atan2
(PHP 4, PHP 5)
atan2 — Арктангенс двух переменных
Описание
float atan2
( float
$y
, float $x
)
Функция вычисляет арктангенс переменных
x и y. Это подобно вычислению арктангенса
y / x, за исключением того, что
знаки обоих аргументов используются для вычисления квадранта результата.
Функция возвращает значение в радианах в диапазоне от -PI до PI (включительно).
Список параметров
-
y -
Делитель
-
x -
Делимое
Возвращаемые значения
Арктангенс y/x
в радианах.
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Коментарии
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. :)
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);
}
<?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 °
*/
?>
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;
}
?>
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// if $radians is between -PI … +PI then
atan2( sin( $radians ), cos( $radians )) ≈ $radians
?>