atan2

andyidol at gmail dot com (2010-08-10 08:18:10)

This function will return degree by vertex coordinates in general trigonometrical coordinate system where zero is located at position (1, 0), 90' at (0, 1), 180' at (-1, 0) and so on.

<?php

function GetDegree($x, $y)
{
  // we don't want to cause division by zero
  if($x == 0) $x = 1 / 10000;
      
  $deg = rad2deg(atan(abs($y / $x)));
      
  if($y >= 0) $deg = $x < 0 ? 180 - $deg : $deg;
  else        $deg = $x < 0 ? 180 + $deg : 360 - $deg;
      
  return $deg;
      
}

?>

fred dot beck at rrd dot com (2009-01-11 12:39:01)

<?php
/**
 *    Given an origin point of (0,0) and a destination point $x,$y
 *  somewhere on an axis grid, compass() determines the compass
 *  heading(direction) of the destination point from the origin
 *    
 *  HOWEVER, atan2(y,x)'s natural compass thinks east is north, 
 * 
 *  {135}-------{ 90}-------{45}
 *      | +-----[ +y]-----+ |  
 *      | |               | |  
 *      | |               | |  
 *  {180} [-x]  [0,0]  [+x] {0} <--------- North ?
 *      | |               | |  
 *      | |               | |  
 *      | +-----[ -y]-----+ | 
 * {-135}-------{-90}-------{-45}
 *
 *
 *    SO, we simply transpose the (y,x) parameters to atan2(x,y) 
 *     which will both rotate(left) and reflect(mirror) the compass. 
 *
 *  Which gives us this compass
 * 
 *  {-45}-------{ 0 }-------{45}
 *      | +-----[ +y]-----+ |  
 *      | |               | |  
 *      | |               | |  
 *  {-90} [-x]  [0,0]  [+x] {90}
 *      | |               | |  
 *      | |               | |  
 *      | +-----[ -y]-----+ | 
 * {-135}-------{180}-------{135}
 *
 *  FINALLY,` we check if param $x was indeed a negative number, 
 *  if so we simply add 360 to the negative angle returned by atan2() 
 *    
 */
function compass($x,$y)
    {
        if($x==0 AND $y==0){ return 0; } // ...or return 360
        return ($x < 0)
        ? rad2deg(atan2($x,$y))+360      // TRANSPOSED !! y,x params
        : rad2deg(atan2($x,$y)); 
    }
function polar($x,$y)
    {
        $N = ($y>0)?'N':'';
        $S = ($y<0)?'S':'';
        $E = ($x>0)?'E':'';
        $W = ($x<0)?'W':'';        
        return $N.$S.$E.$W;
    }
function show_compass($x,$y)
     {
         return '<BR>'
             .polar($x,$y)
             .' compass( x='.$x.', y='.$y.' )= '
             .number_format(compass($x,$y),3).'&deg';
     }

echo show_compass(0,3);
echo show_compass(.06,3);
echo show_compass(3,3);
echo show_compass(3,.06);
echo show_compass(3,0);
echo show_compass(3,-.06);
echo show_compass(3,-3);
echo show_compass(.06,-3);
echo show_compass(0,-3);
echo show_compass(-.06,-3);
echo show_compass(-3,-3);
echo show_compass(-3,-.06);
echo show_compass(-3,0);
echo show_compass(-3,.06);
echo show_compass(-3,3);
echo show_compass(-.06,3);

/* RENDERS THIS

N compass( x=0, y=3 )= 0 °
NE compass( x=0.06, y=3 )= 1.14576283818 °
NE compass( x=3, y=3 )= 45 °
NE compass( x=3, y=0.06 )= 88.8542371618 °
E compass( x=3, y=0 )= 90 °
SE compass( x=3, y=-0.06 )= 91.1457628382 °
SE compass( x=3, y=-3 )= 135 °
SE compass( x=0.06, y=-3 )= 178.854237162 °
S compass( x=0, y=-3 )= 180 °
SW compass( x=-0.06, y=-3 )= 181.145762838 °
SW compass( x=-3, y=-3 )= 225 °
SW compass( x=-3, y=-0.06 )= 268.854237162 °
W compass( x=-3, y=0 )= 270 °
NW compass( x=-3, y=0.06 )= 271.145762838 °
NW compass( x=-3, y=3 )= 315 °
NW compass( x=-0.06, y=3 )= 358.854237162 °

*/

?>

Monte Shaffer (2007-06-08 11:35:04)

Here is a function that will return a new point [Rotate around non-origin pivot point]
(x,y) is current point
(cx,cy) is pivot point to rotate
=a= is angle in degrees
$_rotation = 1; # -1 = counter, 1 = clockwise
$_precision = 2; # two decimal places
function returnRotatedPoint($x,$y,$cx,$cy,$a)
{
# http://mathforum.org/library/drmath/view/63184.html
global $_rotation; # -1 = counter, 1 = clockwise
global $_precision; # two decimal places

// radius using distance formula
$r = sqrt(pow(($x-$cx),2)+pow(($y-$cy),2));
// initial angle in relation to center
$iA = $_rotation * rad2deg(atan2(($y-$cy),($x-$cx)));
$nx = number_format($r * cos(deg2rad($_rotation * $a + $iA)),$_precision);
$ny = number_format($r * sin(deg2rad($_rotation * $a + $iA)),$_precision);
return array("x"=>$cx+$nx,"y"=>$cy+$ny);
}

reubs at idsdatanet dot com (2003-05-23 13:01:59)

Just a note:
PHP's atan2 function receives parameters in (y,x) and Excel receives it in (x,y) format. Just in case you are porting formulas across. :)