Added GTX_easing for interpolation functions #761

This commit is contained in:
Christophe Riccio 2018-05-07 15:39:25 +02:00
parent e560ce01d4
commit 69f94334e0
5 changed files with 684 additions and 0 deletions

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glm/gtx/easing.hpp Normal file
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/// @ref gtx_easing
/// @file glm/gtx/easing.hpp
/// @author Robert Chisholm
///
/// @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/qualifier.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"

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/// @ref gtx_easing
/// @file glm/gtx/easing.inl
#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 < static_cast<genType>(0.5))
{
return static_cast<genType>(0.5) * (one<genType>() - sqrt(one<genType>() - static_cast<genType>(4) * (a * a)));
}
else
{
return static_cast<genType>(0.5) * (sqrt(-((static_cast<genType>(2) * a) - static_cast<genType>(3)) * ((static_cast<genType>(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>(static_cast<genType>(2), static_cast<genType>(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>(static_cast<genType>(2), -static_cast<genType>(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 < static_cast<genType>(0.5))
{
return static_cast<genType>(0.5) * pow<genType>(2, (20 * a) - 10);
}
else
{
return -static_cast<genType>(0.5) * 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>(static_cast<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>(static_cast<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 < static_cast<genType>(0.5))
{
return static_cast<genType>(0.5) * sin(static_cast<genType>(13) * half_pi<genType>() * (static_cast<genType>(2) * a)) * pow<genType>(static_cast<genType>(2), static_cast<genType>(10) * ((static_cast<genType>(2) * a) - one<genType>()));
}
else
{
return static_cast<genType>(0.5) * (sin(-static_cast<genType>(13) * half_pi<genType>() * ((static_cast<genType>(2) * a - one<genType>()) + one<genType>())) * pow<genType>(static_cast<genType>(2), -static_cast<genType>(10) * (static_cast<genType>(2) * a - one<genType>())) + static_cast<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>());
genType 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>());
genType n = a - one<genType>();
genType 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>());
genType s = o * static_cast<genType>(1.525);
genType x = static_cast<genType>(0.5);
genType n = a / static_cast<genType>(0.5);
if (n < static_cast<genType>(1))
{
genType z = ((s + static_cast<genType>(1)) * n) - s;
genType m = n * n * z;
return x * m;
}
else
{
n -= static_cast<genType>(2);
genType z = ((s + static_cast<genType>(1)) * n) + s;
genType m = (n*n*z) + static_cast<genType>(2);
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 < static_cast<genType>(4.0 / 11.0))
{
return (static_cast<genType>(121) * a * a) / static_cast<genType>(16);
}
else if(a < static_cast<genType>(8.0 / 11.0))
{
return (static_cast<genType>(363.0 / 40.0) * a * a) - (static_cast<genType>(99.0 / 10.0) * a) + static_cast<genType>(17.0 / 5.0);
}
else if(a < static_cast<genType>(9.0 / 10.0))
{
return (static_cast<genType>(4356.0 / 361.0) * a * a) - (static_cast<genType>(35442.0 / 1805.0) * a) + static_cast<genType>(16061.0 / 1805.0);
}
else
{
return (static_cast<genType>(54.0 / 5.0) * a * a) - (static_cast<genType>(513.0 / 25.0) * a) + static_cast<genType>(268.0 / 25.0);
}
}
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 < static_cast<genType>(0.5))
{
return static_cast<genType>(0.5) * (one<genType>() - bounceEaseOut(a * static_cast<genType>(2)));
}
else
{
return static_cast<genType>(0.5) * bounceEaseOut(a * static_cast<genType>(2) - one<genType>()) + static_cast<genType>(0.5);
}
}
}//namespace glm

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@ -69,6 +69,7 @@ glm::mat4 camera(float Translate, glm::vec2 const& Rotate)
- Added GTX_texture: levels function
- Added spearate functions to use both nagative one and zero near clip plans #680
- Added GLM_FORCE_SINGLE_ONLY to use GLM on platforms that don't support double #627
- Added GTX_easing for interpolation functions #761
#### Improvements:
- No more default initialization of vector, matrix and quaternion types

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@ -7,6 +7,7 @@ glmCreateTestGTC(gtx_color_space)
glmCreateTestGTC(gtx_common)
glmCreateTestGTC(gtx_compatibility)
glmCreateTestGTC(gtx_component_wise)
glmCreateTestGTC(gtx_easing)
glmCreateTestGTC(gtx_euler_angle)
glmCreateTestGTC(gtx_extend)
glmCreateTestGTC(gtx_extended_min_max)

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test/gtx/gtx_easing.cpp Normal file
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#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 = static_cast<float>(0.5);
T 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);
}
}
int main()
{
int Error = 0;
_test_easing<float>();
_test_easing<double>();
return Error;
}