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Added atan and atan2. Refs #1193

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This was SVN commit r11231.
This commit is contained in:
Jonathan Waller 2012-03-03 23:37:47 +00:00
parent 649cb7ee7b
commit 291a9e797b
1 changed files with 90 additions and 0 deletions
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90
binaries/data/mods/public/globalscripts/Math.js
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@ -23,3 +23,93 @@ Math.sin = function(a)
{
return Math.cos(a - Math.PI/2);
};
// Returns angle from -pi/2 to pi/2
Math.atan = function(a)
{
var tanPiBy6 = 0.5773502691896257;
var tanPiBy12 = 0.2679491924311227;
var sign = 1;
var inverted = false;
var tanPiBy6Shift = 0;
if (a < 0){
// tan(x) = -tan(-x) so remove sign now and put it back at the end
sign = -1;
a *= -1;
}
if (a > 1){
// tan(pi/2 - x) = 1/tan(x)
inverted = true;
a = 1/a;
}
if (a > tanPiBy12){
// tan(x-pi/6) = (tan(x) - tan(pi/6)) / (1 + tan(pi/6)tan(x))
tanPiBy6Shift = Math.PI/6;
a = (a - tanPiBy6) / (1 + tanPiBy6*a);
}
// Now a will be in the range [-tan(pi/12), tan(pi/12)]
// Use the taylor expansion around 0 with a correction to the linear term to match the pi/12 boundary
// atan(x) = x - x^3/3 + x^5/5 - ...
var r = a*(1.0000000000390272 - a*a*(1/3 - a*a*(1/5 - a*a*(1/7 - a*a*(1/9 - a*a*(1/11 - a*a*(1/13 - a*a/15)))))));
// shift the result back where necessary
r += tanPiBy6Shift;
if (inverted)
r = Math.PI/2 - r;
return sign * r;
};
Math.atan2 = function(y,x)
{
// get unsigned x,y for ease of calculation, this means all angles are in the range [0, pi/2]
var ux = Math.abs(x);
var uy = Math.abs(y);
// holds the result in the upper right quadrant
var r;
// Handle all edges cases to match the spec
if (uy === 0)
{
r = 0;
}
else
{
if (ux === 0)
{
r = Math.PI / 2;
}
if (uy === Infinity)
{
if (ux === Infinity)
r = Math.PI / 4;
else
r = Math.PI / 2;
}
else
{
if (ux === Infinity)
r = 0;
else
r = Math.atan(uy/ux);
}
}
// puts the result into the correct quadrant
// 1/(-0) is the only way to determine the sign for a 0 value
if (x < 0 || 1/x === -Infinity)
{
if (y < 0 || 1/y === -Infinity)
return -Math.PI + r;
else
return Math.PI - r;
}
else
{
if (y < 0 || 1/y === -Infinity)
return -r;
else
return r;
}
};