The easing class implements the functions of the predefined IEnums::Interpolation curves. More...

#include "murl_math_easing.h"

Public Types
using	ValueType = DataType
	The template parameter value type.

using	Interpolate = DataType(*)(DataType x)
	Definition of the easing function type.

Static Public Member Functions
static DataType	Constant (DataType x)
	Constant interpolation. More...

static DataType	Linear (DataType x)
	Linear interpolation. More...

static DataType	SmoothstepInOut (DataType x)
	Smoothstep "in-out" interpolation. More...

static DataType	SmoothstepIn (DataType x)
	Smoothstep "in" interpolation. More...

static DataType	SmoothstepOut (DataType x)
	Smoothstep "out" interpolation. More...

static DataType	SmoothstepOutIn (DataType x)
	Smoothstep "out-in" interpolation. More...

static DataType	SmootherstepInOut (DataType x)
	Smootherstep "in-out" interpolation. More...

static DataType	SmootherstepIn (DataType x)
	Smootherstep "in" interpolation. More...

static DataType	SmootherstepOut (DataType x)
	Smootherstep "out" interpolation. More...

static DataType	SmootherstepOutIn (DataType x)
	Smootherstep "out-in" interpolation. More...

static DataType	EaseIn (DataType x)
	Ease (cubic) "in" interpolation. More...

static DataType	EaseOut (DataType x)
	Ease (cubic) "out" interpolation. More...

static DataType	EaseInOut (DataType x)
	Ease (cubic) "in-out" interpolation. More...

static DataType	EaseOutIn (DataType x)
	Ease (cubic) "out-in" interpolation. More...

static DataType	EaseQuartIn (DataType x)
	Ease Quart "in" interpolation. More...

static DataType	EaseQuartOut (DataType x)
	Ease Quart "out" interpolation. More...

static DataType	EaseQuartInOut (DataType x)
	Ease Quart "in-out" interpolation. More...

static DataType	EaseQuartOutIn (DataType x)
	Ease Quart "out-in" interpolation. More...

static DataType	EaseExponentialIn (DataType x)
	Ease Exponential "in" interpolation. More...

static DataType	EaseExponentialOut (DataType x)
	Ease Exponential "out" interpolation. More...

static DataType	EaseExponentialInOut (DataType x)
	Ease Exponential "in-out" interpolation. More...

static DataType	EaseExponentialOutIn (DataType x)
	Ease Exponential "out-in" interpolation. More...

static DataType	EaseCircularIn (DataType x)
	Ease Circular "in" interpolation. More...

static DataType	EaseCircularOut (DataType x)
	Ease Circular "out" interpolation. More...

static DataType	EaseCircularHelper (DataType x)
	Ease Circular helper interpolation. More...

static DataType	EaseCircularInOut (DataType x)
	Ease Circular "in-out" interpolation. More...

static DataType	EaseCircularOutIn (DataType x)
	Ease Circular "out-in" interpolation. More...

static DataType	EaseBackIn (DataType x)
	Ease Back "in" interpolation. More...

static DataType	EaseBackOut (DataType x)
	Ease Back "out" interpolation. More...

static DataType	EaseBackInOut (DataType x)
	Ease Back "in-out" interpolation. More...

static DataType	EaseBackOutIn (DataType x)
	Ease Back "out-in" interpolation. More...

static DataType	EaseElasticIn (DataType x)
	Ease Elastic "in" interpolation. More...

static DataType	EaseElasticOut (DataType x)
	Ease Elastic "out" interpolation. More...

static DataType	EaseElasticInOut (DataType x)
	Ease Elastic "in-out" interpolation. More...

static DataType	EaseElasticOutIn (DataType x)
	Ease Elastic "out-in" interpolation. More...

static DataType	EaseBounceOut (DataType x)
	Ease Bounce "out" interpolation. More...

static DataType	EaseBounceIn (DataType x)
	Ease Bounce "in" interpolation. More...

static DataType	EaseBounceInOut (DataType x)
	Ease Bounce "in-out" interpolation. More...

static DataType	EaseBounceOutIn (DataType x)
	Ease Bounce "in-out" interpolation. More...

Detailed Description

template<class DataType>
class Murl::Math::Easing< DataType >

The easing class implements the functions of the predefined IEnums::Interpolation curves.

Smoothstep functions description can be found at http://wikipedia.org/wiki/Smoothstep
Easing functions description can be found at http://easings.net

Member Function Documentation

◆ Constant()

template<class DataType >

static DataType Murl::Math::Easing< DataType >::Constant ( DataType x )

inlinestatic

Constant interpolation.

Function: f(x)=0

Parameters

x	The value to interpolate in range [0 .. 1].

Returns: The result for f(x).

◆ Linear()

template<class DataType >

static DataType Murl::Math::Easing< DataType >::Linear ( DataType x )

inlinestatic

Linear interpolation.

Function: f(x)=x

Parameters

x	The value to interpolate in range [0 .. 1].

Returns: The result for f(x).

◆ SmoothstepInOut()

template<class DataType >

static DataType Murl::Math::Easing< DataType >::SmoothstepInOut ( DataType x )

inlinestatic

Smoothstep "in-out" interpolation.

Function: f(x)=(x^2)*(3-2*x)

Parameters

x	The value to interpolate in range [0 .. 1].

Returns: The result for f(x).

Referenced by Murl::Math::Easing< DataType >::SmoothstepIn(), Murl::Math::Easing< DataType >::SmoothstepOut(), and Murl::Math::Easing< DataType >::SmoothstepOutIn().

◆ SmoothstepIn()

template<class DataType >

static DataType Murl::Math::Easing< DataType >::SmoothstepIn ( DataType x )

inlinestatic

Smoothstep "in" interpolation.

Function: f(x)=SmoothstepInOut(x/2)*2

Parameters

x	The value to interpolate in range [0 .. 1].

Returns: The result for f(x).

References Murl::Math::Easing< DataType >::SmoothstepInOut().

◆ SmoothstepOut()

template<class DataType >

static DataType Murl::Math::Easing< DataType >::SmoothstepOut ( DataType x )

inlinestatic

Smoothstep "out" interpolation.

Function: f(x)=SmoothstepInOut((x+1)/2)*2-1

Parameters

x	The value to interpolate in range [0 .. 1].

Returns: The result for f(x).

References Murl::Math::Easing< DataType >::SmoothstepInOut().

◆ SmoothstepOutIn()

template<class DataType >

static DataType Murl::Math::Easing< DataType >::SmoothstepOutIn ( DataType x )

inlinestatic

Smoothstep "out-in" interpolation.

Function: f(x)=(x < 0.5) ? SmoothstepInOut(x+0.5)-0.5 : SmoothstepInOut(x-0.5)+0.5

Parameters

x	The value to interpolate in range [0 .. 1].

Returns: The result for f(x).

References Murl::Math::Easing< DataType >::SmoothstepInOut().

◆ SmootherstepInOut()

template<class DataType >

static DataType Murl::Math::Easing< DataType >::SmootherstepInOut ( DataType x )

inlinestatic

Smootherstep "in-out" interpolation.

Function: f(x)=(x^3)*(x*(6*x-15)+10)

Parameters

x	The value to interpolate in range [0 .. 1].

Returns: The result for f(x).

Referenced by Murl::Math::Easing< DataType >::SmootherstepIn(), Murl::Math::Easing< DataType >::SmootherstepOut(), and Murl::Math::Easing< DataType >::SmootherstepOutIn().

◆ SmootherstepIn()

template<class DataType >

static DataType Murl::Math::Easing< DataType >::SmootherstepIn ( DataType x )

inlinestatic

Smootherstep "in" interpolation.

Function: f(x)=SmootherstepInOut(x/2)*2

Parameters

x	The value to interpolate in range [0 .. 1].

Returns: The result for f(x).

References Murl::Math::Easing< DataType >::SmootherstepInOut().

◆ SmootherstepOut()

template<class DataType >

static DataType Murl::Math::Easing< DataType >::SmootherstepOut ( DataType x )

inlinestatic

Smootherstep "out" interpolation.

Function: f(x)=SmootherstepInOut((x+1)/2)*2-1

Parameters

x	The value to interpolate in range [0 .. 1].

Returns: The result for f(x).

References Murl::Math::Easing< DataType >::SmootherstepInOut().

◆ SmootherstepOutIn()

template<class DataType >

static DataType Murl::Math::Easing< DataType >::SmootherstepOutIn ( DataType x )

inlinestatic

Smootherstep "out-in" interpolation.

Function: f(x)=(x < 0.5) ? SmootherstepInOut(x+0.5)-0.5 : SmootherstepInOut(x-0.5)+0.5

Parameters

x	The value to interpolate in range [0 .. 1].

Returns: The result for f(x).

References Murl::Math::Easing< DataType >::SmootherstepInOut().

◆ EaseIn()

template<class DataType >

static DataType Murl::Math::Easing< DataType >::EaseIn ( DataType x )

inlinestatic

Ease (cubic) "in" interpolation.

Function: f(x)=x^3

Parameters

x	The value to interpolate in range [0 .. 1].

Returns: The result for f(x).

Referenced by Murl::Math::Easing< DataType >::EaseInOut(), Murl::Math::Easing< DataType >::EaseOut(), and Murl::Math::Easing< DataType >::EaseOutIn().

◆ EaseOut()

template<class DataType >

static DataType Murl::Math::Easing< DataType >::EaseOut ( DataType x )

inlinestatic

Ease (cubic) "out" interpolation.

Function: f(x)=1-EaseIn(1-x)

Parameters

x	The value to interpolate in range [0 .. 1].

Returns: The result for f(x).

References Murl::Math::Easing< DataType >::EaseIn().

◆ EaseInOut()

template<class DataType >

static DataType Murl::Math::Easing< DataType >::EaseInOut ( DataType x )

inlinestatic

Ease (cubic) "in-out" interpolation.

Function: f(x)=(x < 0.5) ? EaseIn(2*x)/2 : 1-EaseIn(2-2*x)/2

Parameters

x	The value to interpolate in range [0 .. 1].

Returns: The result for f(x).

References Murl::Math::Easing< DataType >::EaseIn().

◆ EaseOutIn()

template<class DataType >

static DataType Murl::Math::Easing< DataType >::EaseOutIn ( DataType x )

inlinestatic

Ease (cubic) "out-in" interpolation.

Function: f(x)=4*EaseIn(x-0.5)+0.5

Parameters

x	The value to interpolate in range [0 .. 1].

Returns: The result for f(x).

References Murl::Math::Easing< DataType >::EaseIn().

◆ EaseQuartIn()

template<class DataType >

static DataType Murl::Math::Easing< DataType >::EaseQuartIn ( DataType x )

inlinestatic

Ease Quart "in" interpolation.

Function: f(x)=x^4

Parameters

x	The value to interpolate in range [0 .. 1].

Returns: The result for f(x).

Referenced by Murl::Math::Easing< DataType >::EaseQuartInOut(), Murl::Math::Easing< DataType >::EaseQuartOut(), and Murl::Math::Easing< DataType >::EaseQuartOutIn().

◆ EaseQuartOut()

template<class DataType >

static DataType Murl::Math::Easing< DataType >::EaseQuartOut ( DataType x )

inlinestatic

Ease Quart "out" interpolation.

Function: f(x)=1-EaseQuartIn(1-x)

Parameters

x	The value to interpolate in range [0 .. 1].

Returns: The result for f(x).

References Murl::Math::Easing< DataType >::EaseQuartIn().

◆ EaseQuartInOut()

template<class DataType >

static DataType Murl::Math::Easing< DataType >::EaseQuartInOut ( DataType x )

inlinestatic

Ease Quart "in-out" interpolation.

Function: f(x)=(x < 0.5) ? EaseQuartIn(2*x)/2 : 1-EaseQuartIn(2-2*x)/2

Parameters

x	The value to interpolate in range [0 .. 1].

Returns: The result for f(x).

References Murl::Math::Easing< DataType >::EaseQuartIn().

◆ EaseQuartOutIn()

template<class DataType >

static DataType Murl::Math::Easing< DataType >::EaseQuartOutIn ( DataType x )

inlinestatic

Ease Quart "out-in" interpolation.

Function: f(x)=(x < 0.5) ? 0.5-EaseQuartIn(1-2*x)/2 : 0.5+EaseQuartIn(2*x-1)/2

Parameters

x	The value to interpolate in range [0 .. 1].

Returns: The result for f(x).

References Murl::Math::Easing< DataType >::EaseQuartIn().

◆ EaseExponentialIn()

template<class DataType >

static DataType Murl::Math::Easing< DataType >::EaseExponentialIn ( DataType x )

inlinestatic

Ease Exponential "in" interpolation.

Function: f(x)=(2^8x)*x/256

Parameters

x	The value to interpolate in range [0 .. 1].

Returns: The result for f(x).

References Murl::Math::Pow().

Referenced by Murl::Math::Easing< DataType >::EaseExponentialInOut(), Murl::Math::Easing< DataType >::EaseExponentialOut(), and Murl::Math::Easing< DataType >::EaseExponentialOutIn().

◆ EaseExponentialOut()

template<class DataType >

static DataType Murl::Math::Easing< DataType >::EaseExponentialOut ( DataType x )

inlinestatic

Ease Exponential "out" interpolation.

Function: f(x)=1-EaseExponentialIn(1-x)

Parameters

x	The value to interpolate in range [0 .. 1].

Returns: The result for f(x).

References Murl::Math::Easing< DataType >::EaseExponentialIn().

◆ EaseExponentialInOut()

template<class DataType >

static DataType Murl::Math::Easing< DataType >::EaseExponentialInOut ( DataType x )

inlinestatic

Ease Exponential "in-out" interpolation.

Function: f(x)=(x < 0.5) ? EaseExponentialIn(2*x)/2 : 1-EaseExponentialIn(2-2*x)/2

Parameters

x	The value to interpolate in range [0 .. 1].

Returns: The result for f(x).

References Murl::Math::Easing< DataType >::EaseExponentialIn().

◆ EaseExponentialOutIn()

template<class DataType >

static DataType Murl::Math::Easing< DataType >::EaseExponentialOutIn ( DataType x )

inlinestatic

Ease Exponential "out-in" interpolation.

Function: f(x)=(x < 0.5) ? 0.5-EaseExponentialIn(1-2*x)/2 : 0.5+EaseExponentialIn(2*x-1)/2

Parameters

x	The value to interpolate in range [0 .. 1].

Returns: The result for f(x).

References Murl::Math::Easing< DataType >::EaseExponentialIn().

◆ EaseCircularIn()

template<class DataType >

static DataType Murl::Math::Easing< DataType >::EaseCircularIn ( DataType x )

inlinestatic

Ease Circular "in" interpolation.

Function: f(x)=1-sqrt(1-x^2)

Parameters

x	The value to interpolate in range [0 .. 1].

Returns: The result for f(x).

References Murl::Math::Sqrt().

◆ EaseCircularOut()

template<class DataType >

static DataType Murl::Math::Easing< DataType >::EaseCircularOut ( DataType x )

inlinestatic

Ease Circular "out" interpolation.

Function: f(x)=sqrt((2-x)*x)

Parameters

x	The value to interpolate in range [0 .. 1].

Returns: The result for f(x).

References Murl::Math::Sqrt().

◆ EaseCircularHelper()

template<class DataType >

static DataType Murl::Math::Easing< DataType >::EaseCircularHelper ( DataType x )

inlinestatic

Ease Circular helper interpolation.

Function: f(x)=sqrt(x-x^2)

Parameters

x	The value to interpolate in range [0 .. 1].

Returns: The result for f(x).

References Murl::Math::Sqrt().

Referenced by Murl::Math::Easing< DataType >::EaseCircularInOut(), and Murl::Math::Easing< DataType >::EaseCircularOutIn().

◆ EaseCircularInOut()

template<class DataType >

static DataType Murl::Math::Easing< DataType >::EaseCircularInOut ( DataType x )

inlinestatic

Ease Circular "in-out" interpolation.

Function: f(x)=(x < 0.5) ? 0.5-EaseCircularHelper(x+0.5) : 0.5+EaseCircularHelper(x-0.5)

Parameters

x	The value to interpolate in range [0 .. 1].

Returns: The result for f(x).

References Murl::Math::Easing< DataType >::EaseCircularHelper().

◆ EaseCircularOutIn()

template<class DataType >

static DataType Murl::Math::Easing< DataType >::EaseCircularOutIn ( DataType x )

inlinestatic

Ease Circular "out-in" interpolation.

Function: f(x)=(x < 0.5) ? EaseCircularHelper(x) : 1-EaseCircularHelper(x)

Parameters

x	The value to interpolate in range [0 .. 1].

Returns: The result for f(x).

References Murl::Math::Easing< DataType >::EaseCircularHelper().

◆ EaseBackIn()

template<class DataType >

static DataType Murl::Math::Easing< DataType >::EaseBackIn ( DataType x )

inlinestatic

Ease Back "in" interpolation.

Function: f(x)=(x^3)-x*sin(x*PI)

Parameters

x	The value to interpolate in range [0 .. 1].

Returns: The result for f(x).

References Murl::Math::PI, and Murl::Math::Sin().

Referenced by Murl::Math::Easing< DataType >::EaseBackInOut(), Murl::Math::Easing< DataType >::EaseBackOut(), and Murl::Math::Easing< DataType >::EaseBackOutIn().

◆ EaseBackOut()

template<class DataType >

static DataType Murl::Math::Easing< DataType >::EaseBackOut ( DataType x )

inlinestatic

Ease Back "out" interpolation.

Function: f(x)=1-EaseBackIn(1-x)

Parameters

x	The value to interpolate in range [0 .. 1].

Returns: The result for f(x).

References Murl::Math::Easing< DataType >::EaseBackIn().

◆ EaseBackInOut()

template<class DataType >

static DataType Murl::Math::Easing< DataType >::EaseBackInOut ( DataType x )

inlinestatic

Ease Back "in-out" interpolation.

Function: f(x)=(x < 0.5) ? EaseBackIn(2*x)/2 : 1-EaseBackIn(2-2*x)/2

Parameters

x	The value to interpolate in range [0 .. 1].

Returns: The result for f(x).

References Murl::Math::Easing< DataType >::EaseBackIn().

◆ EaseBackOutIn()

template<class DataType >

static DataType Murl::Math::Easing< DataType >::EaseBackOutIn ( DataType x )

inlinestatic

Ease Back "out-in" interpolation.

Function: f(x)=(x < 0.5) ? 0.5-EaseBackIn(1-2*x)/2 : 0.5+EaseBackIn(2*x-1)/2

Parameters

x	The value to interpolate in range [0 .. 1].

Returns: The result for f(x).

References Murl::Math::Easing< DataType >::EaseBackIn().

◆ EaseElasticIn()

template<class DataType >

static DataType Murl::Math::Easing< DataType >::EaseElasticIn ( DataType x )

inlinestatic

Ease Elastic "in" interpolation.

Function: f(x)=sin(13*PI/2*x)*2^(10*(x-1))

Parameters

x	The value to interpolate in range [0 .. 1].

Returns: The result for f(x).

References Murl::Math::HALF_PI, Murl::Math::Pow(), and Murl::Math::Sin().

Referenced by Murl::Math::Easing< DataType >::EaseElasticInOut(), Murl::Math::Easing< DataType >::EaseElasticOut(), and Murl::Math::Easing< DataType >::EaseElasticOutIn().

◆ EaseElasticOut()

template<class DataType >

static DataType Murl::Math::Easing< DataType >::EaseElasticOut ( DataType x )

inlinestatic

Ease Elastic "out" interpolation.

Function: f(x)=1-EaseElasticIn(1-x)

Parameters

x	The value to interpolate in range [0 .. 1].

Returns: The result for f(x).

References Murl::Math::Easing< DataType >::EaseElasticIn().

◆ EaseElasticInOut()

template<class DataType >

static DataType Murl::Math::Easing< DataType >::EaseElasticInOut ( DataType x )

inlinestatic

Ease Elastic "in-out" interpolation.

Function: f(x)=(x < 0.5) ? EaseElasticIn(2*x)/2 : 1-EaseElasticIn(2-2*x)/2

Parameters

x	The value to interpolate in range [0 .. 1].

Returns: The result for f(x).

References Murl::Math::Easing< DataType >::EaseElasticIn().

◆ EaseElasticOutIn()

template<class DataType >

static DataType Murl::Math::Easing< DataType >::EaseElasticOutIn ( DataType x )

inlinestatic

Ease Elastic "out-in" interpolation.

Function: f(x)=(x < 0.5) ? 0.5-EaseElasticIn(1-2*x)/2 : 0.5+EaseElasticIn(2*x-1)/2

Parameters

x	The value to interpolate in range [0 .. 1].

Returns: The result for f(x).

References Murl::Math::Easing< DataType >::EaseElasticIn().

◆ EaseBounceOut()

template<class DataType >

static DataType Murl::Math::Easing< DataType >::EaseBounceOut ( DataType x )

inlinestatic

Ease Bounce "out" interpolation.

Function: f(x)= ... = a halve and three shrinking bounces

Parameters

x	The value to interpolate in range [0 .. 1].

Returns: The result for f(x).

Referenced by Murl::Math::Easing< DataType >::EaseBounceIn(), Murl::Math::Easing< DataType >::EaseBounceInOut(), and Murl::Math::Easing< DataType >::EaseBounceOutIn().

◆ EaseBounceIn()

template<class DataType >

static DataType Murl::Math::Easing< DataType >::EaseBounceIn ( DataType x )

inlinestatic

Ease Bounce "in" interpolation.

Function: f(x)=1-EaseBounceOut(1-x) = three and a halve growing bounces

Parameters

x	The value to interpolate in range [0 .. 1].

Returns: The result for f(x).

References Murl::Math::Easing< DataType >::EaseBounceOut().

Referenced by Murl::Math::Easing< DataType >::EaseBounceInOut(), and Murl::Math::Easing< DataType >::EaseBounceOutIn().

◆ EaseBounceInOut()

template<class DataType >

static DataType Murl::Math::Easing< DataType >::EaseBounceInOut ( DataType x )

inlinestatic

Ease Bounce "in-out" interpolation.

Function: f(x)=(x < 0.5) ? EaseBounceIn(2*x)/2 : 0.5+EaseBounceOut(2*x-1)/2

Parameters

x	The value to interpolate in range [0 .. 1].

Returns: The result for f(x).

References Murl::Math::Easing< DataType >::EaseBounceIn(), and Murl::Math::Easing< DataType >::EaseBounceOut().

◆ EaseBounceOutIn()

template<class DataType >

static DataType Murl::Math::Easing< DataType >::EaseBounceOutIn ( DataType x )

inlinestatic

Ease Bounce "in-out" interpolation.

Function: f(x)=(x < 0.5) ? EaseBounceOut(2*x)/2 : 0.5+EaseBounceIn(2*x-1)/2

Parameters

x	The value to interpolate in range [0 .. 1].

Returns: The result for f(x).

References Murl::Math::Easing< DataType >::EaseBounceIn(), and Murl::Math::Easing< DataType >::EaseBounceOut().

The documentation for this class was generated from the following file:

murl_math_easing.h

Public Types

Static Public Member Functions

Detailed Description

template<class DataType> class Murl::Math::Easing< DataType >

Member Function Documentation

◆ Constant()

◆ Linear()

◆ SmoothstepInOut()

◆ SmoothstepIn()

◆ SmoothstepOut()

◆ SmoothstepOutIn()

◆ SmootherstepInOut()

◆ SmootherstepIn()

◆ SmootherstepOut()

◆ SmootherstepOutIn()

◆ EaseIn()

◆ EaseOut()

◆ EaseInOut()

◆ EaseOutIn()

◆ EaseQuartIn()

◆ EaseQuartOut()

◆ EaseQuartInOut()

◆ EaseQuartOutIn()

◆ EaseExponentialIn()

◆ EaseExponentialOut()

◆ EaseExponentialInOut()

◆ EaseExponentialOutIn()

◆ EaseCircularIn()

◆ EaseCircularOut()

◆ EaseCircularHelper()

◆ EaseCircularInOut()

◆ EaseCircularOutIn()

◆ EaseBackIn()

◆ EaseBackOut()

◆ EaseBackInOut()

◆ EaseBackOutIn()

◆ EaseElasticIn()

◆ EaseElasticOut()

◆ EaseElasticInOut()

◆ EaseElasticOutIn()

◆ EaseBounceOut()

◆ EaseBounceIn()

◆ EaseBounceInOut()

◆ EaseBounceOutIn()

template<class DataType>
class Murl::Math::Easing< DataType >