EaseFunctions.h

// Copyright (c) 2016-2018 Kiwano - Nomango
//
// Permission is hereby granted, free of charge, to any person obtaining a copy
// of this software and associated documentation files (the "Software"), to deal
// in the Software without restriction, including without limitation the rights
// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
// copies of the Software, and to permit persons to whom the Software is
// furnished to do so, subject to the following conditions:
//
// The above copyright notice and this permission notice shall be included in
// all copies or substantial portions of the Software.
//
// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
// THE SOFTWARE.
 
#pragma once
#include <kiwano/math/Scalar.h>
 
namespace kiwano
{
namespace math
{
 
inline float Linear(float step)
{
    return step;
}
 
// Ease
 
inline float EaseIn(float step, float rate)
{
    return math::Pow(step, rate);
}
 
inline float EaseOut(float step, float rate)
{
    return math::Pow(step, 1.f / rate);
}
 
inline float EaseInOut(float step, float rate)
{
    if (step < .5f)
        return .5f * math::Pow(2 * step, rate);
    return 1.f - .5f * math::Pow(2.f - 2 * step, rate);
}
 
// Exponential Ease
 
inline float EaseExponentialIn(float step)
{
    return math::Pow(2.f, 10 * (step - 1));
}
 
inline float EaseExponentialOut(float step)
{
    return 1.f - math::Pow(2.f, -10 * step);
}
 
inline float EaseExponentialInOut(float step)
{
    if (step < .5f)
        return .5f * math::Pow(2.f, 10 * (2 * step - 1));
    return 0.5f * (2 - math::Pow(2, -10 * (step * 2 - 1)));
}
 
// Bounce Ease
 
inline float EaseBounceOut(float step)
{
    if (step < 1 / 2.75f)
    {
        return 7.5625f * step * step;
    }
    else if (step < 2 / 2.75f)
    {
        step -= 1.5f / 2.75f;
        return 7.5625f * step * step + 0.75f;
    }
    else if (step < 2.5f / 2.75f)
    {
        step -= 2.25f / 2.75f;
        return 7.5625f * step * step + 0.9375f;
    }
 
    step -= 2.625f / 2.75f;
    return 7.5625f * step * step + 0.984375f;
}
 
inline float EaseBounceIn(float step)
{
    return 1 - EaseBounceOut(1 - step);
}
 
inline float EaseBounceInOut(float step)
{
    if (step < 0.5f)
    {
        return EaseBounceIn(step * 2) * 0.5f;
    }
    else
    {
        return EaseBounceOut(step * 2 - 1) * 0.5f + 0.5f;
    }
}
 
// Elastic Ease
 
inline float EaseElasticIn(float step, float period)
{
    if (step == 0 || step == 1)
        return step;
 
    step = step - 1;
    return -math::Pow(2, 10 * step) * math::Sin((step - period / 4) * 360.f / period);
}
 
inline float EaseElasticOut(float step, float period)
{
    if (step == 0 || step == 1)
        return step;
 
    return math::Pow(2, -10 * step) * math::Sin((step - period / 4) * 360.f / period) + 1;
}
 
inline float EaseElasticInOut(float step, float period)
{
    if (step == 0 || step == 1)
        return step;
 
    step = step * 2 - 1;
    if (step < 0)
    {
        return -0.5f * math::Pow(2, 10 * step) * math::Sin((step - period / 4) * 360.f / period);
    }
    return math::Pow(2, -10 * step) * math::Sin((step - period / 4) * 360.f / period) * 0.5f + 1;
}
 
// Back Ease
 
inline float EaseBackIn(float step)
{
    const float overshoot = 1.70158f;
    return step * step * ((overshoot + 1) * step - overshoot);
}
 
inline float EaseBackOut(float step)
{
    const float overshoot = 1.70158f;
    step                  = step - 1;
    return step * step * ((overshoot + 1) * step + overshoot) + 1;
}
 
inline float EaseBackInOut(float step)
{
    const float overshoot = 1.70158f * 1.525f;
 
    step = step * 2;
    if (step < 1)
    {
        return (step * step * ((overshoot + 1) * step - overshoot)) / 2;
    }
 
    step = step - 2;
    return (step * step * ((overshoot + 1) * step + overshoot)) / 2 + 1;
}
 
// Sine Ease
 
inline float EaseSineIn(float step)
{
    return 1.f - math::Cos(step * 90);
}
 
inline float EaseSineOut(float step)
{
    return math::Sin(step * 90);
}
 
inline float EaseSineInOut(float step)
{
    return -0.5f * (math::Cos(step * 180) - 1);
}
 
// Quad Ease
 
inline float EaseQuadIn(float step)
{
    return step * step;
}
 
inline float EaseQuadOut(float step)
{
    return -1 * step * (step - 2);
}
 
inline float EaseQuadInOut(float step)
{
    step = step * 2;
    if (step < 1)
        return 0.5f * step * step;
    --step;
    return -0.5f * (step * (step - 2) - 1);
}
 
// Cubic Ease
 
inline float EaseCubicIn(float step)
{
    return step * step * step;
}
 
inline float EaseCubicOut(float step)
{
    step -= 1;
    return (step * step * step + 1);
}
 
inline float EaseCubicInOut(float step)
{
    step = step * 2;
    if (step < 1)
        return 0.5f * step * step * step;
    step -= 2;
    return 0.5f * (step * step * step + 2);
}
 
// Quart Ease
 
inline float EaseQuartIn(float step)
{
    return step * step * step * step;
}
 
inline float EaseQuartOut(float step)
{
    step -= 1;
    return -(step * step * step * step - 1);
}
 
inline float EaseQuartInOut(float step)
{
    step = step * 2;
    if (step < 1)
        return 0.5f * step * step * step * step;
    step -= 2;
    return -0.5f * (step * step * step * step - 2);
}
 
// Quint Ease
 
inline float EaseQuintIn(float step)
{
    return step * step * step * step * step;
}
 
inline float EaseQuintOut(float step)
{
    step -= 1;
    return (step * step * step * step * step + 1);
}
 
inline float EaseQuintInOut(float step)
{
    step = step * 2;
    if (step < 1)
        return 0.5f * step * step * step * step * step;
    step -= 2;
    return 0.5f * (step * step * step * step * step + 2);
}
 
}  // namespace math
}  // namespace kiwano