The russian translation for this article contains a translation error.
Делитель and Делимое should be visa versa:
Делимое is the dividend
Делитель is the divisor
Thank you in advance for fixing this issue. It's quite confusing
(PHP 4, PHP 5, PHP 7)
atan2 — 两个参数的反正切
$y
, float $x
) : float
本函数计算两个变量
x 和 y
的反正切值。和计算
y / x
的反正切相似，只除了两个参数的符号是用来确定结果的象限之外。
本函数的结果为弧度，其值在 -PI 和 PI 之间（包括 -PI 和 PI）。
yDividend parameter
xDivisor parameter
x 和 y
的反正切弧度值。
The russian translation for this article contains a translation error.
Делитель and Делимое should be visa versa:
Делимое is the dividend
Делитель is the divisor
Thank you in advance for fixing this issue. It's quite confusing
This function will return degree by vertex coordinates in general trigonometrical coordinate system where zero is located at position (1, 0), 90' at (0, 1), 180' at (-1, 0) and so on.
<?php
function GetDegree($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;
}
?>
<?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 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 °
*/
?>
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);
}
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. :)