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593 lines
19 KiB
C++
593 lines
19 KiB
C++
/*
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ROBERT PENNER'S MOST EXCELLENT EASING METHODS - ported to Torque C++ by Paul Dana
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Easing Equations v1.5
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May 1, 2003
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(c) 2003 Robert Penner, all rights reserved.
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This work is subject to the terms in http://www.robertpenner.com/easing_terms_of_use.html.
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These tweening functions provide different flavors of
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math-based motion under a consistent API.
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Types of easing:
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Linear
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Quadratic
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Cubic
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Quartic
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Quintic
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Sinusoidal
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Exponential
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Circular
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Elastic
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Back
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Bounce
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Changes:
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1.5 - added bounce easing
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1.4 - added elastic and back easing
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1.3 - tweaked the exponential easing functions to make endpoints exact
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1.2 - inline optimizations (changing t and multiplying in one step)--thanks to Tatsuo Kato for the idea
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Discussed in Chapter 7 of
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Robert Penner's Programming Macromedia Flash MX
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(including graphs of the easing equations)
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http://www.robertpenner.com/profmx
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http://www.amazon.com/exec/obidos/ASIN/0072223561/robertpennerc-20
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*/
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#ifndef _MEASE_H_
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#define _MEASE_H_
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// the ease methods below all are static and take atomic types as params
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// so they are the most generally useful. for convenience, define here
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// a type that can contain all the params needed for below to make
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// data structures that use these methods cleaner...
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//------------------------------------------------------------------------------
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class Ease
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{
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//-------------------------------------- Public data
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public:
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enum enumDirection
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{
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InOut=0,
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In,
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Out
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};
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enum enumType
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{
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Linear=0,
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Quadratic,
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Cubic,
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Quartic,
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Quintic,
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Sinusoidal,
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Exponential,
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Circular,
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Elastic,
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Back,
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Bounce,
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};
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};
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class EaseF : public Ease
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{
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//-------------------------------------- Public data
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public:
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S32 dir; // inout, in, out
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S32 type; // linear, etc...
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F32 param[2]; // optional params
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//-------------------------------------- Public interface
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public:
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EaseF();
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EaseF(const EaseF &ease);
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EaseF(const S32 dir, const S32 type);
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EaseF(const S32 dir, const S32 type, F32 param[2]);
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//-------------------------------------- Non-math mutators and misc functions
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void set(const S32 dir, const S32 type);
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void set(const S32 dir, const S32 type, F32 param[2]);
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void set(const S32 dir, const S32 type, F32 param0, F32 param1);
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void set(const char *s);
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F32 getValue(F32 t, F32 b, F32 c, F32 d) const;
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F32 getUnitValue(F32 t, bool noExtrapolation) const
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{
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F32 v = getValue(t,0.0f,1.0f,1.0f);
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if (noExtrapolation)
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v = mClampF(v,0.0f,1.0f);
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return v;
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}
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F32 getUnitValue(F32 t) const
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{
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return getValue(t,0.0f,1.0f,1.0f);
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}
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};
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// simple linear tweening - no easing
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// t: current time, b: beginning value, c: change in value, d: duration
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inline F32 mLinearTween(F32 t, F32 b, F32 c, F32 d) {
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return c*t/d + b;
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}
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///////////// QUADRATIC EASING: t^2 ///////////////////
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// quadratic easing in - accelerating from zero velocity
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// t: current time, b: beginning value, c: change in value, d: duration
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// t and d can be in frames or seconds/milliseconds
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inline F32 mEaseInQuad(F32 t, F32 b, F32 c, F32 d) {
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return c*(t/=d)*t + b;
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};
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// quadratic easing out - decelerating to zero velocity
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inline F32 mEaseOutQuad(F32 t, F32 b, F32 c, F32 d) {
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return -c *(t/=d)*(t-2) + b;
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};
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// quadratic easing in/out - acceleration until halfway, then deceleration
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inline F32 mEaseInOutQuad(F32 t, F32 b, F32 c, F32 d) {
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if ((t/=d/2) < 1) return c/2*t*t + b;
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return -c/2 * ((--t)*(t-2) - 1) + b;
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};
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///////////// CUBIC EASING: t^3 ///////////////////////
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// cubic easing in - accelerating from zero velocity
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// t: current time, b: beginning value, c: change in value, d: duration
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// t and d can be frames or seconds/milliseconds
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inline F32 mEaseInCubic(F32 t, F32 b, F32 c, F32 d) {
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return c*(t/=d)*t*t + b;
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};
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// cubic easing out - decelerating to zero velocity
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inline F32 mEaseOutCubic(F32 t, F32 b, F32 c, F32 d) {
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return c*((t=t/d-1)*t*t + 1) + b;
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};
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// cubic easing in/out - acceleration until halfway, then deceleration
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inline F32 mEaseInOutCubic(F32 t, F32 b, F32 c, F32 d) {
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if ((t/=d/2) < 1) return c/2*t*t*t + b;
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return c/2*((t-=2)*t*t + 2) + b;
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};
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///////////// QUARTIC EASING: t^4 /////////////////////
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// quartic easing in - accelerating from zero velocity
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// t: current time, b: beginning value, c: change in value, d: duration
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// t and d can be frames or seconds/milliseconds
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inline F32 mEaseInQuart(F32 t, F32 b, F32 c, F32 d) {
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return c*(t/=d)*t*t*t + b;
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};
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// quartic easing out - decelerating to zero velocity
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inline F32 mEaseOutQuart(F32 t, F32 b, F32 c, F32 d) {
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return -c * ((t=t/d-1)*t*t*t - 1) + b;
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};
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// quartic easing in/out - acceleration until halfway, then deceleration
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inline F32 mEaseInOutQuart(F32 t, F32 b, F32 c, F32 d) {
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if ((t/=d/2) < 1) return c/2*t*t*t*t + b;
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return -c/2 * ((t-=2)*t*t*t - 2) + b;
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};
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///////////// QUINTIC EASING: t^5 ////////////////////
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// quintic easing in - accelerating from zero velocity
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// t: current time, b: beginning value, c: change in value, d: duration
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// t and d can be frames or seconds/milliseconds
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inline F32 mEaseInQuint(F32 t, F32 b, F32 c, F32 d) {
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return c*(t/=d)*t*t*t*t + b;
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};
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// quintic easing out - decelerating to zero velocity
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inline F32 mEaseOutQuint(F32 t, F32 b, F32 c, F32 d) {
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return c*((t=t/d-1)*t*t*t*t + 1) + b;
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};
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// quintic easing in/out - acceleration until halfway, then deceleration
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inline F32 mEaseInOutQuint(F32 t, F32 b, F32 c, F32 d) {
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if ((t/=d/2) < 1) return c/2*t*t*t*t*t + b;
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return c/2*((t-=2)*t*t*t*t + 2) + b;
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};
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///////////// SINUSOIDAL EASING: sin(t) ///////////////
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// sinusoidal easing in - accelerating from zero velocity
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// t: current time, b: beginning value, c: change in position, d: duration
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inline F32 mEaseInSine(F32 t, F32 b, F32 c, F32 d) {
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return -c * mCos(t/d * (M_PI_F/2)) + c + b;
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};
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// sinusoidal easing out - decelerating to zero velocity
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inline F32 mEaseOutSine(F32 t, F32 b, F32 c, F32 d) {
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return c * mSin(t/d * (M_PI_F/2)) + b;
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};
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// sinusoidal easing in/out - accelerating until halfway, then decelerating
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inline F32 mEaseInOutSine(F32 t, F32 b, F32 c, F32 d) {
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return -c/2 * (mCos(M_PI_F*t/d) - 1) + b;
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};
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///////////// EXPONENTIAL EASING: 2^t /////////////////
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// exponential easing in - accelerating from zero velocity
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// t: current time, b: beginning value, c: change in position, d: duration
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inline F32 mEaseInExpo(F32 t, F32 b, F32 c, F32 d) {
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return (t==0) ? b : c * mPow(2, 10 * (t/d - 1)) + b;
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};
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// exponential easing out - decelerating to zero velocity
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inline F32 mEaseOutExpo(F32 t, F32 b, F32 c, F32 d) {
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return (t==d) ? b+c : c * (-mPow(2, -10 * t/d) + 1) + b;
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};
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// exponential easing in/out - accelerating until halfway, then decelerating
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inline F32 mEaseInOutExpo(F32 t, F32 b, F32 c, F32 d) {
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if (t==0) return b;
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if (t==d) return b+c;
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if ((t/=d/2) < 1) return c/2 * mPow(2, 10 * (t - 1)) + b;
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return c/2 * (-mPow(2, -10 * --t) + 2) + b;
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};
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/////////// CIRCULAR EASING: sqrt(1-t^2) //////////////
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// circular easing in - accelerating from zero velocity
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// t: current time, b: beginning value, c: change in position, d: duration
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inline F32 mEaseInCirc (F32 t, F32 b, F32 c, F32 d) {
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return -c * (mSqrt(1 - (t/=d)*t) - 1) + b;
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};
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// circular easing out - decelerating to zero velocity
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inline F32 mEaseOutCirc (F32 t, F32 b, F32 c, F32 d) {
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return c * mSqrt(1 - (t=t/d-1)*t) + b;
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};
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// circular easing in/out - acceleration until halfway, then deceleration
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inline F32 mEaseInOutCirc(F32 t, F32 b, F32 c, F32 d) {
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if ((t/=d/2) < 1) return -c/2 * (mSqrt(1 - t*t) - 1) + b;
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return c/2 * (mSqrt(1 - (t-=2)*t) + 1) + b;
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};
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/////////// ELASTIC EASING: exponentially decaying sine wave //////////////
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// t: current time, b: beginning value, c: change in value, d: duration, a: amplitude (optional), p: period (optional)
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// t and d can be in frames or seconds/milliseconds
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inline F32 mEaseInElastic(F32 t, F32 b, F32 c, F32 d, F32 a, F32 p) {
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if (t==0) return b; if ((t/=d)==1) return b+c; if (p<=0) p=d*.3f;
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F32 s;
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if (a < mFabs(c)) { a=c; s=p/4; }
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else s = p/(2*M_PI_F) * mAsin (c/a);
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return -(a*mPow(2,10*(t-=1)) * mSin( (t*d-s)*(2*M_PI_F)/p )) + b;
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};
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inline F32 mEaseOutElastic(F32 t, F32 b, F32 c, F32 d, F32 a, F32 p) {
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if (t==0) return b; if ((t/=d)==1) return b+c; if (p<=0) p=d*.3f;
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F32 s;
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if (a < mFabs(c)) { a=c; s=p/4; }
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else s = p/(2*M_PI_F) * mAsin (c/a);
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return a*mPow(2,-10*t) * mAsin( (t*d-s)*(2*M_PI_F)/p ) + c + b;
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};
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inline F32 mEaseInOutElastic(F32 t, F32 b, F32 c, F32 d, F32 a, F32 p) {
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if (t==0) return b; if ((t/=d/2)==2) return b+c; if (p<=0) p=d*(.3f*1.5f);
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F32 s;
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if (a < mFabs(c)) { a=c; s=p/4; }
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else s = p/(2*M_PI_F) * mAsin (c/a);
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if (t < 1) return -.5f*(a*mPow(2,10*(t-=1)) * mSin( (t*d-s)*(2*M_PI_F)/p )) + b;
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return a*mPow(2,-10*(t-=1)) * mSin( (t*d-s)*(2*M_PI_F)/p )*.5f + c + b;
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};
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/////////// BACK EASING: overshooting cubic easing: (s+1)*t^3 - s*t^2 //////////////
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// back easing in - backtracking slightly, then reversing direction and moving to target
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// t: current time, b: beginning value, c: change in value, d: duration, s: overshoot amount (optional)
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// t and d can be in frames or seconds/milliseconds
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// s controls the amount of overshoot: higher s means greater overshoot
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// s has a default value of 1.70158, which produces an overshoot of 10 percent
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// s==0 produces cubic easing with no overshoot
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inline F32 mEaseInBack(F32 t, F32 b, F32 c, F32 d, F32 s) {
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if (s < 0) s = 1.70158f;
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return c*(t/=d)*t*((s+1)*t - s) + b;
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};
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// back easing out - moving towards target, overshooting it slightly, then reversing and coming back to target
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inline F32 mEaseOutBack(F32 t, F32 b, F32 c, F32 d, F32 s) {
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if (s < 0) s = 1.70158f;
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return c*((t=t/d-1)*t*((s+1)*t + s) + 1) + b;
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};
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// back easing in/out - backtracking slightly, then reversing direction and moving to target,
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// then overshooting target, reversing, and finally coming back to target
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inline F32 mEaseInOutBack(F32 t, F32 b, F32 c, F32 d, F32 s) {
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if (s < 0) s = 1.70158f;
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if ((t/=d/2) < 1) return c/2*(t*t*(((s*=(1.525f))+1)*t - s)) + b;
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return c/2*((t-=2)*t*(((s*=(1.525f))+1)*t + s) + 2) + b;
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};
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/////////// BOUNCE EASING: exponentially decaying parabolic bounce //////////////
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// bounce easing out
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inline F32 mEaseOutBounce(F32 t, F32 b, F32 c, F32 d) {
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if ((t/=d) < (1/2.75f)) {
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return c*(7.5625f*t*t) + b;
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} else if (t < (2/2.75)) {
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return c*(7.5625f*(t-=(1.5f/2.75f))*t + .75f) + b;
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} else if (t < (2.5/2.75)) {
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return c*(7.5625f*(t-=(2.25f/2.75f))*t + .9375f) + b;
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} else {
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return c*(7.5625f*(t-=(2.625f/2.75f))*t + .984375f) + b;
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}
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};
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// bounce easing in
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// t: current time, b: beginning value, c: change in position, d: duration
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inline F32 mEaseInBounce(F32 t, F32 b, F32 c, F32 d) {
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return c - mEaseOutBounce (d-t, 0, c, d) + b;
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};
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// bounce easing in/out
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inline F32 mEaseInOutBounce(F32 t, F32 b, F32 c, F32 d) {
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if (t < d/2) return mEaseInBounce (t*2, 0, c, d) * .5f + b;
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return mEaseOutBounce (t*2-d, 0, c, d) * .5f + c*.5f + b;
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};
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#if 0
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// ORIGINAL ACTION SCRIPT CODE:
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// simple linear tweening - no easing
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// t: current time, b: beginning value, c: change in value, d: duration
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Math.linearTween = function (t, b, c, d) {
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return c*t/d + b;
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};
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///////////// QUADRATIC EASING: t^2 ///////////////////
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// quadratic easing in - accelerating from zero velocity
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// t: current time, b: beginning value, c: change in value, d: duration
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// t and d can be in frames or seconds/milliseconds
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Math.easeInQuad = function (t, b, c, d) {
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return c*(t/=d)*t + b;
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};
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// quadratic easing out - decelerating to zero velocity
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Math.easeOutQuad = function (t, b, c, d) {
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return -c *(t/=d)*(t-2) + b;
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};
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// quadratic easing in/out - acceleration until halfway, then deceleration
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Math.easeInOutQuad = function (t, b, c, d) {
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if ((t/=d/2) < 1) return c/2*t*t + b;
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return -c/2 * ((--t)*(t-2) - 1) + b;
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};
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///////////// CUBIC EASING: t^3 ///////////////////////
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// cubic easing in - accelerating from zero velocity
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// t: current time, b: beginning value, c: change in value, d: duration
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// t and d can be frames or seconds/milliseconds
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Math.easeInCubic = function (t, b, c, d) {
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return c*(t/=d)*t*t + b;
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};
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// cubic easing out - decelerating to zero velocity
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Math.easeOutCubic = function (t, b, c, d) {
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return c*((t=t/d-1)*t*t + 1) + b;
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};
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// cubic easing in/out - acceleration until halfway, then deceleration
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Math.easeInOutCubic = function (t, b, c, d) {
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if ((t/=d/2) < 1) return c/2*t*t*t + b;
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return c/2*((t-=2)*t*t + 2) + b;
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};
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///////////// QUARTIC EASING: t^4 /////////////////////
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// quartic easing in - accelerating from zero velocity
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// t: current time, b: beginning value, c: change in value, d: duration
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// t and d can be frames or seconds/milliseconds
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Math.easeInQuart = function (t, b, c, d) {
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return c*(t/=d)*t*t*t + b;
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};
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// quartic easing out - decelerating to zero velocity
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Math.easeOutQuart = function (t, b, c, d) {
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return -c * ((t=t/d-1)*t*t*t - 1) + b;
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};
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// quartic easing in/out - acceleration until halfway, then deceleration
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Math.easeInOutQuart = function (t, b, c, d) {
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if ((t/=d/2) < 1) return c/2*t*t*t*t + b;
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return -c/2 * ((t-=2)*t*t*t - 2) + b;
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};
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///////////// QUINTIC EASING: t^5 ////////////////////
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// quintic easing in - accelerating from zero velocity
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// t: current time, b: beginning value, c: change in value, d: duration
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// t and d can be frames or seconds/milliseconds
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Math.easeInQuint = function (t, b, c, d) {
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return c*(t/=d)*t*t*t*t + b;
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};
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// quintic easing out - decelerating to zero velocity
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Math.easeOutQuint = function (t, b, c, d) {
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return c*((t=t/d-1)*t*t*t*t + 1) + b;
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};
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// quintic easing in/out - acceleration until halfway, then deceleration
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Math.easeInOutQuint = function (t, b, c, d) {
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if ((t/=d/2) < 1) return c/2*t*t*t*t*t + b;
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return c/2*((t-=2)*t*t*t*t + 2) + b;
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};
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///////////// SINUSOIDAL EASING: sin(t) ///////////////
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// sinusoidal easing in - accelerating from zero velocity
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// t: current time, b: beginning value, c: change in position, d: duration
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Math.easeInSine = function (t, b, c, d) {
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return -c * Math.cos(t/d * (Math.PI/2)) + c + b;
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};
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// sinusoidal easing out - decelerating to zero velocity
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Math.easeOutSine = function (t, b, c, d) {
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return c * Math.sin(t/d * (Math.PI/2)) + b;
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};
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// sinusoidal easing in/out - accelerating until halfway, then decelerating
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Math.easeInOutSine = function (t, b, c, d) {
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return -c/2 * (Math.cos(Math.PI*t/d) - 1) + b;
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};
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///////////// EXPONENTIAL EASING: 2^t /////////////////
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// exponential easing in - accelerating from zero velocity
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// t: current time, b: beginning value, c: change in position, d: duration
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Math.easeInExpo = function (t, b, c, d) {
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return (t==0) ? b : c * Math.pow(2, 10 * (t/d - 1)) + b;
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};
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// exponential easing out - decelerating to zero velocity
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Math.easeOutExpo = function (t, b, c, d) {
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return (t==d) ? b+c : c * (-Math.pow(2, -10 * t/d) + 1) + b;
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};
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// exponential easing in/out - accelerating until halfway, then decelerating
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Math.easeInOutExpo = function (t, b, c, d) {
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if (t==0) return b;
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if (t==d) return b+c;
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if ((t/=d/2) < 1) return c/2 * Math.pow(2, 10 * (t - 1)) + b;
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return c/2 * (-Math.pow(2, -10 * --t) + 2) + b;
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};
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/////////// CIRCULAR EASING: sqrt(1-t^2) //////////////
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// circular easing in - accelerating from zero velocity
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// t: current time, b: beginning value, c: change in position, d: duration
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Math.easeInCirc = function (t, b, c, d) {
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return -c * (Math.sqrt(1 - (t/=d)*t) - 1) + b;
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};
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// circular easing out - decelerating to zero velocity
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Math.easeOutCirc = function (t, b, c, d) {
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return c * Math.sqrt(1 - (t=t/d-1)*t) + b;
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};
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// circular easing in/out - acceleration until halfway, then deceleration
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Math.easeInOutCirc = function (t, b, c, d) {
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if ((t/=d/2) < 1) return -c/2 * (Math.sqrt(1 - t*t) - 1) + b;
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return c/2 * (Math.sqrt(1 - (t-=2)*t) + 1) + b;
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};
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/////////// ELASTIC EASING: exponentially decaying sine wave //////////////
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// t: current time, b: beginning value, c: change in value, d: duration, a: amplitude (optional), p: period (optional)
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// t and d can be in frames or seconds/milliseconds
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Math.easeInElastic = function (t, b, c, d, a, p) {
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if (t==0) return b; if ((t/=d)==1) return b+c; if (!p) p=d*.3;
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if (a < Math.abs(c)) { a=c; var s=p/4; }
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else var s = p/(2*Math.PI) * Math.asin (c/a);
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return -(a*Math.pow(2,10*(t-=1)) * Math.sin( (t*d-s)*(2*Math.PI)/p )) + b;
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};
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Math.easeOutElastic = function (t, b, c, d, a, p) {
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if (t==0) return b; if ((t/=d)==1) return b+c; if (!p) p=d*.3;
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if (a < Math.abs(c)) { a=c; var s=p/4; }
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else var s = p/(2*Math.PI) * Math.asin (c/a);
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return a*Math.pow(2,-10*t) * Math.sin( (t*d-s)*(2*Math.PI)/p ) + c + b;
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};
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Math.easeInOutElastic = function (t, b, c, d, a, p) {
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if (t==0) return b; if ((t/=d/2)==2) return b+c; if (!p) p=d*(.3*1.5);
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if (a < Math.abs(c)) { a=c; var s=p/4; }
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else var s = p/(2*Math.PI) * Math.asin (c/a);
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if (t < 1) return -.5*(a*Math.pow(2,10*(t-=1)) * Math.sin( (t*d-s)*(2*Math.PI)/p )) + b;
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return a*Math.pow(2,-10*(t-=1)) * Math.sin( (t*d-s)*(2*Math.PI)/p )*.5 + c + b;
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};
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/////////// BACK EASING: overshooting cubic easing: (s+1)*t^3 - s*t^2 //////////////
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// 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
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// 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) {
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|
if (s == undefined) s = 1.70158;
|
|
return c*(t/=d)*t*((s+1)*t - s) + b;
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};
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// 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;
|
|
};
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// 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;
|
|
};
|
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|
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|
/////////// 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;
|
|
};
|
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|
|
// 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;
|
|
};
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#endif
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#endif // _MEASE_H_
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