php script to process data from form

<?php

if(isset($_POST) && !empty($_POST))
{
    $current_star=(isset($_POST["current_star"]) && !empty($_POST["current_star"])) ? $_POST["current_star"] : false;
    $distance_1=(isset($_POST["distance_1"]) && !empty($_POST["distance_1"])) ? (float)0+$_POST["distance_1"] : 0;
    $distance_2=(isset($_POST["distance_2"]) && !empty($_POST["distance_2"])) ? (float)0+$_POST["distance_2"] : 0;
    $distance_3=(isset($_POST["distance_3"]) && !empty($_POST["distance_3"])) ? (float)0+$_POST["distance_3"] : 0;
    $distance_4=(isset($_POST["distance_4"]) && !empty($_POST["distance_4"])) ? (float)0+$_POST["distance_4"] : 0;
    $distance_5=(isset($_POST["distance_5"]) && !empty($_POST["distance_5"])) ? (float)0+$_POST["distance_5"] : 0;
    $distance_6=(isset($_POST["distance_6"]) && !empty($_POST["distance_6"])) ? (float)0+$_POST["distance_6"] : 0;
    $distance_7=(isset($_POST["distance_7"]) && !empty($_POST["distance_7"])) ? (float)0+$_POST["distance_7"] : 0;
    $distance_8=(isset($_POST["distance_8"]) && !empty($_POST["distance_8"])) ? (float)0+$_POST["distance_8"] : 0;
    $distance_9=(isset($_POST["distance_9"]) && !empty($_POST["distance_9"])) ? (float)0+$_POST["distance_9"] : 0;

    $result = array();
    $combination = array();

    $system["SOL"]=array(0,0,0,0);
    $system["WOLF_497"]=array(0.125,41.46875,11.96875,0);
    $system["HUOKANG"]=array(-12.1875,35.46875,-25.28125,0);
    $system["DEMETER"]=array(-55.34375,40.8125,7.5625,0);
    $system["CLOTTI"]=array(-88.03125,47.1875,-6.15625,0);
    $system["FU_HAITING"]=array(-69.46875,32.125,-48.875,0);
    $system["SAN_GUARALARU"]=array(-124.34375,41.8125,-60.71875,0);
    $system["HARAS"]=array(-118.75,14.40625,-21.40625,0);
    $system["ARABHA"]=array(-120.75,43.78125,-22.125,0);

    $system["SOL"][3]=$distance_1;
    $system["WOLF_497"][3]=$distance_2;
    $system["HUOKANG"][3]=$distance_3;
    $system["DEMETER"][3]=$distance_4;
    $system["CLOTTI"][3]=$distance_5;
    $system["FU_HAITING"][3]=$distance_6;
    $system["SAN_GUARALARU"][3]=$distance_7;
    $system["HARAS"][3]=$distance_8;
    $system["ARABHA"][3]=$distance_9;

    $system_with_distance=array();

    foreach($system as $key => $value)
    {
        if($value[3] > 0)
        {
            $system_with_distance[]=$key;
        }
    }
    if(!$current_star)
    {
        die("Please enter the name of the source star!");
    }
    if(count($system_with_distance) < 4)
    {
        die("Distances to at least 4 of the referenced stars are required!");
    }
    elseif(count($system_with_distance) == 4)
    {
        $star_pos=(trilateration3d($system[$system_with_distance[0]], $system[$system_with_distance[1]], $system[$system_with_distance[2]], $system[$system_with_distance[3]]));
        echo "Estimated position of <b>".$current_star."</b>: ".$star_pos[0].", ".$star_pos[1].", ".$star_pos[2].".";
    }
    elseif(count($system_with_distance) > 4)
    {
        $i=0;
        $x_total=0;
        $y_total=0;
        $z_total=0;

        $permutations=combinations($system_with_distance, 4);

        foreach($permutations as $value)
        {
            $calculated_coordinates[$i]=trilateration3d($system[$value[0]],$system[$value[1]],$system[$value[2]],$system[$value[3]]);
            $calculated_coordinates[$i]["permutation"]=str_replace("_", " ", $value[0]) . " | " . str_replace("_", " ", $value[1]) . " | " . str_replace("_", " ", $value[2]) . " | " . str_replace("_", " ", $value[3]);
            if(isset($calculated_coordinates[$i][0]) && !empty($calculated_coordinates[$i][0]) && isset($calculated_coordinates[$i][1]) && !empty($calculated_coordinates[$i][1]) && isset($calculated_coordinates[$i][2]) && !empty($calculated_coordinates[$i][2]))
            {
                $calculated_coordinates[$i]["x"]=$calculated_coordinates[$i][0];
                $calculated_coordinates[$i]["y"]=$calculated_coordinates[$i][1];
                $calculated_coordinates[$i]["z"]=$calculated_coordinates[$i][2];
                unset($calculated_coordinates[$i][0],$calculated_coordinates[$i][1],$calculated_coordinates[$i][2]);
                $x_total+=$calculated_coordinates[$i]["x"];
                $y_total+=$calculated_coordinates[$i]["y"];
                $z_total+=$calculated_coordinates[$i]["z"];
            }
            $i++;
        }
        foreach($calculated_coordinates as $key => $value)
        {
            if(!isset($value["x"]))
                unset($calculated_coordinates[$key]);

        }

        $n=count($calculated_coordinates);
        echo "<pre>";
        echo "Estimated position of <b>".$current_star."</b>: ".number_format(($x_total/$n),6).", ".number_format(($y_total/$n),6).", ".number_format(($z_total/$n),6).".\n<b>(Coordinates averaged from the results below)</b>\n\n";
        print_r($calculated_coordinates);
        echo "</pre>";
        die;
    }
}
else
    die("No data entered!");

function trilateration3d($p1,$p2,$p3,$p4){
        $ex = vector_unit(vector_diff($p2, $p1));
        $i = vector_dot_product($ex, vector_diff($p3, $p1));
        $ey = vector_unit(vector_diff(vector_diff($p3, $p1), vector_multiply($ex, $i)));
        $ez = vector_cross($ex,$ey);
        $d = vector_length($p2, $p1);
        $r1 = $p1[3]; $r2 = $p2[3]; $r3 = $p3[3]; $r4 = $p4[3];
        if($d - $r1 >= $r2 || $r2 >= $d + $r1){
                return array();
        }
        $j = vector_dot_product($ey, vector_diff($p3, $p1));
        $x = (($r1*$r1) - ($r2*$r2) + ($d*$d)) / (2*$d);
        $y = ((($r1*$r1) - ($r3*$r3) + ($i*$i) + ($j*$j)) / (2*$j)) - (($i*$x) / $j);
        $z = $r1*$r1 - $x*$x - $y*$y;

        if($z < 0){
                return array();
        }
        $z1 = sqrt($z);
        $z2 = $z1 * -1;

        $result1 = $p1;
        $result1 = vector_sum($result1, vector_multiply($ex, $x));
        $result1 = vector_sum($result1, vector_multiply($ey, $y));
        $result1 = vector_sum($result1, vector_multiply($ez, $z1));
        $result2 = $p1;
        $result2 = vector_sum($result2, vector_multiply($ex, $x));
        $result2 = vector_sum($result2, vector_multiply($ey, $y));
        $result2 = vector_sum($result2, vector_multiply($ez, $z2));

        $r1 = vector_length($p4, $result1);
        $r2 = vector_length($p4, $result2);
        $t1 = $r1 - $r4;
        $t2 = $r2 - $r4;
        $coords = array();
        if(abs($t1) < abs($t2)){
                $coords = array(round($result1[0], 5), round($result1[1], 5), round($result1[2], 5));
        }
        else{
                $coords = array(round($result2[0], 5), round($result2[1], 5), round($result2[2], 5));
        }
        return $coords;
}

function vector_length($p1, $p2){
        $a1 = $p1[0];
        $a2 = $p2[0];
        $b1 = $p1[1];
        $b2 = $p2[1];
        $c1 = $p1[2];
        $c2 = $p2[2];
        $dist = sqrt((($a2-$a1)*($a2-$a1))+(($b2-$b1)*($b2-$b1))+(($c2-$c1)*($c2-$c1)));

        return round($dist, 3, PHP_ROUND_HALF_EVEN);
}

function vector_sum($v1, $v2){
        $v = array();
        $v[0] = $v1[0] + $v2[0];
        $v[1] = $v1[1] + $v2[1];
        $v[2] = $v1[2] + $v2[2];
        return $v;
}

function vector_cross($v1, $v2){
        $v = array();
        $v[0] = ($v1[1] * $v2[2]) - ($v1[2] * $v2[1]);
        $v[1] = ($v1[2] * $v2[0]) - ($v1[0] * $v2[2]);
        $v[2] = ($v1[0] * $v2[1]) - ($v1[1] * $v2[0]);
        return $v;
}

function vector_multiply($v, $i){
        return array($v[0] * $i, $v[1] * $i, $v[2] * $i);
}

function vector_dot_product($v1, $v2){
        $ret = ($v1[0] * $v2[0]) + ($v1[1] * $v2[1]) + ($v1[2] * $v2[2]);
        return $ret;
}

function vector_diff($p1,$p2){
        $ret = array($p1[0] - $p2[0], $p1[1] - $p2[1], $p1[2] - $p2[2]);
        return $ret;
}

function vector_norm($v){
        $l = sqrt(($v[0]*$v[0])+($v[1]*$v[1])+($v[2]*$v[2]));
        return $l;
}

function vector_div($v, $l){
        return array($v[0]/$l, $v[1] / $l, $v[2] / $l);
}

function vector_unit($v){
        $l = vector_norm($v);
        if($l == 0){
                return -1;
        }
        return vector_div($v, $l);
}

function combinations(array $myArray, $choose) {

  global $result, $combination;

  $n = count($myArray);

  function inner ($start, $choose_, $arr, $n) {
    global $result, $combination;

    if ($choose_ == 0) array_push($result,$combination);
    else for ($i = $start; $i <= $n - $choose_; ++$i) {
           array_push($combination, $arr[$i]);
           inner($i + 1, $choose_ - 1, $arr, $n);
           array_pop($combination);
         }
  }
  inner(0, $choose, $myArray, $n);
  return $result;
}

?>