/*

  Easing Equations v1.5

  May 1, 2003

  (c) 2003 Robert Penner, all rights reserved. 

  This work is subject to the terms in http://www.robertpenner.com/easing_terms_of_use.html.  

  

  These tweening functions provide different flavors of 

  math-based motion under a consistent API. 

  

  Types of easing:

  

	  Linear

	  Quadratic

	  Cubic

	  Quartic

	  Quintic

	  Sinusoidal

	  Exponential

	  Circular

	  Elastic

	  Back

	  Bounce



  Changes:

  1.5 - added bounce easing

  1.4 - added elastic and back easing

  1.3 - tweaked the exponential easing functions to make endpoints exact

  1.2 - inline optimizations (changing t and multiplying in one step)--thanks to Tatsuo Kato for the idea

  

  Discussed in Chapter 7 of 

  Robert Penner's Programming Macromedia Flash MX

  (including graphs of the easing equations)

  

  http://www.robertpenner.com/profmx

  http://www.amazon.com/exec/obidos/ASIN/0072223561/robertpennerc-20

*/





// simple linear tweening - no easing

// t: current time, b: beginning value, c: change in value, d: duration

Math.linearTween = function (t, b, c, d) {

	return c*t/d + b;

};





 ///////////// QUADRATIC EASING: t^2 ///////////////////



// quadratic easing in - accelerating from zero velocity

// t: current time, b: beginning value, c: change in value, d: duration

// t and d can be in frames or seconds/milliseconds

Math.easeInQuad = function (t, b, c, d) {

	return c*(t/=d)*t + b;

};



// quadratic easing out - decelerating to zero velocity

Math.easeOutQuad = function (t, b, c, d) {

	return -c *(t/=d)*(t-2) + b;

};



// quadratic easing in/out - acceleration until halfway, then deceleration

Math.easeInOutQuad = function (t, b, c, d) {

	if ((t/=d/2) < 1) return c/2*t*t + b;

	return -c/2 * ((--t)*(t-2) - 1) + b;

};





 ///////////// CUBIC EASING: t^3 ///////////////////////



// cubic easing in - accelerating from zero velocity

// t: current time, b: beginning value, c: change in value, d: duration

// t and d can be frames or seconds/milliseconds

Math.easeInCubic = function (t, b, c, d) {

	return c*(t/=d)*t*t + b;

};



// cubic easing out - decelerating to zero velocity

Math.easeOutCubic = function (t, b, c, d) {

	return c*((t=t/d-1)*t*t + 1) + b;

};



// cubic easing in/out - acceleration until halfway, then deceleration

Math.easeInOutCubic = function (t, b, c, d) {

	if ((t/=d/2) < 1) return c/2*t*t*t + b;

	return c/2*((t-=2)*t*t + 2) + b;

};





 ///////////// QUARTIC EASING: t^4 /////////////////////



// quartic easing in - accelerating from zero velocity

// t: current time, b: beginning value, c: change in value, d: duration

// t and d can be frames or seconds/milliseconds

Math.easeInQuart = function (t, b, c, d) {

	return c*(t/=d)*t*t*t + b;

};



// quartic easing out - decelerating to zero velocity

Math.easeOutQuart = function (t, b, c, d) {

	return -c * ((t=t/d-1)*t*t*t - 1) + b;

};



// quartic easing in/out - acceleration until halfway, then deceleration

Math.easeInOutQuart = function (t, b, c, d) {

	if ((t/=d/2) < 1) return c/2*t*t*t*t + b;

	return -c/2 * ((t-=2)*t*t*t - 2) + b;

};





 ///////////// QUINTIC EASING: t^5  ////////////////////



// quintic easing in - accelerating from zero velocity

// t: current time, b: beginning value, c: change in value, d: duration

// t and d can be frames or seconds/milliseconds

Math.easeInQuint = function (t, b, c, d) {

	return c*(t/=d)*t*t*t*t + b;

};



// quintic easing out - decelerating to zero velocity

Math.easeOutQuint = function (t, b, c, d) {

	return c*((t=t/d-1)*t*t*t*t + 1) + b;

};



// quintic easing in/out - acceleration until halfway, then deceleration

Math.easeInOutQuint = function (t, b, c, d) {

	if ((t/=d/2) < 1) return c/2*t*t*t*t*t + b;

	return c/2*((t-=2)*t*t*t*t + 2) + b;

};







 ///////////// SINUSOIDAL EASING: sin(t) ///////////////



// sinusoidal easing in - accelerating from zero velocity

// t: current time, b: beginning value, c: change in position, d: duration

Math.easeInSine = function (t, b, c, d) {

	return -c * Math.cos(t/d * (Math.PI/2)) + c + b;

};



// sinusoidal easing out - decelerating to zero velocity

Math.easeOutSine = function (t, b, c, d) {

	return c * Math.sin(t/d * (Math.PI/2)) + b;

};



// sinusoidal easing in/out - accelerating until halfway, then decelerating

Math.easeInOutSine = function (t, b, c, d) {

	return -c/2 * (Math.cos(Math.PI*t/d) - 1) + b;

};





 ///////////// EXPONENTIAL EASING: 2^t /////////////////



// exponential easing in - accelerating from zero velocity

// t: current time, b: beginning value, c: change in position, d: duration

Math.easeInExpo = function (t, b, c, d) {

	return (t==0) ? b : c * Math.pow(2, 10 * (t/d - 1)) + b;

};



// exponential easing out - decelerating to zero velocity

Math.easeOutExpo = function (t, b, c, d) {

	return (t==d) ? b+c : c * (-Math.pow(2, -10 * t/d) + 1) + b;

};



// exponential easing in/out - accelerating until halfway, then decelerating

Math.easeInOutExpo = function (t, b, c, d) {

	if (t==0) return b;

	if (t==d) return b+c;

	if ((t/=d/2) < 1) return c/2 * Math.pow(2, 10 * (t - 1)) + b;

	return c/2 * (-Math.pow(2, -10 * --t) + 2) + b;

};





 /////////// CIRCULAR EASING: sqrt(1-t^2) //////////////



// circular easing in - accelerating from zero velocity

// t: current time, b: beginning value, c: change in position, d: duration

Math.easeInCirc = function (t, b, c, d) {

	return -c * (Math.sqrt(1 - (t/=d)*t) - 1) + b;

};



// circular easing out - decelerating to zero velocity

Math.easeOutCirc = function (t, b, c, d) {

	return c * Math.sqrt(1 - (t=t/d-1)*t) + b;

};



// circular easing in/out - acceleration until halfway, then deceleration

Math.easeInOutCirc = function (t, b, c, d) {

	if ((t/=d/2) < 1) return -c/2 * (Math.sqrt(1 - t*t) - 1) + b;

	return c/2 * (Math.sqrt(1 - (t-=2)*t) + 1) + b;

};





 /////////// ELASTIC EASING: exponentially decaying sine wave  //////////////



// t: current time, b: beginning value, c: change in value, d: duration, a: amplitude (optional), p: period (optional)

// t and d can be in frames or seconds/milliseconds



Math.easeInElastic = function (t, b, c, d, a, p) {

	if (t==0) return b;  if ((t/=d)==1) return b+c;  if (!p) p=d*.3;

	if (a < Math.abs(c)) { a=c; var s=p/4; }

	else var s = p/(2*Math.PI) * Math.asin (c/a);

	return -(a*Math.pow(2,10*(t-=1)) * Math.sin( (t*d-s)*(2*Math.PI)/p )) + b;

};



Math.easeOutElastic = function (t, b, c, d, a, p) {

	if (t==0) return b;  if ((t/=d)==1) return b+c;  if (!p) p=d*.3;

	if (a < Math.abs(c)) { a=c; var s=p/4; }

	else var s = p/(2*Math.PI) * Math.asin (c/a);

	return a*Math.pow(2,-10*t) * Math.sin( (t*d-s)*(2*Math.PI)/p ) + c + b;

};



Math.easeInOutElastic = function (t, b, c, d, a, p) {

	if (t==0) return b;  if ((t/=d/2)==2) return b+c;  if (!p) p=d*(.3*1.5);

	if (a < Math.abs(c)) { a=c; var s=p/4; }

	else var s = p/(2*Math.PI) * Math.asin (c/a);

	if (t < 1) return -.5*(a*Math.pow(2,10*(t-=1)) * Math.sin( (t*d-s)*(2*Math.PI)/p )) + b;

	return a*Math.pow(2,-10*(t-=1)) * Math.sin( (t*d-s)*(2*Math.PI)/p )*.5 + c + b;

};





 /////////// BACK EASING: overshooting cubic easing: (s+1)*t^3 - s*t^2  //////////////



// back easing in - backtracking slightly, then reversing direction and moving to target

// t: current time, b: beginning value, c: change in value, d: duration, s: overshoot amount (optional)

// t and d can be in frames or seconds/milliseconds

// s controls the amount of overshoot: higher s means greater overshoot

// s has a default value of 1.70158, which produces an overshoot of 10 percent

// s==0 produces cubic easing with no overshoot

Math.easeInBack = function (t, b, c, d, s) {

	if (s == undefined) s = 1.70158;

	return c*(t/=d)*t*((s+1)*t - s) + b;

};



// back easing out - moving towards target, overshooting it slightly, then reversing and coming back to target

Math.easeOutBack = function (t, b, c, d, s) {

	if (s == undefined) s = 1.70158;

	return c*((t=t/d-1)*t*((s+1)*t + s) + 1) + b;

};



// back easing in/out - backtracking slightly, then reversing direction and moving to target,

// then overshooting target, reversing, and finally coming back to target

Math.easeInOutBack = function (t, b, c, d, s) {

	if (s == undefined) s = 1.70158; 

	if ((t/=d/2) < 1) return c/2*(t*t*(((s*=(1.525))+1)*t - s)) + b;

	return c/2*((t-=2)*t*(((s*=(1.525))+1)*t + s) + 2) + b;

};





 /////////// BOUNCE EASING: exponentially decaying parabolic bounce  //////////////



// bounce easing in

// t: current time, b: beginning value, c: change in position, d: duration

Math.easeInBounce = function (t, b, c, d) {

	return c - Math.easeOutBounce (d-t, 0, c, d) + b;

};



// bounce easing out

Math.easeOutBounce = function (t, b, c, d) {

	if ((t/=d) < (1/2.75)) {

		return c*(7.5625*t*t) + b;

	} else if (t < (2/2.75)) {

		return c*(7.5625*(t-=(1.5/2.75))*t + .75) + b;

	} else if (t < (2.5/2.75)) {

		return c*(7.5625*(t-=(2.25/2.75))*t + .9375) + b;

	} else {

		return c*(7.5625*(t-=(2.625/2.75))*t + .984375) + b;

	}

};



// bounce easing in/out

Math.easeInOutBounce = function (t, b, c, d) {

	if (t < d/2) return Math.easeInBounce (t*2, 0, c, d) * .5 + b;

	return Math.easeOutBounce (t*2-d, 0, c, d) * .5 + c*.5 + b;

};





//trace (">> Penner easing equations loaded");