<?php

 require_once 'angie.class.php'; //we need to use Angie in this class.
 require_once 'point.class.php'; //we need to use the point structure
 require_once 'triangle.class.php'; //we need to use these methods

 class Buddy {
     protected $speed, $x, $y, $points; //these are the variables in the class

     public function __construct($speed, $displace) {
         $this->speed = $speed; //this is his speed
         $this->x = $displace; //pass in the orignal x-position
         $this->y = 0; //he starts at 0
         $interval = 1;
         $d = 0;

         $this->points = array(); //make the points variable into an array
         $this->points[] = array("buddy" => new Point($this->x, $this->y), "angle" => 0.0, "arctan" => atan(0) . " = arctan(0 / 50)"); //add the initial point

         for ($i = 1; $i < 300; $i++) { //this will make the array 30 items long.
             $angle = $this->Angle(Angie::Position($i - 1), $this->points[$i - 1]["buddy"]);
             		//get the angle of Angie's position 2 seconds ago and Buddy's position 2 seconds ago

             if ($this->points[$i - 1]["buddy"]->X() - ($speed * 2 * cos($angle)) < 0) { //if the next X coordinate will be less than zero (Buddy will run into the water)
                 $point = new Point(0.000000000000001, $this->points[$i - 1]["buddy"]->Y() + ($speed * $interval * sin($angle))); //then... set his x position to 0.000000000000001
             }
             else //else or otherwise... do the normal formula
             	$point = new Point(
             							($this->points[$i - 1]["buddy"]->X() > 0 ? //if the previous point was greater than zero...
             								$this->points[$i - 1]["buddy"]->X() - ($speed * $interval * cos($angle)) //then... take the old point minus the new hypotenuse length
             								: $this->points[$i - 1]["buddy"]->X() + ($speed * $interval * cos($angle))), //else... take the old point plus the new hypotenuse length
             							$this->points[$i - 1]["buddy"]->Y() + ($speed * $interval * sin($angle)) //the Y-coordinate
             						);
             $this->points[] = array(
             							"buddy"  => $point, //this is the only important element in this associative array. the others are for debugging purposes.
             							"angie"  => Angie::Position($i),
             							"rads  " => $angle,
             							"atan  " => atan($angle) . " = " .
             											"arctan((" . Angie::Position($i - 1)->Y() . " - " . $this->points[$i - 1]["buddy"]->Y() . ") / " . $this->points[$i - 1]["buddy"]->X() . ")",
             							"cosine" => (($this->points[$i - 1]["buddy"]->X() < 0 ? "-" : "") . $speed * $interval * cos($angle)) . " = 2 * 7 * cos({$angle})",
             							"sine  " => ($speed * $interval * sin($angle)) . " = 2 * 7 * sin({$angle})"
             							);

             if ($this->points[$i]["buddy"]->Y() > $this->points[$i]["angie"]->Y()) { //if Buddy has ran farther than Angie, he has caught up to her so exit the loop (break).
                 break;
             }

             $d += $this->points[$i]["buddy"]->distanceTo($this->points[$i - 1]["buddy"]);
         }

         //print_r($this->points); //this line is for debugging.
         echo "\nBuddy caught up with her in {$i} seconds\n"; //this tells the user after how many seconds they will meet up again.
         echo $this->csv($this->points);
         echo "\n" . Angie::Position($i)->Y();
         echo "\n$d\n";
     }

     public function csv($arr) {
         $s="Time,Buddy X, Buddy Y, Angie X, Angie Y\n";
         for($x=0;$x<sizeof($arr);$x++)
             $s.=$x.",".$arr[$x]["buddy"]->X().",".$arr[$x]["buddy"]->Y().",0," . Angie::Position($x)->Y() . "\n";
         return $s;
     }

     public function getPoint($second) {
         return $this->points[$second];
     }

     public function Angle($point1, $point2) {
         return atan(
         				($point1->Y() - $point2->Y()) //take the difference between the two
         					/ $point2->X()			  //divide by the X-coordinate
         			); 								  //return the arc tangent of the quotient
     }
 }

?>
<?php

 //The class or structure of a point as defined by me, Kyle Stevenson
 class Point {
     protected $x, $y;

     public function __construct($x, $y) {
         $this->x = $x;
         $this->y = $y;
     }

     //The X coordinate in the current coordinate-point.
     public function X() {
         return $this->x;
     }

     //The Y coordinate in the current coordinate-point.
     public function Y() {
         return $this->y;
     }

     //This uses the pythagorean theorem to find the hypotenuse or the distance between this, and the point given.
     public function distanceTo($point) {
         return sqrt(pow($this->x - $point->x, 2) + pow($this->y - $point->y, 2));
     }
 }

?>
<?php

 require_once 'point.class.php';

 class Angie {
     public static function Position($seconds) {
         return new Point(0.0, 1.0 * 3.0/*658*/ * $seconds);
     }
 }

?>