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 — 2 変数のアークタンジェント
この関数は、2 つの変数 x および
y のアークタンジェントを計算します。
y / x
のアークタンジェントを計算するのに似ていますが、
2 つの引数の符号を用いて結果の象限を定義することが異なっています。
この関数は、結果を -PI から PI の間(両端を含む)のラジアンで返します。
y被除数。
x除数。
y/x
のアークタンジェントをラジアンで返します。
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 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 °
*/
?>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 confusingHere 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
// if $radians is between -PI … +PI then
atan2( sin( $radians ), cos( $radians )) ≈ $radians
?>This function will return degree by vertex coordinates in general trigonometrical coordinate system where zero is located at position (1, 0), 90' at (0, 1), 180' at (-1, 0) and so on.
<?php
function GetDegree($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;
}
?>