// JavaScript needs (1) constants, and (2) true UTF8 support for variable names…
if (typeof _ !== 'object') _=new Array(); // can't think of why this should be an array, but why limit ourselves in the future?
_['12°']=Math.PI/30;
_['24°']=Math.PI/15;
_['30°']=Math.PI/6;
_['60°']=Math.PI/3;
_['90°']=Math.PI/2;
_['360°']=Math.PI*2;
_['π×2']=Math.PI*2;
_['π'] =Math.PI;
_['π÷2']=Math.PI/2;
_['π×3÷2']=Math.PI*3/2;
_['1÷3']=1/3;
//rounds x to dp decimal places.
if (typeof Math.roundTo !== 'function')
Math.roundTo=function(x, dp) {return Math.round(x*Math.pow(10,dp))/Math.pow(10,dp);}
// a “sawtooth” in the sense below is the infinite set of numbers from 0 to p.
// The Math.sawtooth() periodic function below will return the same result as x%p (a.k.a. x modulus p)
// when both x and p are positive or negative.
// However, opposing signs: sawtooth(-x,p) or sawtooth(x,-p) do NOT equal the equivelent modulus
// Instead, the sawtooth ALWAYS progresses in the “direction” of p (does not reverse direction for negative numbers),
// so: Math.sawtooth(-10,360) = 350 and Math.sawtooth(-850, 360) = 230
// whereas: (-10 % 360) = -10 and (-850 % 360) = -130
if (typeof Math.sawtooth !== 'function')
Math.sawtooth=function(x,p) {return x-Math.floor(x/p)*p;}
if (typeof Math._2hex !== 'function')
Math._2hex=function(d) {return ((Math.round(d)<16) ? "0" : "") + Math.round(d).toString(16).toUpperCase();}
if (typeof Math.Trig !== 'object') Math.Trig={};
Math.Trig.getAngle=function(x, y, hwRatio) { var angle;
if (typeof hwRatio !== 'number') hwRatio=1;
if (x==0) angle=Math.PI/2;
else angle=Math.atan( Math.abs(y/x) / hwRatio );
if (x<0 && y>0) return Math.PI-angle;
if (x<=0 && y<=0) return Math.PI+angle;
if (x>=0 && y<0) return _['π×2']-angle;
return angle; }
// In a circle, if you divide the circumference into 360 equal segments, each segment corresponds to 1 degree (1°).
// This is not so with an ellipse. This method will adjust the angle passed in ($a) accordingly based on the value
// of the height/width ratio ($hw) of the ellipse.
Math.Trig.scrunchAngle=function($a, $hw) { with (Math) {
$a=sawtooth($a, _['360°']);
// if (sawtooth($a, _['π÷2'])==0) return $a;
if ($a===0) return $a;
if (_['π×3÷2'] < $a) return _['π×2'] - atan(tan(_['π×2'] - $a) * $hw);
if (_['π'] < $a) return _['π'] + atan(tan($a - _['π']) * $hw);
if (_['π÷2'] < $a) return _['π'] - atan(tan(_['π'] - $a) * $hw);
return atan(tan($a) * $hw); } }
Math.Trig.polarToCartesian=function(r, a) {a=Math.sawtooth(a, _['360°']); return {x: r*Math.cos(a), y: r*Math.sin(a)};}
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