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/* 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");