462,32.42409376747,31.348964445127,32.648079042958,32.707808449754,31.782002644404,30.811399783956,31.961190864794,23.852923892129,25.629873744334,22.688200459591,25.495482579041,23.434818044551,32.095582030087,33.394696627918,31.274302686631,29.825864571809,29.124044041946,29.392826372532,30.960723300948,30.91592624585,29.392826372532,28.257967643393,29.497352834426,32.78247020825,30.796467432257,30.378361584679,29.781067516711,29.213638152142,33.036320187137,29.407758724231,30.960723300948,29.258435207239,29.42269107593,29.736270461614,30.587414508468,31.319099741729,32.110514381786,33.051252538836,26.406356032692,24.226232684609,24.868323807674,32.080649678388,33.738140716999,29.646676351418,33.245373110926,31.184708576436,28.914991118158,32.60328198786,32.095582030087,28.840329359662,32.872064318446,30.124511605793,31.931326161396,29.542149889524,24.375556201601,22.792726921486,24.405420904999,26.734867770074,32.78247020825,30.423158639777,33.320034869422,22.210365205217,25.122173786561,29.258435207239,25.674670799431,33.320034869422,33.484290738113,28.825397007962,32.78247020825,24.823526752577,29.198705800442,30.378361584679,24.136638574414,33.260305462625,29.497352834426,26.481017791188,29.258435207239,31.692408534209,30.079714550695,23.82305918873,25.644806096033,24.330759146503,24.300894443105,24.19636798121,31.961190864794,29.124044041946,28.959788173255,28.929923469857,28.959788173255,23.166035713966,23.166035713966,23.166035713966,27.511350058433,29.900526330305,33.066184890535,29.198705800442,29.721338109914,29.288299910638,29.661608703118,32.005987919892,33.17071135243,29.586946944622,24.405420904999,29.377894020833,33.200576055828,29.900526330305,24.659270883886,24.987782621268,13.221089482298,29.213638152142,25.614941392634,33.125914297332,31.66254383081,33.753073068698,29.661608703118,26.018114888513,21.523477027054,26.928988342164,23.882788595527,26.197303108903,29.452555779329,32.170243788583,33.334967221121,29.512285186126,27.257500079546,21.926650522932,24.509947366894,28.213170588295,29.586946944622,29.975188088801,28.944855821556,23.106306307169,25.032579676366,25.674670799431,30.303699826183,28.929923469857,30.438090991476,25.286429655252,26.06291194361,25.420820820545,32.304634953876,29.124044041946,29.019517580052,29.258435207239,29.288299910638,29.183773448743,29.183773448743,28.929923469857,28.780599952865,28.601411732474,28.989652876654,29.452555779329,28.720870546068,28.765667601166,29.034449931751,29.198705800442,29.736270461614,29.228570503841,29.333096965735,29.258435207239,29.138976393646,29.258435207239,24.285962091406,23.345223934356,24.21130033291,22.479147535802,23.539344506446,24.450217960097,24.405420904999,23.494547451348,23.584141561543,30.049849847297,29.691473406516,22.882321031681,23.882788595527,23.673735671738,24.330759146503,23.524412154746,22.404485777306,25.346159062049,22.195432853518,30.886061542452,30.273835122785,29.288299910638,29.138976393646,29.960255737102,29.258435207239,23.166035713966,29.213638152142,32.483823174266,20.582738870004,22.434350480705,26.555679549684,28.511817622279,19.552406602759,23.852923892129,26.555679549684,23.628938616641,22.434350480705,23.688668023438,20.46328005641,22.255162260314,23.494547451348,23.44975039625,24.704067938983,23.509479803047,23.584141561543,23.599073913242,24.689135587284,29.362961669134,32.065717326689,30.93085859755,30.512752749972,32.722740801454,19.432947789166,28.765667601166,24.315826794804,28.67607349097,29.198705800442,21.792259357639,30.109579254094,32.931793725242,18.820721369498,18.97004488649,25.286429655252,55.300456570644,50.820751060884,28.705938194369,28.287832346791,16.192627470439,28.586479380775,22.449282832404,21.553341730452,23.001779845274,22.956982790177,28.481952918881,27.959320609409,28.183305884897,31.871596754599,20.343821242817,23.106306307169,20.6574006285,28.30276469849,30.034917495598,23.09137395547,23.240697472462,28.183305884897,25.868791371521,24.644338532186,21.538409378753,28.452088215482,31.28923503833,20.537941814906,21.822124061038,13.250954185697,28.631276435873,20.702197683598,21.95651522633,15.102565796398,19.567338954458,20.134768319028,28.422223512084,19.925715395239,20.582738870004,22.628471052794,20.881385903988,22.434350480705,17.581336178465,26.525814846286,23.703600375137,17.939712619246,29.318164614036,23.539344506446,20.448347704711,14.654595245422,24.01717976082,19.985444802036,29.781067516711,29.258435207239,28.929923469857,29.04938228345,29.61681164802,30.766602728858,21.433882916858,29.138976393646,30.453023343175,17.237892089383,29.452555779329,32.319567305575,21.359221158362,20.612603573402,22.882321031681,19.597203657857,16.909380352001,26.182370757204,22.986847493575,19.940647746938,21.150168234574,22.255162260314,22.135703446721,20.746994738695,22.449282832404,21.20989764137,24.56967677369,17.909847915847,19.014841941588,19.865985988442,21.642935840647,20.896318255687,19.507609547662,19.642000712954,18.731127259303,19.552406602759,23.509479803047,26.645273659879,20.119835967329,49.865080552135,32.483823174266,33.7232083653,32.289702602177,32.42409376747,32.334499657274,32.961658428641,33.140846649031,32.185176140282,32.304634953876,32.140379085185,31.811867347802,32.648079042958,32.827267263348,32.334499657274,32.110514381786,32.185176140282,32.379296712372,32.394229064071,33.066184890535,32.020920271591,32.364364360673,32.334499657274,32.259837898778,32.095582030087,32.528620229364,33.932261289089,32.364364360673,32.677943746356,33.215508407527,32.857131966746,34.305570081569,32.97659078034,32.737673153153,32.40916141577,32.379296712372,31.826799699502,33.678411310202,32.274770250478,32.22997319538,31.737205589306,31.498287962119,32.498755525966,31.050317411143,32.633146691258,32.633146691258,31.558017368916,32.42409376747,32.259837898778,32.364364360673,32.155311436884,32.901929021844,32.722740801454,33.275237814324,32.78247020825,33.90239658569,32.379296712372,32.364364360673,33.140846649031,34.425028895162,32.663011394657,32.379296712372,30.856196839054,34.350367136666,33.439493683015,32.513687877665,32.244905547079,32.633146691258,32.827267263348,32.42409376747,32.722740801454,32.244905547079,32.752605504852,33.215508407527,32.991523132039,32.259837898778,32.722740801454,32.663011394657,32.663011394657,33.588817200007,32.543552581063,32.842199615047,32.558484932762,32.364364360673,32.737673153153,30.826332135655,33.245373110926,32.752605504852,32.946726076942,30.990588004346,32.22997319538,32.78247020825,32.319567305575,34.380231840065,31.991055568193,34.425028895162,29.138976393646,32.468890822567,31.468423258721,34.425028895162,33.469358386414,32.961658428641,33.245373110926,33.394696627918,30.034917495598,32.767537856551,31.617746775713,33.34989957282,34.201043619674,32.185176140282,32.439026119169,32.827267263348,33.185643704129,33.484290738113,32.961658428641,32.692876098055,32.79740255995,32.483823174266,32.588349636161,32.961658428641,31.8566644029,31.199640928135,32.737673153153,32.513687877665,32.588349636161,32.901929021844,33.066184890535,33.334967221121,32.588349636161,33.514155441511,32.513687877665,33.051252538836,32.857131966746,33.7232083653,32.692876098055,32.453958470868,32.468890822567,32.901929021844,32.648079042958,33.857599530593,32.379296712372,32.483823174266,32.558484932762,33.379764276218,34.514623005358,32.274770250478,32.633146691258,32.916861373543,32.812334911649,33.215508407527,32.304634953876,34.245840674772,33.125914297332,32.259837898778,32.588349636161,33.618681903406,32.633146691258,33.603749551706,32.543552581063,33.364831924519,32.827267263348,33.15577900073,33.17071135243,32.125446733486,31.826799699502,32.857131966746,32.901929021844,32.05078497499,32.42409376747,32.78247020825,32.79740255995,32.677943746356,32.78247020825,32.379296712372,32.692876098055,32.334499657274,32.857131966746,32.215040843681,32.42409376747,32.558484932762,32.40916141577,32.573417284462,31.408693851924,32.513687877665,32.40916141577,32.03585262329,32.125446733486,32.05078497499,30.841264487354,33.290170166023,32.215040843681,32.319567305575,31.961190864794,32.274770250478,32.364364360673,32.03585262329,32.543552581063,31.946258513095,33.364831924519,32.379296712372,32.961658428641,32.513687877665,32.916861373543,33.051252538836,32.827267263348,31.468423258721,32.349432008974,32.498755525966,32.40916141577,32.842199615047,32.05078497499,32.60328198786,32.215040843681,32.140379085185,32.125446733486,32.364364360673,32.394229064071,32.349432008974,32.394229064071,32.543552581063,32.349432008974,32.40916141577,32.304634953876,32.618214339559,32.394229064071,32.22997319538,32.080649678388,32.289702602177,32.200108491982,32.707808449754,33.588817200007,32.349432008974,32.005987919892,33.603749551706,32.140379085185,32.453958470868,33.454426034714,31.871596754599,32.42409376747,32.439026119169,31.543085017217,32.633146691258,32.394229064071,32.200108491982,32.22997319538,32.155311436884,32.125446733486,32.125446733486,32.60328198786,32.886996670145,31.528152665518,32.60328198786,34.215975971374,32.200108491982,32.03585262329,32.334499657274,32.857131966746,32.185176140282,32.200108491982,32.155311436884,33.275237814324,32.886996670145,32.274770250478,32.946726076942,32.573417284462,33.17071135243,32.42409376747,31.020452707745,32.244905547079,32.304634953876,32.439026119169,32.110514381786,33.379764276218,32.289702602177,32.304634953876,33.17071135243,32.259837898778,32.588349636161,33.006455483738,31.214573279834,32.22997319538,32.483823174266,32.40916141577,32.498755525966,32.200108491982,32.080649678388,32.364364360673,32.110514381786,32.170243788583,32.737673153153,32.140379085185,32.752605504852,32.379296712372,30.691940970362,32.05078497499,32.767537856551,31.752137941006,32.289702602177,32.767537856551,24.987782621268,32.334499657274,33.081117242234,32.200108491982,32.080649678388,32.483823174266,32.543552581063,32.170243788583,32.42409376747,32.215040843681,32.707808449754,32.633146691258,32.289702602177,32.618214339559,32.558484932762,32.244905547079,32.140379085185,32.304634953876,32.737673153153,32.244905547079,32.97659078034,33.215508407527,32.961658428641,32.394229064071,32.394229064071,32.170243788583,32.005987919892,32.767537856551,31.961190864794,32.304634953876,32.170243788583,31.8566644029,33.364831924519,32.185176140282,31.841732051201,32.722740801454,32.185176140282,33.081117242234,32.274770250478,32.543552581063,32.931793725242,32.498755525966,32.543552581063,32.528620229364,30.199173364289,32.60328198786,33.439493683015,32.42409376747,32.543552581063,31.946258513095,32.722740801454,31.871596754599,32.439026119169,32.842199615047,32.648079042958,32.692876098055,29.572014592922,32.857131966746,32.42409376747,29.661608703118,31.767070292705,32.60328198786,32.364364360673,32.588349636161,32.78247020825,32.304634953876,32.812334911649,32.707808449754,30.034917495598,32.379296712372,32.543552581063,32.498755525966,32.648079042958,33.409628979617,32.005987919892,32.364364360673,32.498755525966,33.364831924519,33.409628979617,34.708743577447,31.841732051201,33.066184890535,32.752605504852,32.349432008974,32.498755525966,32.304634953876,32.498755525966,32.663011394657,33.021387835438,32.767537856551,32.528620229364,32.991523132039,32.618214339559,33.991990695886,32.752605504852,32.513687877665,33.633614255105,32.528620229364,32.558484932762,32.498755525966,32.79740255995,32.543552581063,33.54402014491,33.140846649031,32.42409376747,32.543552581063,32.110514381786,32.872064318446,32.588349636161,33.678411310202,32.633146691258,32.543552581063,32.79740255995,32.364364360673,32.812334911649,32.215040843681,32.901929021844,32.498755525966,32.468890822567,32.274770250478,32.78247020825,32.558484932762,32.185176140282,32.453958470868,32.991523132039,32.97659078034,32.42409376747,32.543552581063,32.79740255995,31.976123216494,32.78247020825,31.782002644404,32.722740801454,32.080649678388,32.901929021844,33.021387835438,33.275237814324,32.42409376747,32.663011394657,32.663011394657,32.244905547079,32.60328198786,32.648079042958,32.42409376747,32.468890822567,32.274770250478,32.289702602177,32.543552581063,32.901929021844,32.304634953876,32.752605504852,32.200108491982,32.573417284462,32.752605504852,32.349432008974,32.42409376747,32.244905547079,32.767537856551,32.827267263348,32.40916141577,32.752605504852,32.79740255995,32.259837898778,32.618214339559,32.483823174266,32.618214339559,32.588349636161,33.514155441511,32.379296712372,32.78247020825,32.663011394657,32.349432008974,32.79740255995,32.618214339559,32.692876098055,32.528620229364,33.051252538836,32.677943746356,32.573417284462,32.394229064071,32.648079042958,32.722740801454,32.991523132039,32.78247020825,30.064782198996,28.153441181498,33.424561331316,32.78247020825,33.484290738113,32.663011394657,32.78247020825,33.066184890535,33.34989957282,33.036320187137,33.320034869422,33.200576055828,32.468890822567,33.15577900073,32.618214339559,32.857131966746,32.573417284462,32.185176140282,32.42409376747,32.513687877665,32.663011394657,32.812334911649,32.857131966746,33.245373110926,32.394229064071,32.931793725242,31.931326161396,32.05078497499,32.872064318446,32.60328198786,33.245373110926,32.648079042958,32.872064318446,33.066184890535,32.78247020825,32.97659078034,32.931793725242,32.663011394657,33.140846649031,33.081117242234,32.439026119169,32.439026119169,32.663011394657,33.021387835438,33.125914297332,20.299024187719,33.066184890535,33.618681903406,33.290170166023,32.707808449754,32.573417284462,32.857131966746,30.990588004346,30.124511605793,29.870661626906,31.632679127412,32.319567305575,32.961658428641,32.946726076942,33.200576055828,32.78247020825,32.767537856551,32.737673153153,32.812334911649,32.588349636161,33.110981945633,32.722740801454,32.961658428641,30.079714550695,31.8566644029,32.901929021844,32.663011394657,32.453958470868,33.17071135243,32.901929021844,32.60328198786,32.633146691258,32.648079042958,32.663011394657,33.066184890535,32.901929021844,33.021387835438,32.42409376747,33.245373110926,31.931326161396,33.006455483738,32.42409376747,33.125914297332,32.961658428641,32.78247020825,32.767537856551,32.020920271591,33.334967221121,31.826799699502,32.42409376747,32.543552581063,33.021387835438,32.931793725242,32.78247020825,32.453958470868,32.707808449754,32.737673153153,32.737673153153,32.543552581063,32.573417284462,32.752605504852,33.066184890535,33.857599530593,33.125914297332,32.42409376747,32.827267263348,32.513687877665,32.961658428641,32.722740801454,33.15577900073,33.200576055828,32.78247020825,32.03585262329,32.558484932762,30.019985143898,32.767537856551,32.379296712372,32.005987919892,32.394229064071,32.22997319538,32.379296712372,32.095582030087,32.468890822567,31.976123216494,32.22997319538,31.468423258721,32.42409376747,32.916861373543,32.170243788583,33.499223089812,33.051252538836,32.842199615047,32.931793725242,32.79740255995,32.394229064071,32.842199615047,32.42409376747,32.633146691258,32.558484932762,33.15577900073,32.677943746356,33.34989957282,31.423626203623,32.588349636161,33.738140716999,31.513220313818,31.28923503833,33.021387835438,32.991523132039,31.378829148526,32.439026119169,31.453490907022,33.215508407527,32.468890822567,32.60328198786,32.857131966746,32.558484932762,32.40916141577,32.513687877665,32.528620229364,32.020920271591,33.006455483738,31.916393809697,32.468890822567,32.215040843681,32.692876098055,31.408693851924,32.020920271591,32.080649678388,32.663011394657,32.483823174266,32.857131966746);
$l = count($p);
$n = $l-1;
echo "n = ".$n.";\n";
//$B = array();


//Discretizando $t ->(0,1)
for($j = 0; $j<=$n; $j++){
	$t = $j/($n);
   // echo "j = ".$j.";\n";
   // echo "\t t = ".$t.";\n";

    $r = (1-$t);
    $B[$j] = 0;

    //Recorriendo el array $p para Calcular los puntos de Bezier
    for($i = 0; $i <=$n; $i++){
    //    echo "\t i = ".$i.";\n";        
        $e = ($n-$i);
    //    echo "\t \t p[".$i."] =".$p[$i].";\n";
        $B[$j] += binomial_coeff($n, $i)*pow($r, $e)*pow($t, $i)*$p[$i];
    }
    //echo "\t \t \t B[".$j."] =".$B[$j].";\n";
    echo $j." ".$B[$j]."\n";
}

?>