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. :)
(PHP 4, PHP 5, PHP 7, PHP 8)
atan2 — Arc tangent of two variables
This function calculates the arc tangent of the two variables
x
and y
. It is
similar to calculating the arc tangent of
y
/ x
, except that
the signs of both arguments are used to determine the quadrant of
the result.
The function returns the result in radians, which is between -PI and PI (inclusive).
y
Dividend parameter
x
Divisor parameter
The arc tangent of y
/x
in radians.
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. :)
<?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).'°'; }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 THISN 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 °*/?>
The russian translation for this article contains a translation error.Делитель and Делимое should be visa versa:Делимое is the dividendДелитель is the divisorThank you in advance for fixing this issue. It's quite confusing
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 $_precision = 2; # two decimal placesfunction returnRotatedPoint($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); }