glm gtx_easing proposal

easing.hpp

/// @ref gtx_easing
/// @file glm/gtx/easing.hpp
///
/// @see core (dependence)
///
/// @defgroup gtx_easing GLM_GTX_easing
/// @ingroup gtx
///
/// Include <glm/gtx/easing.hpp> to use the features of this extension.
///
/// Easing functions for animations and transitons
/// All functions take a parameter x in the range [0.0,1.0]
///
/// Based on the AHEasing project of Warren Moore (https://github.com/warrenm/AHEasing)

#pragma once

#include "../detail/setup.hpp"
#include "../detail/precision.hpp"
#include "../detail/type_int.hpp"


#ifndef GLM_ENABLE_EXPERIMENTAL
#	error "GLM: GLM_GTX_easing is an experimental extension and may change in the future. Use #define GLM_ENABLE_EXPERIMENTAL before including it, if you really want to use it."
#endif

#if GLM_MESSAGES == GLM_MESSAGES_ENABLED && !defined(GLM_EXT_INCLUDED)
#	pragma message("GLM: GLM_GTX_easing extension included")
#endif

namespace glm{
	/// @addtogroup gtx_easing
	/// @{

	/// Modelled after the line y = x
	/// @see gtx_easing
	template <typename genType>
	GLM_FUNC_DECL genType linearInterpolation(genType const & a);

	/// Modelled after the parabola y = x^2
	/// @see gtx_easing
	template <typename genType>
	GLM_FUNC_DECL genType quadraticEaseIn(genType const & a);

	/// Modelled after the parabola y = -x^2 + 2x
	/// @see gtx_easing
	template <typename genType>
	GLM_FUNC_DECL genType quadraticEaseOut(genType const & a);

	/// Modelled after the piecewise quadratic
	/// y = (1/2)((2x)^2)				; [0, 0.5)
	/// y = -(1/2)((2x-1)*(2x-3) - 1)	; [0.5, 1]
	/// @see gtx_easing
	template <typename genType>
	GLM_FUNC_DECL genType quadraticEaseInOut(genType const & a);

	/// Modelled after the cubic y = x^3
	template <typename genType>
	GLM_FUNC_DECL genType cubicEaseIn(genType const & a);

	/// Modelled after the cubic y = (x - 1)^3 + 1
	/// @see gtx_easing
	template <typename genType>
	GLM_FUNC_DECL genType cubicEaseOut(genType const & a);

	/// Modelled after the piecewise cubic
	/// y = (1/2)((2x)^3)		; [0, 0.5)
	/// y = (1/2)((2x-2)^3 + 2)	; [0.5, 1]
	/// @see gtx_easing
	template <typename genType>
	GLM_FUNC_DECL genType cubicEaseInOut(genType const & a);

	/// Modelled after the quartic x^4
	/// @see gtx_easing
	template <typename genType>
	GLM_FUNC_DECL genType quarticEaseIn(genType const & a);

	/// Modelled after the quartic y = 1 - (x - 1)^4
	/// @see gtx_easing
	template <typename genType>
	GLM_FUNC_DECL genType quarticEaseOut(genType const & a);

	/// Modelled after the piecewise quartic
	/// y = (1/2)((2x)^4)			; [0, 0.5)
	/// y = -(1/2)((2x-2)^4 - 2)	; [0.5, 1]
	/// @see gtx_easing
	template <typename genType>
	GLM_FUNC_DECL genType quarticEaseInOut(genType const & a);

	/// Modelled after the quintic y = x^5
	/// @see gtx_easing
	template <typename genType>
	GLM_FUNC_DECL genType quinticEaseIn(genType const & a);

	/// Modelled after the quintic y = (x - 1)^5 + 1
	/// @see gtx_easing
	template <typename genType>
	GLM_FUNC_DECL genType quinticEaseOut(genType const & a);

	/// Modelled after the piecewise quintic
	/// y = (1/2)((2x)^5)		; [0, 0.5)
	/// y = (1/2)((2x-2)^5 + 2) ; [0.5, 1]
	/// @see gtx_easing
	template <typename genType>
	GLM_FUNC_DECL genType quinticEaseInOut(genType const & a);

	/// Modelled after quarter-cycle of sine wave
	/// @see gtx_easing
	template <typename genType>
	GLM_FUNC_DECL genType sineEaseIn(genType const & a);

	/// Modelled after quarter-cycle of sine wave (different phase)
	/// @see gtx_easing
	template <typename genType>
	GLM_FUNC_DECL genType sineEaseOut(genType const & a);

	/// Modelled after half sine wave
	/// @see gtx_easing
	template <typename genType>
	GLM_FUNC_DECL genType sineEaseInOut(genType const & a);

	/// Modelled after shifted quadrant IV of unit circle
	/// @see gtx_easing
	template <typename genType>
	GLM_FUNC_DECL genType circularEaseIn(genType const & a);

	/// Modelled after shifted quadrant II of unit circle
	/// @see gtx_easing
	template <typename genType>
	GLM_FUNC_DECL genType circularEaseOut(genType const & a);

	/// Modelled after the piecewise circular function
	/// y = (1/2)(1 - sqrt(1 - 4x^2))			; [0, 0.5)
	/// y = (1/2)(sqrt(-(2x - 3)*(2x - 1)) + 1) ; [0.5, 1]
	/// @see gtx_easing
	template <typename genType>
	GLM_FUNC_DECL genType circularEaseInOut(genType const & a);

	/// Modelled after the exponential function y = 2^(10(x - 1))
	/// @see gtx_easing
	template <typename genType>
	GLM_FUNC_DECL genType exponentialEaseIn(genType const & a);

	/// Modelled after the exponential function y = -2^(-10x) + 1
	/// @see gtx_easing
	template <typename genType>
	GLM_FUNC_DECL genType exponentialEaseOut(genType const & a);

	/// Modelled after the piecewise exponential
	/// y = (1/2)2^(10(2x - 1))			; [0,0.5)
	/// y = -(1/2)*2^(-10(2x - 1))) + 1 ; [0.5,1]
	/// @see gtx_easing
	template <typename genType>
	GLM_FUNC_DECL genType exponentialEaseInOut(genType const & a);

	/// Modelled after the damped sine wave y = sin(13pi/2*x)*pow(2, 10 * (x - 1))
	/// @see gtx_easing
	template <typename genType>
	GLM_FUNC_DECL genType elasticEaseIn(genType const & a);

	/// Modelled after the damped sine wave y = sin(-13pi/2*(x + 1))*pow(2, -10x) + 1
	/// @see gtx_easing
	template <typename genType>
	GLM_FUNC_DECL genType elasticEaseOut(genType const & a);

	/// Modelled after the piecewise exponentially-damped sine wave:
	/// y = (1/2)*sin(13pi/2*(2*x))*pow(2, 10 * ((2*x) - 1))		; [0,0.5)
	/// y = (1/2)*(sin(-13pi/2*((2x-1)+1))*pow(2,-10(2*x-1)) + 2)	; [0.5, 1]
	/// @see gtx_easing
	template <typename genType>
	GLM_FUNC_DECL genType elasticEaseInOut(genType const & a);

	/// @param o Optional overshoot modifier
	/// @see gtx_easing
	template <typename genType>
	GLM_FUNC_DECL genType backEaseIn(genType const & a, genType const & o = 1.70158f);

	/// @param o Optional overshoot modifier
	/// @see gtx_easing
	template <typename genType>
	GLM_FUNC_DECL genType backEaseOut(genType const & a, genType const & o = 1.70158f);

	/// @param o Optional overshoot modifier
	/// @see gtx_easing
	template <typename genType>
	GLM_FUNC_DECL genType backEaseInOut(genType const & a, genType const & o = 1.70158f);

	template <typename genType>
	GLM_FUNC_DECL genType bounceEaseIn(genType const & a);

	template <typename genType>
	GLM_FUNC_DECL genType bounceEaseOut(genType const & a);

	template <typename genType>
	GLM_FUNC_DECL genType bounceEaseInOut(genType const & a, genType);

	/// @}
}//namespace glm
#include "easing.inl"

easing.inl

///////////////////////////////////////////////////////////////////////////////////
/// OpenGL Mathematics (glm.g-truc.net)
///
/// Copyright (c) 2005 - 2015 G-Truc Creation (www.g-truc.net)
/// 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.
/// 
/// Restrictions:
///		By making use of the Software for military purposes, you choose to make
///		a Bunny unhappy.
/// 
/// 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.
///
/// @ref gtx_easing
/// @file glm/gtx/easing.inl
/// @date 2018-05-05
/// @author Robert Chisholm
/// @note Based on the AHEasing project of Warren Moore (https://github.com/warrenm/AHEasing)
///////////////////////////////////////////////////////////////////////////////////

#include <cmath>

namespace glm{

	template <typename genType>
	GLM_FUNC_QUALIFIER genType linearInterpolation(genType const & a)
	{
		// Only defined in [0, 1]
		assert(a >= zero<genType>());
		assert(a <= one<genType>());
    
		return a;
	}

	template <typename genType>
	GLM_FUNC_QUALIFIER genType quadraticEaseIn(genType const & a)
	{
		// Only defined in [0, 1]
		assert(a >= zero<genType>());
		assert(a <= one<genType>());
    
		return a * a;
	}

	template <typename genType>
	GLM_FUNC_QUALIFIER genType quadraticEaseOut(genType const & a)
	{
		// Only defined in [0, 1]
		assert(a >= zero<genType>());
		assert(a <= one<genType>());
    
		return -(a * (a - 2));
	}

	template <typename genType>
	GLM_FUNC_QUALIFIER genType quadraticEaseInOut(genType const & a)
	{
		// Only defined in [0, 1]
		assert(a >= zero<genType>());
		assert(a <= one<genType>());
    
		if(a < 0.5)
		{
			return 2 * a * a;
		}
		else
		{
			return (-2 * a * a) + (4 * a) - one<genType>();
		}
	}

	template <typename genType>
	GLM_FUNC_QUALIFIER genType cubicEaseIn(genType const & a)
	{
		// Only defined in [0, 1]
		assert(a >= zero<genType>());
		assert(a <= one<genType>());
    
		return a * a * a;
	}

	template <typename genType>
	GLM_FUNC_QUALIFIER genType cubicEaseOut(genType const & a)
	{
		// Only defined in [0, 1]
		assert(a >= zero<genType>());
		assert(a <= one<genType>());
    
		genType const f = a - one<genType>();
		return f * f * f + one<genType>();
	}

	template <typename genType>
	GLM_FUNC_QUALIFIER genType cubicEaseInOut(genType const & a)
	{
		// Only defined in [0, 1]
		assert(a >= zero<genType>());
		assert(a <= one<genType>());
    
		if (a < 0.5)
		{
			return 4 * a * a * a;
		}
		else
		{
			genType const f = ((2 * a) - 2);
			return 0.5f * f * f * f + one<genType>();
		}
	}

	template <typename genType>
	GLM_FUNC_QUALIFIER genType quarticEaseIn(genType const & a)
	{
		// Only defined in [0, 1]
		assert(a >= zero<genType>());
		assert(a <= one<genType>());
    
		return a * a * a * a;
	}

	template <typename genType>
	GLM_FUNC_QUALIFIER genType quarticEaseOut(genType const & a)
	{
		// Only defined in [0, 1]
		assert(a >= zero<genType>());
		assert(a <= one<genType>());
    
		genType const f = (a - one<genType>());
		return f * f * f * (one<genType>() - a) + one<genType>();
	}

	template <typename genType>
	GLM_FUNC_QUALIFIER genType quarticEaseInOut(genType const & a) 
	{
		// Only defined in [0, 1]
		assert(a >= zero<genType>());
		assert(a <= one<genType>());
    
		if (a < 0.5)
		{
			return 8 * a * a * a * a;
		}
		else
		{
			genType const f = (a - one<genType>());
			return -8 * f * f * f * f + one<genType>();
		}
	}

	template <typename genType>
	GLM_FUNC_QUALIFIER genType quinticEaseIn(genType const & a) 
	{
		// Only defined in [0, 1]
		assert(a >= zero<genType>());
		assert(a <= one<genType>());
    
		return a * a * a * a * a;
	}

	template <typename genType>
	GLM_FUNC_QUALIFIER genType quinticEaseOut(genType const & a) 
	{
		// Only defined in [0, 1]
		assert(a >= zero<genType>());
		assert(a <= one<genType>());
    
		genType const f = (a - one<genType>());
		return f * f * f * f * f + one<genType>();
	}

	template <typename genType>
	GLM_FUNC_QUALIFIER genType quinticEaseInOut(genType const & a) 
	{
		// Only defined in [0, 1]
		assert(a >= zero<genType>());
		assert(a <= one<genType>());
    
		if (a < 0.5)
		{
			return 16 * a * a * a * a * a;
		}
		else
		{
			genType const f = ((2 * a) - 2);
			return 0.5f * f * f * f * f * f + one<genType>();
		}
	}

	template <typename genType>
	GLM_FUNC_QUALIFIER genType sineEaseIn(genType const & a)
	{
		// Only defined in [0, 1]
		assert(a >= zero<genType>());
		assert(a <= one<genType>());
    
		return sin((a - one<genType>()) * half_pi<genType>()) + one<genType>();
	}

	template <typename genType>
	GLM_FUNC_QUALIFIER genType sineEaseOut(genType const & a)
	{
		// Only defined in [0, 1]
		assert(a >= zero<genType>());
		assert(a <= one<genType>());
    
		return sin(a * half_pi<genType>());
	}

	template <typename genType>
	GLM_FUNC_QUALIFIER genType sineEaseInOut(genType const & a)
	{
		// Only defined in [0, 1]
		assert(a >= zero<genType>());
		assert(a <= one<genType>());
    
		return 0.5f * (one<genType>() - cos(a * pi<genType>()));
	}

	template <typename genType>
	GLM_FUNC_QUALIFIER genType circularEaseIn(genType const & a)
	{
		// Only defined in [0, 1]
		assert(a >= zero<genType>());
		assert(a <= one<genType>());
    
		return one<genType>() - sqrt(one<genType>() - (a * a));
	}

	template <typename genType>
	GLM_FUNC_QUALIFIER genType circularEaseOut(genType const & a)
	{
		// Only defined in [0, 1]
		assert(a >= zero<genType>());
		assert(a <= one<genType>());
    
		return sqrt((2 - a) * a);
	}

	template <typename genType>
	GLM_FUNC_QUALIFIER genType circularEaseInOut(genType const & a)
	{
		// Only defined in [0, 1]
		assert(a >= zero<genType>());
		assert(a <= one<genType>());
    
		if(a < 0.5)
		{
			return 0.5f * (one<genType>() - sqrt(one<genType>() - 4 * (a * a)));
		}
		else
		{
			return 0.5f * (sqrt(-((2 * a) - 3) * ((2 * a) - one<genType>())) + one<genType>());
		}
	}

	template <typename genType>
	GLM_FUNC_QUALIFIER genType exponentialEaseIn(genType const & a)
	{
		// Only defined in [0, 1]
		assert(a >= zero<genType>());
		assert(a <= one<genType>());
    
		return (a == zero<genType>()) ? a : pow<genType>(2, 10 * (a - one<genType>()));
	}

	template <typename genType>
	GLM_FUNC_QUALIFIER genType exponentialEaseOut(genType const & a)
	{
		// Only defined in [0, 1]
		assert(a >= zero<genType>());
		assert(a <= one<genType>());
    
		return (a == one<genType>()) ? a : one<genType>() - pow<genType>(2, -10 * a);
	}

	template <typename genType>
	GLM_FUNC_QUALIFIER genType exponentialEaseInOut(genType const & a)
	{
		// Only defined in [0, 1]
		assert(a >= zero<genType>());
		assert(a <= one<genType>());
    
		if(a == zero<genType>() || a == one<genType>()) return a;
		
		if(a < 0.5)
		{
			return 0.5f * pow<genType>(2, (20 * a) - 10);
		}
		else
		{
			return -0.5f * pow<genType>(2, (-20 * a) + 10) + one<genType>();
		}
	}

	template <typename genType>
	GLM_FUNC_QUALIFIER genType elasticEaseIn(genType const & a)
	{
		// Only defined in [0, 1]
		assert(a >= zero<genType>());
		assert(a <= one<genType>());
    
		return sin(13 * half_pi<genType>() * a) * pow<genType>(2, 10 * (a - one<genType>()));
	}

	template <typename genType>
	GLM_FUNC_QUALIFIER genType elasticEaseOut(genType const & a)
	{
		// Only defined in [0, 1]
		assert(a >= zero<genType>());
		assert(a <= one<genType>());
    
		return sin(-13 * half_pi<genType>() * (a + one<genType>())) * pow<genType>(2, -10 * a) + one<genType>();
	}

	template <typename genType>
	GLM_FUNC_QUALIFIER genType elasticEaseInOut(genType const & a)
	{
		// Only defined in [0, 1]
		assert(a >= zero<genType>());
		assert(a <= one<genType>());
    
		if(a < 0.5)
		{
			return 0.5f * sin(13 * half_pi<genType>() * (2 * a)) * pow<genType>(2, 10 * ((2 * a) - one<genType>()));
		}
		else
		{
			return 0.5f * (sin(-13 * half_pi<genType>() * ((2 * a - one<genType>()) + one<genType>())) * pow<genType>(2, -10 * (2 * a - one<genType>())) + 2);
		}
	}

	template <typename genType>
	GLM_FUNC_QUALIFIER genType backEaseIn(genType const & a, genType const & o)
	{
		// Only defined in [0, 1]
		assert(a >= zero<genType>());
		assert(a <= one<genType>());

		float z = ((o + one<genType>()) * a) - o;
		return (a*a*z);
	}

	template <typename genType>
	GLM_FUNC_QUALIFIER genType backEaseOut(genType const & a, genType const & o)
	{
		// Only defined in [0, 1]
		assert(a >= zero<genType>());
		assert(a <= one<genType>());

		float n = a - one<genType>();
		float z = ((o + one<genType>()) * n) + o;
		return (n*n*z) + one<genType>();
	}

	template <typename genType>
	GLM_FUNC_QUALIFIER genType backEaseInOut(genType const & a, genType const & o)
	{
		// Only defined in [0, 1]
		assert(a >= zero<genType>());
		assert(a <= one<genType>());

		float s = o * 1.525f;
		float x = 0.5f;
		float n = a / 0.5f;

		if (n < 1.0f){
			float z = ((s + 1.0f) * n) - s;
			float m = n*n*z;
			return x * m;
		}
		else 
		{
			n -= 2.0f;
			float z = ((s + 1.0f) * n) + s;
			float m = (n*n*z) + 2.0f;
			return x * m;
		}
	}

	template <typename genType>
	GLM_FUNC_QUALIFIER genType bounceEaseOut(genType const & a)
	{
		// Only defined in [0, 1]
		assert(a >= zero<genType>());
		assert(a <= one<genType>());
    
		if(a < 4/11.0f)
		{
			return (121 * a * a)/16.0f;
		}
		else if(a < 8/11.0)
		{
			return (363/40.0f * a * a) - (99/10.0f * a) + 17/5.0f;
		}
		else if(a < 9/10.0)
		{
			return (4356/361.0f * a * a) - (35442/1805.0f * a) + 16061/1805.0f;
		}
		else
		{
			return (54/5.0f * a * a) - (513/25.0f * a) + 268/25.0f;
		}
	}

	template <typename genType>
	GLM_FUNC_QUALIFIER genType bounceEaseIn(genType const & a)
	{
		// Only defined in [0, 1]
		assert(a >= zero<genType>());
		assert(a <= one<genType>());

		return one<genType>() - bounceEaseOut(one<genType>() - a);
	}

	template <typename genType>
	GLM_FUNC_QUALIFIER genType bounceEaseInOut(genType const & a)
	{
		// Only defined in [0, 1]
		assert(a >= zero<genType>());
		assert(a <= one<genType>());
    
		if(a < 0.5)
		{
			return 0.5f * (one<genType>() - bounceEaseOut(a * 2));
		}
		else
		{
			return 0.5f * bounceEaseOut(a * 2 - one<genType>()) + 0.5f;
		}
	}
  
}//namespace glm

easing_test.cpp

#define GLM_ENABLE_EXPERIMENTAL
#include <glm/glm.hpp>
#include <glm/gtx/quaternion.hpp>
#include <glm/gtx/easing.hpp>

namespace
{

	template<typename T>
	void _test_easing()
	{
		T a, r;
		r = glm::linearInterpolation(a);
		//
		r = glm::quadraticEaseIn(a);
		r = glm::quadraticEaseOut(a);
		r = glm::quadraticEaseInOut(a);
		//
		r = glm::cubicEaseIn(a);
		r = glm::cubicEaseOut(a);
		r = glm::cubicEaseInOut(a);
		//
		r = glm::quarticEaseIn(a);
		r = glm::quarticEaseOut(a);
		r = glm::quinticEaseInOut(a);
		//
		r = glm::sineEaseIn(a);
		r = glm::sineEaseOut(a);
		r = glm::sineEaseInOut(a);
		//
		r = glm::circularEaseIn(a);
		r = glm::circularEaseOut(a);
		r = glm::circularEaseInOut(a);
		//
		r = glm::exponentialEaseIn(a);;
		r = glm::exponentialEaseOut(a);
		r = glm::exponentialEaseInOut(a);
		//
		r = glm::elasticEaseIn(a);
		r = glm::elasticEaseOut(a);
		r = glm::elasticEaseInOut(a);
		//
		r = glm::backEaseIn(a);
		r = glm::backEaseOut(a);
		r = glm::backEaseInOut(a);
		//
		r = glm::bounceEaseIn(a);;
		r = glm::bounceEaseOut(a);
		r = glm::bounceEaseInOut(a);
	}

}

void testEasing()
{
	_test_easing<float>();
	_test_easing<double>();
}