Easing.h

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/*
 Copyright (c) 2011, The Cinder Project, All rights reserved.
 This code is intended for use with the Cinder C++ library: http://libcinder.org

 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.

 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 HOLDER 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.

Documentation and easeOutIn* algorithms adapted from Qt: http://qt.nokia.com/products/

Disclaimer for Robert Penner's Easing Equations license:
TERMS OF USE - EASING EQUATIONS
Open source under the BSD License.

Copyright © 2001 Robert Penner
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 the author nor the names of 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.
*/

#pragma once
#include "cinder/CinderMath.h"

namespace cinder {

// None

inline float easeNone( float t )
{
    return t;
}

struct EaseNone{ float operator()( float t ) const { return easeNone( t ); } };


// Quadratic

inline float easeInQuad( float t )
{
    return t*t;
}

struct EaseInQuad{ float operator()( float t ) const { return easeInQuad( t ); } };

inline float easeOutQuad( float t )
{ 
    return -t * ( t - 2 );
}

struct EaseOutQuad{ float operator()( float t ) const { return easeOutQuad( t ); } };

inline float easeInOutQuad( float t )
{
    t *= 2;
    if( t < 1 ) return 0.5f * t * t;
    
    t -= 1;
    return -0.5f * ((t)*(t-2) - 1);
}

struct EaseInOutQuad{ float operator()( float t ) const { return easeInOutQuad( t ); } };

inline float easeOutInQuad( float t )
{
    if( t < 0.5f) return easeOutQuad( t*2 ) * 0.5f;
    return easeInQuad( (2*t)-1 ) * 0.5f + 0.5f;
}

struct EaseOutInQuad{ float operator()( float t ) const { return easeOutInQuad( t ); } };

// Cubic

inline float easeInCubic( float t )
{
    return t*t*t;
}

struct EaseInCubic{ float operator()( float t ) const { return easeInCubic( t ); } };

inline float easeOutCubic( float t )
{
    t -= 1;
    return t*t*t + 1;
}

struct EaseOutCubic{ float operator()( float t ) const { return easeOutCubic( t ); } };

inline float easeInOutCubic( float t )
{
    t *= 2;
    if( t < 1 )
        return 0.5f * t*t*t;
    t -= 2;
    return 0.5f*(t*t*t + 2);
}

struct EaseInOutCubic{ float operator()( float t ) const { return easeInOutCubic( t ); } };

inline float easeOutInCubic( float t )
{
    if( t < 0.5f ) return easeOutCubic( 2 * t ) / 2;
    return easeInCubic(2*t - 1)/2 + 0.5f;
}

struct EaseOutInCubic{ float operator()( float t ) const { return easeOutInCubic( t ); } };

// Quartic

inline float easeInQuart( float t )
{
    return t*t*t*t;
}

struct EaseInQuart{ float operator()( float t ) const { return easeInQuart( t ); } };

inline float easeOutQuart( float t )
{
    t -= 1;
    return -(t*t*t*t - 1);
}

struct EaseOutQuart{ float operator()( float t ) const { return easeOutQuart( t ); } };

inline float easeInOutQuart( float t )
{
    t *= 2;
    if( t < 1 ) return 0.5f*t*t*t*t;
    else {
        t -= 2;
        return -0.5f * (t*t*t*t - 2);
    }
}

struct EaseInOutQuart{ float operator()( float t ) const { return easeInOutQuart( t ); } };

inline float easeOutInQuart( float t )
{
    if( t < 0.5f ) return easeOutQuart( 2*t ) / 2;
    return easeInQuart(2*t-1)/2 + 0.5f;
}

struct EaseOutInQuart{ float operator()( float t ) const { return easeOutInQuart( t ); } };

// Quintic

inline float easeInQuint( float t )
{
    return t*t*t*t*t;
}

struct EaseInQuint{ float operator()( float t ) const { return easeInQuint( t ); } };

inline float easeOutQuint( float t )
{
    t -= 1;
    return t*t*t*t*t + 1;
}

struct EaseOutQuint{ float operator()( float t ) const { return easeOutQuint( t ); } };

inline float easeInOutQuint( float t )
{
    t *= 2;
    if( t < 1 ) return 0.5f*t*t*t*t*t;
    else {
        t -= 2;
        return 0.5f*(t*t*t*t*t + 2);
    }
}

struct EaseInOutQuint{ float operator()( float t ) const { return easeInOutQuint( t ); } };

inline float easeOutInQuint( float t )
{
    if( t < 0.5f ) return easeOutQuint( 2*t ) / 2;
    return easeInQuint( 2*t - 1 ) / 2 + 0.5f;
}

struct EaseOutInQuint{ float operator()( float t ) const { return easeOutInQuint( t ); } };

// Sine

inline float easeInSine( float t )
{
    return -math<float>::cos( t * (float)M_PI / 2 ) + 1;
}

struct EaseInSine{ float operator()( float t ) const { return easeInSine( t ); } };

inline float easeOutSine( float t )
{
    return math<float>::sin( t * (float)M_PI / 2 );
}

struct EaseOutSine{ float operator()( float t ) const { return easeOutSine( t ); } };

inline float easeInOutSine( float t )
{
    return -0.5f * ( math<float>::cos( (float)M_PI * t ) - 1 ); 
}

struct EaseInOutSine{ float operator()( float t ) const { return easeInOutSine( t ); } };

inline float easeOutInSine( float t )
{
    if( t < 0.5f ) return easeOutSine( 2 * t ) / 2;
    return easeInSine( 2*t - 1 ) / 2 + 0.5f;
}

struct EaseOutInSine{ float operator()( float t ) const { return easeOutInSine( t ); } };

// Exponential

inline float easeInExpo( float t )
{
    return t == 0 ? 0 : math<float>::pow( 2, 10 * (t - 1) );
}

struct EaseInExpo{ float operator()( float t ) const { return easeInExpo( t ); } };

inline float easeOutExpo( float t )
{
    return t == 1 ? 1 : -math<float>::pow( 2, -10 * t ) + 1;
}

struct EaseOutExpo{ float operator()( float t ) const { return easeOutExpo( t ); } };

inline float easeInOutExpo( float t )
{
    if( t == 0 ) return 0;
    if( t == 1 ) return 1;
    t *= 2;
    if( t < 1 ) return 0.5f * math<float>::pow( 2, 10 * (t - 1) );
    return 0.5f * ( - math<float>::pow( 2, -10 * (t - 1)) + 2);
}

struct EaseInOutExpo{ float operator()( float t ) const { return easeInOutExpo( t ); } };

inline float easeOutInExpo( float t )
{
    if( t < 0.5f ) return easeOutExpo( 2 * t ) / 2;
    return easeInExpo( 2 * t - 1 ) / 2 + 0.5f;
}

struct EaseOutInExpo{ float operator()( float t ) const { return easeOutInExpo( t ); } };

// Circular

inline float easeInCirc( float t )
{
    return -( math<float>::sqrt( 1 - t*t ) - 1);
}

struct EaseInCirc{ float operator()( float t ) const { return easeInCirc( t ); } };

inline float easeOutCirc( float t )
{
    t -= 1;
    return math<float>::sqrt( 1 - t*t );
}

struct EaseOutCirc{ float operator()( float t ) const { return easeOutCirc( t ); } };

inline float easeInOutCirc( float t )
{
    t *= 2;
    if( t < 1 ) {
        return -0.5f * (math<float>::sqrt( 1 - t*t ) - 1);
    }
    else {
        t -= 2;
        return 0.5f * (math<float>::sqrt( 1 - t*t ) + 1);
    }
}

struct EaseInOutCirc{ float operator()( float t ) const { return easeInOutCirc( t ); } };

inline float easeOutInCirc( float t )
{
    if( t < 0.5f ) return easeOutCirc( 2*t ) / 2;
    return easeInCirc( 2*t - 1 ) / 2 + 0.5f;
}

struct EaseOutInCirc{ float operator()( float t ) const { return easeOutInCirc( t ); } };


// Bounce
inline float easeOutBounceHelper_( float t, float c, float a )
{
    if( t == 1 ) return c;
    if( t < (4/11.0f) ) {
        return c*( 7.5625f*t*t);
    }
    else if( t < (8/11.0f) ) {
        t -= (6/11.0f);
        return -a * (1 - (7.5625f*t*t + 0.75f)) + c;
    }
    else if( t < (10/11.0f) ) {
        t -= (9/11.0f);
        return -a * (1 - (7.5625f*t*t + 0.9375f)) + c;
    }
    else {
        t -= (21/22.0f);
        return -a * (1 - (7.5625f*t*t + 0.984375f)) + c;
    }
}

inline float easeInBounce( float t, float a = 1.70158f )
{
     return 1 - easeOutBounceHelper_( 1-t, 1, a );
}

struct EaseInBounce {
    EaseInBounce( float a = 1.70158f ) : mA( a ) {}
    float operator()( float t ) { return easeInBounce( t, mA ); }
    float mA;
};

inline float easeOutBounce( float t, float a = 1.70158f )
{
    return easeOutBounceHelper_( t, 1, a );
}

struct EaseOutBounce {
    EaseOutBounce( float a = 1.70158f ) : mA( a ) {}
    float operator()( float t ) { return easeOutBounce( t, mA ); }
    float mA;
};

inline float easeInOutBounce( float t, float a = 1.70158f )
{
    if( t < 0.5f ) return easeInBounce( 2*t, a ) / 2;
    else return ( t == 1 ) ? 1 : easeOutBounce( 2*t - 1, a )/2 + 0.5f;
}

struct EaseInOutBounce {
    EaseInOutBounce( float a = 1.70158f ) : mA( a ) {}
    float operator()( float t ) { return easeInOutBounce( t, mA ); }
    float mA;
};

inline float easeOutInBounce( float t, float a = 1.70158f )
{
    if( t < 0.5f ) return easeOutBounceHelper_( t*2, 0.5, a );
    return 1 - easeOutBounceHelper_( 2 - 2*t, 0.5, a );
}

struct EaseOutInBounce {
    EaseOutInBounce( float a = 1.70158f ) : mA( a ) {}
    float operator()( float t ) { return easeOutInBounce( t, mA ); }
    float mA;
};


// Back

inline float easeInBack( float t, float s = 1.70158f )
{
    return t * t * ((s+1)*t - s);
}

struct EaseInBack {
    EaseInBack( float s = 1.70158f ) : mS( s ) {}
    float operator()( float t ) { return easeInBack( t, mS ); }
    float mS;
};

inline float easeOutBack( float t, float s = 1.70158f )
{ 
    t -= 1;
    return (t*t*((s+1)*t + s) + 1);
}

struct EaseOutBack {
    EaseOutBack( float s = 1.70158f ) : mS( s ) {}
    float operator()( float t ) { return easeOutBack( t, mS ); }
    float mS;
};

inline float easeInOutBack( float t, float s = 1.70158f )
{
    t *= 2;
    if( t < 1 ) {
        s *= 1.525f;
        return 0.5f*(t*t*((s+1)*t - s));
    }
    else {
        t -= 2;
        s *= 1.525f;
        return 0.5f*(t*t*((s+1)*t+ s) + 2);
    }
}

struct EaseInOutBack {
    EaseInOutBack( float s = 1.70158f ) : mS( s ) {}
    float operator()( float t ) { return easeInOutBack( t, mS ); }
    float mS;
};

inline float easeOutInBack( float t, float s )
{
    if( t < 0.5f ) return easeOutBack( 2*t, s ) / 2;
    return easeInBack( 2*t - 1, s )/2 + 0.5f;
}

struct EaseOutInBack {
    EaseOutInBack( float s = 1.70158f ) : mS( s ) {}
    float operator()( float t ) { return easeOutInBack( t, mS ); }
    float mS;
};


// Elastic

inline float easeInElasticHelper_( float t, float b, float c, float d, float a, float p )
{
    if( t == 0 ) return b;
    float t_adj = t / d;
    if( t_adj == 1 ) return b+c;

    float s;
    if( a < math<float>::abs(c) ) {
        a = c;
        s = p / 4.0f;
    }
    else {
        s = p / (2 * (float)M_PI) * math<float>::asin( c / a );
    }

    t_adj -= 1;
    return -( a * math<float>::pow( 2,10*t_adj) * math<float>::sin( (t_adj*d-s)*(2*(float)M_PI)/p )) + b;
}

inline float easeOutElasticHelper_( float t, float /*b*/, float c, float /*d*/, float a, float p )
{
    if( t == 0 ) return 0;
    if( t == 1) return c;

    float s;
    if( a < c ) {
        a = c;
        s = p / 4;
    }
    else {
        s = p / ( 2 * (float)M_PI ) * math<float>::asin( c / a );
    }

    return a * math<float>::pow( 2, -10*t ) * math<float>::sin( (t-s)*(2*(float)M_PI)/p ) + c;
}

inline float easeInElastic( float t, float amplitude, float period )
{
    return easeInElasticHelper_( t, 0, 1, 1, amplitude, period );
}

struct EaseInElastic {
    EaseInElastic( float amplitude, float period ) : mA( amplitude ), mP( period ) {}
    float operator()( float t ) { return easeInElastic( t, mA, mP ); }
    float mA, mP;
};

inline float easeOutElastic( float t, float amplitude, float period )
{
    return easeOutElasticHelper_( t, 0, 1, 1, amplitude, period );
}

struct EaseOutElastic {
    EaseOutElastic( float amplitude, float period ) : mA( amplitude ), mP( period ) {}
    float operator()( float t ) { return easeOutElastic( t, mA, mP ); }
    float mA, mP;
};

inline float easeInOutElastic( float t, float amplitude, float period )
{
    if( t == 0 ) return 0;
    t *= 2;
    if( t == 2 ) return 1;

    float s;
    if( amplitude < 1 ) {
        amplitude = 1;
        s = period / 4;
    }
    else {
        s = period / (2 * (float)M_PI) * math<float>::asin( 1 / amplitude );
    }

    if( t < 1 ) return -0.5f * ( amplitude * math<float>::pow( 2.0f, 10*(t-1) ) * math<float>::sin( (t-1-s)*(2*(float)M_PI)/period ));
    return amplitude * math<float>::pow( 2,-10*(t-1) ) * math<float>::sin( (t-1-s)*(2*(float)M_PI)/period ) * 0.5f + 1;
}

struct EaseInOutElastic {
    EaseInOutElastic( float amplitude, float period ) : mA( amplitude ), mP( period ) {}
    float operator()( float t ) { return easeInOutElastic( t, mA, mP ); }
    float mA, mP;
};

inline float easeOutInElastic( float t, float amplitude, float period )
{
    if (t < 0.5) return easeOutElasticHelper_(t*2, 0, 0.5, 1.0, amplitude, period );
    return easeInElasticHelper_(2*t - 1, 0.5f, 0.5f, 1, amplitude, period );
}

struct EaseOutInElastic {
    EaseOutInElastic( float amplitude, float period ) : mA( amplitude ), mP( period ) {}
    float operator()( float t ) { return easeOutInElastic( t, mA, mP ); }
    float mA, mP;
};

// Atan

inline float easeInAtan( float t, float a = 15 )
{
    float m = math<float>::atan( a );
    return ( math<float>::atan( (t - 1)*a ) / m ) + 1;
}

struct EaseInAtan {
    EaseInAtan( float a = 15 ) : mInvM( 1.0f / math<float>::atan( a ) ), mA( a ) {}
    float operator()( float t ) const { return ( math<float>::atan( (t - 1) * mA ) * mInvM ) + 1; } 
    float mA, mInvM;
};

inline float easeOutAtan( float t, float a = 15 )
{
    float m = math<float>::atan( a );
    return math<float>::atan( t*a ) / m;
}

struct EaseOutAtan {
    EaseOutAtan( float a = 15 ) : mInvM( 1.0f / math<float>::atan( a ) ), mA( a ) {}
    float operator()( float t ) const { return math<float>::atan( t * mA ) * mInvM; }   
    float mA, mInvM;
};

inline float easeInOutAtan( float t, float a = 15 )
{
    float m = math<float>::atan( 0.5f * a );
    return ( math<float>::atan((t - 0.5f)*a) / (2*m) ) + 0.5f;
}

struct EaseInOutAtan {
    EaseInOutAtan( float a = 15 ) : mInv2M( 1.0f / ( 2 * math<float>::atan( 0.5f * a ) ) ), mA( a ) {}
    float operator()( float t ) const { return ( math<float>::atan((t - 0.5f)*mA) * mInv2M ) + 0.5f; }  
    float mA, mInv2M;
};

} // namespace cinder