mirror of
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491 lines
11 KiB
C++
491 lines
11 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 mDir; // inout, in, out
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S32 mType; // linear, etc...
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F32 mParam[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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{
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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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{
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t /= d;
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return c*t*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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{
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t /= d;
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return -c * t*(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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{
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t /= d/2;
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if (t < 1)
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return c/2*t*t + b;
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t--;
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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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{
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t /= d;
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return c*t*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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{
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t /= d;
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t--;
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return c*(t*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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{
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t /= d/2;
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if (t < 1)
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return c/2*t*t*t + b;
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t -= 2;
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return c/2*(t*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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{
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t /= d;
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return c*t*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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{
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t /= d;
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t--;
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return -c * (t*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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{
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t /= d/2;
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if (t < 1)
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return c/2*t*t*t*t + b;
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t -= 2;
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return -c/2 * (t*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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{
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t /= d;
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return c*t*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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{
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t /= d;
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t--;
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return c*(t*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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{
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t /= d/2;
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if (t < 1)
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return c/2*t*t*t*t*t + b;
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t -= 2;
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return c/2*(t*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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{
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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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{
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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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{
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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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{
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return 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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{
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return 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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{
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t /= d/2;
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if (t < 1)
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return c/2 * mPow( 2, 10 * (t - 1) ) + b;
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t--;
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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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{
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t/=d;
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return -c * (mSqrt(1 - (t)*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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{
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t/=d;
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t--;
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return c * mSqrt(1 - (t)*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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{
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if ((t/=d/2) < 1)
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return -c/2 * (mSqrt(1 - t*t) - 1) + b;
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t-=2;
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return c/2 * (mSqrt(1 - (t)*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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{
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if (t==0)
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return b;
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F32 dt = t /= d;
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if (dt == 1)
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return b+c;
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if (p<=0)
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p=d*.3f;
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F32 s;
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if (a < mFabs(c))
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{
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a=c;
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s=p/4;
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}
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else
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s = p/(2*M_PI_F) * mAsin (c/a);
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t -= 1;
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return -(a*mPow(2,10*t) * 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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{
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if (t==0)
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return b;
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F32 dt = t /= d;
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if (dt == 1)
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return b+c;
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if (p<=0)
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p=d*.3f;
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F32 s;
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if (a < mFabs(c))
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{
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a=c;
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s=p/4;
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}
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else
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s = p/(2*M_PI_F) * mAsin (c/a);
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return a*mPow(2,-10*t) * mSin( (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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{
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if (t==0)
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return b;
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F32 dt = t /= d / 2;
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if (dt == 2)
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return b+c;
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if (p<=0)
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p=d*(.3f*1.5f);
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F32 s;
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if (a < mFabs(c))
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{
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a=c;
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s=p/4;
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}
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else
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s = p/(2*M_PI_F) * mAsin (c/a);
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if (t < 1)
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{
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t -= 1;
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return -.5f*(a*mPow(2, 10 * t) * mSin((t*d - s)*(2 * M_PI_F) / p)) + b;
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}
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t -= 1;
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return a*mPow(2,-10*t) * 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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{
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if (s < 0)
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s = 1.70158f;
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F32 td = t /= d;
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return c*td*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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{
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if (s < 0)
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s = 1.70158f;
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F32 td = t / d - 1;
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t = td;
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return c*(td*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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{
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if (s < 0)
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s = 1.70158f;
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F32 td = t /= d / 2;
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if (td < 1)
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{
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s *= 1.525f;
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return c / 2 * (t*t*((s + 1)*t - s)) + b;
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}
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s *= 1.525f;
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t -= 2;
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return c/2*(t*t*((s+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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{
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if ((t/=d) < (1/2.75f))
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{
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return c*(7.5625f*t*t) + b;
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}
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else if (t < (2/2.75))
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{
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t -= 1.5f / 2.75f;
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return c*(7.5625f*t*t + .75f) + b;
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}
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else if (t < (2.5/2.75))
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{
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t -= 2.25f / 2.75f;
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return c*(7.5625f*t*t + .9375f) + b;
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}
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else
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{
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t -= 2.625f / 2.75f;
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return c*(7.5625f*t*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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{
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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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{
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if (t < d/2)
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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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#endif // _MEASE_H_
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