<?php

$segmentos =30;
$x=array(0,10,80,30);
$y=array(0,10,40,50);

function bezier($p,$steps){
  $t = 1 / $steps;
  $temp = $t * $t;
  $ret = array();
  $f = $p[0];
  $fd = 3 * ($p[1] - $p[0]) * $t;
  $fdd_per_2=3*($p[0]-2*$p[1]+$p[2])*$temp;
  $fddd_per_2=3*(3*($p[1]-$p[2])+$p[3]-$p[0])*$temp*$t;
  $fddd = $fddd_per_2 + $fddd_per_2;
  $fdd = $fdd_per_2 + $fdd_per_2;
  $fddd_per_6 = $fddd_per_2 * (1.0 / 3);
  for ($loop=0; $loop<$steps; $loop++) {
  array_push($ret,$f);
  $f = $f + $fd + $fdd_per_2 + $fddd_per_6;
  $fd = $fd + $fdd + $fddd_per_2;
  $fdd = $fdd + $fddd;
  $fdd_per_2 = $fdd_per_2 + $fddd_per_2;
  }
  return $ret;
}

$by = bezier($y,$segmentos);
$bx = bezier($x,$segmentos);
header ("Content-type: image/jpeg");
$tam = 200;
$im = imagecreate($tam,$tam);
$background_color = imagecolorallocate ($im, 200, 200, 200);
$tc = imagecolorallocate ($im, 233, 14, 91);
for($i=0;$i<$segmentos-1;$i++)
  imageline($im,$bx[$i],$tam-$by[$i],$bx[$i+1],$tam-$by[$i+1],$tc);
imagejpeg($im); 
imagedestroy($im);
?>