/*
*   ----------------------------------------------------
*   Application: EasingEquations.as
*   ----------------------------------------------------
*   Version: 1.5
*   ----------------------------------------------------
*   Latest update: May 1, 2003
*   ----------------------------------------------------
*   Developer: Richard Wright 2003 [wisolutions2002@shaw.ca]
*   ----------------------------------------------------
*   Copyright: (c) 2003 Robert Penner [www.robertpenner.com]
*
*   All rights reserved.
*
*   Redistribution and use in source and binary forms, with or without
*   modification, are permitted provided that the following conditions are met:
*
*      -  Redistributions of source code must retain the above copyright notice,
*         this list of conditions and the following disclaimer.
*
*       - Redistributions in binary form must reproduce the above copyright
*         notice, this list of conditions and the following disclaimer in the
*         documentation and/or other materials provided with the distribution.
*
*       - Neither the name of this software nor the names of its contributors
*         may be used to endorse or promote products derived from this software
*         without specific prior written permission.
*
*   THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND
*   ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
*   WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
*   DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR
*   ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
*   (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
*   LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON
*   ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
*   (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
*   SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
*   ---------------------------------------------------- 
*   These tweening functions provide different flavors of 
*   math-based motion under a consistent API. 
*   ----------------------------------------------------  
*   Functions:
*        - Math object extensions
*        Math.
*            Linear
*	         1.  linearTween(t,b,c,d)
*            Quadratic
*	         2.  easeInQuad(t,b,c,d)
(            3.  easeOutQuad(t,b,c,d)
*            4.  easeInOutQuad(t,b,c,d)
*            Cubic
*	         5.  easeInCubic(t,b,c,d)
*	         6.  easeOutCubic(t,b,c,d)
*	         7.  easeInOutCubic(t,b,c,d)
*            Quartic
*	         8.  easeInQuart(t,b,c,d)
*	         9.  easeOutQuart(t,b,c,d)
*	         10. easeInOutQuart(t,b,c,d)
*            Quintic
*	         11. easeInQuint(t,b,c,d)
*	         12. easeOutQuint(t,b,c,d)
*	         13. easeInOutQuint(t,b,c,d)
*	         Sinusoidal
*            14. easeInSine(t,b,c,d)
*            15. easeOutSine(t,b,c,d)
*            16. easeInOutSine(t,b,c,d)
*	         Exponential
*            17. easeInExpo(t,b,c,d)
*            18. easeOutExpo(t,b,c,d)
*            19. easeInOutExpo(t,b,c,d)
*	         Circular
*            20. easeInCirc(t,b,c,d)
*            21. easeOutCirc(t,b,c,d)
*            22. easeInOutCirc(t,b,c,d)
*	         Elastic
*            23. easeInElastic(t,b,c,d,a,p)
*            24. easeOutElastic(t,b,c,d,a,p)
*            25. easeInOutElastic(t,b,c,d,a,p)
*	         Back
*            26. easeInBack(t,b,c,d,s)
*            27. easeOutBack(t,b,c,d,s)
*            28. easeInOutBack(t,b,c,d,s)
*	         Bounce
*            29. easeInBounce(t,b,c,d)
*            30. easeOutBounce(t,b,c,d)
*            31. easeInOutBounce(t,b,c,d)
*  ----------------------------------------------------
*  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
*  ----------------------------------------------------
*  Updates may be available at:
*       http://members.shaw.ca/flashmath101/as/
*  ----------------------------------------------------
*/

// 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");