EasingEquations

touchgfx/EasingEquations.hpp

Defines the "Penner easing functions", which are a de facto standard for computing aesthetically pleasing motion animations. See http://easings.net/ for visual illustrations of the easing equations.

Public Functions

int16_t	backEaseIn(uint16_t t, int16_t b, int16_t c, uint16_t d)
	Back easing in: Overshooting cubic easing: (s+1)t^3 - st^2.
int16_t	backEaseInOut(uint16_t t, int16_t b, int16_t c, uint16_t d)
	Back easing in/out: Overshooting cubic easing: (s+1)t^3 - st^2.
int16_t	backEaseOut(uint16_t t, int16_t b, int16_t c, uint16_t d)
	Back easing out: Overshooting cubic easing: (s+1)t^3 - st^2.
int16_t	bounceEaseIn(uint16_t t, int16_t b, int16_t c, uint16_t d)
	Bounce easing in - exponentially decaying parabolic bounce.
int16_t	bounceEaseInOut(uint16_t t, int16_t b, int16_t c, uint16_t d)
	Bounce easing in/out - exponentially decaying parabolic bounce.
int16_t	bounceEaseOut(uint16_t t, int16_t b, int16_t c, uint16_t d)
	Bounce easing out - exponentially decaying parabolic bounce.
int16_t	circEaseIn(uint16_t t, int16_t b, int16_t c, uint16_t d)
	Circular easing in: sqrt(1-t^2).
int16_t	circEaseInOut(uint16_t t, int16_t b, int16_t c, uint16_t d)
	Circular easing in/out: sqrt(1-t^2).
int16_t	circEaseOut(uint16_t t, int16_t b, int16_t c, uint16_t d)
	Circular easing out: sqrt(1-t^2).
int16_t	cubicEaseIn(uint16_t t, int16_t b, int16_t c, uint16_t d)
	Cubic easing in: t^3.
int16_t	cubicEaseInOut(uint16_t t, int16_t b, int16_t c, uint16_t d)
	Cubic easing in/out: t^3.
int16_t	cubicEaseOut(uint16_t t, int16_t b, int16_t c, uint16_t d)
	Cubic easing out: t^3.
int16_t	elasticEaseIn(uint16_t t, int16_t b, int16_t c, uint16_t d)
	Elastic easing in - exponentially decaying sine wave.
int16_t	elasticEaseInOut(uint16_t t, int16_t b, int16_t c, uint16_t d)
	Elastic easing in/out - exponentially decaying sine wave.
int16_t	elasticEaseOut(uint16_t t, int16_t b, int16_t c, uint16_t d)
	Elastic easing out - exponentially decaying sine wave.
int16_t	expoEaseIn(uint16_t t, int16_t b, int16_t c, uint16_t d)
	Exponential easing in: 2^t.
int16_t	expoEaseInOut(uint16_t t, int16_t b, int16_t c, uint16_t d)
	Exponential easing in/out: 2^t.
int16_t	expoEaseOut(uint16_t t, int16_t b, int16_t c, uint16_t d)
	Exponential easing out: 2^t.
int16_t	linearEaseIn(uint16_t t, int16_t b, int16_t c, uint16_t d)
	Simple linear tweening - no easing.
int16_t	linearEaseInOut(uint16_t t, int16_t b, int16_t c, uint16_t d)
	Simple linear tweening - no easing.
int16_t	linearEaseNone(uint16_t t, int16_t b, int16_t c, uint16_t d)
	Simple linear tweening - no easing.
int16_t	linearEaseOut(uint16_t t, int16_t b, int16_t c, uint16_t d)
	Simple linear tweening - no easing.
int16_t	quadEaseIn(uint16_t t, int16_t b, int16_t c, uint16_t d)
	Quadratic easing in: t^2.
int16_t	quadEaseInOut(uint16_t t, int16_t b, int16_t c, uint16_t d)
	Quadratic easing in/out: t^2.
int16_t	quadEaseOut(uint16_t t, int16_t b, int16_t c, uint16_t d)
	Quadratic easing out: t^2.
int16_t	quartEaseIn(uint16_t t, int16_t b, int16_t c, uint16_t d)
	Quartic easing in: t^4.
int16_t	quartEaseInOut(uint16_t t, int16_t b, int16_t c, uint16_t d)
	Quartic easing in/out: t^4.
int16_t	quartEaseOut(uint16_t t, int16_t b, int16_t c, uint16_t d)
	Quartic easing out: t^4.
int16_t	quintEaseIn(uint16_t t, int16_t b, int16_t c, uint16_t d)
	Quintic/strong easing in: t^5.
int16_t	quintEaseInOut(uint16_t t, int16_t b, int16_t c, uint16_t d)
	Quintic/strong easing in/out: t^5.
int16_t	quintEaseOut(uint16_t t, int16_t b, int16_t c, uint16_t d)
	Quintic/strong easing out: t^5.
int16_t	sineEaseIn(uint16_t t, int16_t b, int16_t c, uint16_t d)
	Sinusoidal easing in: sin(t).
int16_t	sineEaseInOut(uint16_t t, int16_t b, int16_t c, uint16_t d)
	Sinusoidal easing in/out: sin(t).
int16_t	sineEaseOut(uint16_t t, int16_t b, int16_t c, uint16_t d)
	Sinusoidal easing out: sin(t).

Public Functions Documentation

backEaseIn

static int16_t backEaseIn	(	uint16_t	t ,
		int16_t	b ,
		int16_t	c ,
		uint16_t	d
		)

Back easing in: Overshooting cubic easing: (s+1)t^3 - st^2.

Backtracking slightly, then reversing direction and moving to target.

Parameters:

t	Time. The current time or step.
b	Beginning. The beginning value.
c	Change. The change between the beginning value and the destination value.
d	Duration. The total time or total number of steps.

Returns:

The current value as a function of the current time or step.

backEaseInOut

static int16_t backEaseInOut	(	uint16_t	t ,
		int16_t	b ,
		int16_t	c ,
		uint16_t	d
		)

Back easing in/out: Overshooting cubic easing: (s+1)t^3 - st^2.

Backtracking slightly, then reversing direction and moving to target, then overshooting target, reversing, and finally coming back to target.

Parameters:

t	Time. The current time or step.
b	Beginning. The beginning value.
c	Change. The change between the beginning value and the destination value.
d	Duration. The total time or total number of steps.

Returns:

The current value as a function of the current time or step.

backEaseOut

static int16_t backEaseOut	(	uint16_t	t ,
		int16_t	b ,
		int16_t	c ,
		uint16_t	d
		)

Back easing out: Overshooting cubic easing: (s+1)t^3 - st^2.

Moving towards target, overshooting it slightly, then reversing and coming back to target.

Parameters:

t	Time. The current time or step.
b	Beginning. The beginning value.
c	Change. The change between the beginning value and the destination value.
d	Duration. The total time or total number of steps.

Returns:

The current value as a function of the current time or step.

bounceEaseIn

static int16_t bounceEaseIn	(	uint16_t	t ,
		int16_t	b ,
		int16_t	c ,
		uint16_t	d
		)

Bounce easing in - exponentially decaying parabolic bounce.

Parameters:

t	Time. The current time or step.
b	Beginning. The beginning value.
c	Change. The change between the beginning value and the destination value.
d	Duration. The total time or total number of steps.

Returns:

The current value as a function of the current time or step.

bounceEaseInOut

static int16_t bounceEaseInOut	(	uint16_t	t ,
		int16_t	b ,
		int16_t	c ,
		uint16_t	d
		)

Bounce easing in/out - exponentially decaying parabolic bounce.

Parameters:

t	Time. The current time or step.
b	Beginning. The beginning value.
c	Change. The change between the beginning value and the destination value.
d	Duration. The total time or total number of steps.

Returns:

The current value as a function of the current time or step.

bounceEaseOut

static int16_t bounceEaseOut	(	uint16_t	t ,
		int16_t	b ,
		int16_t	c ,
		uint16_t	d
		)

Bounce easing out - exponentially decaying parabolic bounce.

Parameters:

t	Time. The current time or step.
b	Beginning. The beginning value.
c	Change. The change between the beginning value and the destination value.
d	Duration. The total time or total number of steps.

Returns:

The current value as a function of the current time or step.

circEaseIn

static int16_t circEaseIn	(	uint16_t	t ,
		int16_t	b ,
		int16_t	c ,
		uint16_t	d
		)

Circular easing in: sqrt(1-t^2).

Accelerating from zero velocity.

Parameters:

t	Time. The current time or step.
b	Beginning. The beginning value.
c	Change. The change between the beginning value and the destination value.
d	Duration. The total time or total number of steps.

Returns:

The current value as a function of the current time or step.

circEaseInOut

static int16_t circEaseInOut	(	uint16_t	t ,
		int16_t	b ,
		int16_t	c ,
		uint16_t	d
		)

Circular easing in/out: sqrt(1-t^2).

Acceleration until halfway, then deceleration.

Parameters:

t	Time. The current time or step.
b	Beginning. The beginning value.
c	Change. The change between the beginning value and the destination value.
d	Duration. The total time or total number of steps.

Returns:

The current value as a function of the current time or step.

circEaseOut

static int16_t circEaseOut	(	uint16_t	t ,
		int16_t	b ,
		int16_t	c ,
		uint16_t	d
		)

Circular easing out: sqrt(1-t^2).

Decelerating to zero velocity.

Parameters:

t	Time. The current time or step.
b	Beginning. The beginning value.
c	Change. The change between the beginning value and the destination value.
d	Duration. The total time or total number of steps.

Returns:

The current value as a function of the current time or step.

cubicEaseIn

static int16_t cubicEaseIn	(	uint16_t	t ,
		int16_t	b ,
		int16_t	c ,
		uint16_t	d
		)

Cubic easing in: t^3.

Accelerating from zero velocity.

Parameters:

t	Time. The current time or step.
b	Beginning. The beginning value.
c	Change. The change between the beginning value and the destination value.
d	Duration. The total time or total number of steps.

Returns:

The current value as a function of the current time or step.

cubicEaseInOut

static int16_t cubicEaseInOut	(	uint16_t	t ,
		int16_t	b ,
		int16_t	c ,
		uint16_t	d
		)

Cubic easing in/out: t^3.

Acceleration until halfway, then deceleration.

Parameters:

t	Time. The current time or step.
b	Beginning. The beginning value.
c	Change. The change between the beginning value and the destination value.
d	Duration. The total time or total number of steps.

Returns:

The current value as a function of the current time or step.

cubicEaseOut

static int16_t cubicEaseOut	(	uint16_t	t ,
		int16_t	b ,
		int16_t	c ,
		uint16_t	d
		)

Cubic easing out: t^3.

Decelerating to zero velocity.

Parameters:

t	Time. The current time or step.
b	Beginning. The beginning value.
c	Change. The change between the beginning value and the destination value.
d	Duration. The total time or total number of steps.

Returns:

The current value as a function of the current time or step.

elasticEaseIn

static int16_t elasticEaseIn	(	uint16_t	t ,
		int16_t	b ,
		int16_t	c ,
		uint16_t	d
		)

Elastic easing in - exponentially decaying sine wave.

Parameters:

t	Time. The current time or step.
b	Beginning. The beginning value.
c	Change. The change between the beginning value and the destination value.
d	Duration. The total time or total number of steps.

Returns:

The current value as a function of the current time or step.

elasticEaseInOut

static int16_t elasticEaseInOut	(	uint16_t	t ,
		int16_t	b ,
		int16_t	c ,
		uint16_t	d
		)

Elastic easing in/out - exponentially decaying sine wave.

Parameters:

t	Time. The current time or step.
b	Beginning. The beginning value.
c	Change. The change between the beginning value and the destination value.
d	Duration. The total time or total number of steps.

Returns:

The current value as a function of the current time or step.

elasticEaseOut

static int16_t elasticEaseOut	(	uint16_t	t ,
		int16_t	b ,
		int16_t	c ,
		uint16_t	d
		)

Elastic easing out - exponentially decaying sine wave.

Parameters:

t	Time. The current time or step.
b	Beginning. The beginning value.
c	Change. The change between the beginning value and the destination value.
d	Duration. The total time or total number of steps.

Returns:

The current value as a function of the current time or step.

expoEaseIn

static int16_t expoEaseIn	(	uint16_t	t ,
		int16_t	b ,
		int16_t	c ,
		uint16_t	d
		)

Exponential easing in: 2^t.

Accelerating from zero velocity.

Parameters:

t	Time. The current time or step.
b	Beginning. The beginning value.
c	Change. The change between the beginning value and the destination value.
d	Duration. The total time or total number of steps.

Returns:

The current value as a function of the current time or step.

expoEaseInOut

static int16_t expoEaseInOut	(	uint16_t	t ,
		int16_t	b ,
		int16_t	c ,
		uint16_t	d
		)

Exponential easing in/out: 2^t.

Accelerating until halfway, then decelerating.

Parameters:

t	Time. The current time or step.
b	Beginning. The beginning value.
c	Change. The change between the beginning value and the destination value.
d	Duration. The total time or total number of steps.

Returns:

The current value as a function of the current time or step.

expoEaseOut

static int16_t expoEaseOut	(	uint16_t	t ,
		int16_t	b ,
		int16_t	c ,
		uint16_t	d
		)

Exponential easing out: 2^t.

Deceleration to zero velocity.

Parameters:

t	Time. The current time or step.
b	Beginning. The beginning value.
c	Change. The change between the beginning value and the destination value.
d	Duration. The total time or total number of steps.

Returns:

The current value as a function of the current time or step.

linearEaseIn

static int16_t linearEaseIn	(	uint16_t	t ,
		int16_t	b ,
		int16_t	c ,
		uint16_t	d
		)

Simple linear tweening - no easing.

Parameters:

t	Time. The current time or step.
b	Beginning. The beginning value.
c	Change. The change between the beginning value and the destination value.
d	Duration. The total time or total number of steps.

Returns:

The current value as a function of the current time or step.

linearEaseInOut

static int16_t linearEaseInOut	(	uint16_t	t ,
		int16_t	b ,
		int16_t	c ,
		uint16_t	d
		)

Simple linear tweening - no easing.

Parameters:

t	Time. The current time or step.
b	Beginning. The beginning value.
c	Change. The change between the beginning value and the destination value.
d	Duration. The total time or total number of steps.

Returns:

The current value as a function of the current time or step.

linearEaseNone

static int16_t linearEaseNone	(	uint16_t	t ,
		int16_t	b ,
		int16_t	c ,
		uint16_t	d
		)

Simple linear tweening - no easing.

Parameters:

t	Time. The current time or step.
b	Beginning. The beginning value.
c	Change. The change between the beginning value and the destination value.
d	Duration. The total time or total number of steps.

Returns:

The current value as a function of the current time or step.

linearEaseOut

static int16_t linearEaseOut	(	uint16_t	t ,
		int16_t	b ,
		int16_t	c ,
		uint16_t	d
		)

Simple linear tweening - no easing.

Parameters:

t	Time. The current time or step.
b	Beginning. The beginning value.
c	Change. The change between the beginning value and the destination value.
d	Duration. The total time or total number of steps.

Returns:

The current value as a function of the current time or step.

quadEaseIn

static int16_t quadEaseIn	(	uint16_t	t ,
		int16_t	b ,
		int16_t	c ,
		uint16_t	d
		)

Quadratic easing in: t^2.

Accelerating from zero velocity.

Parameters:

t	Time. The current time or step.
b	Beginning. The beginning value.
c	Change. The change between the beginning value and the destination value.
d	Duration. The total time or total number of steps.

Returns:

The current value as a function of the current time or step.

quadEaseInOut

static int16_t quadEaseInOut	(	uint16_t	t ,
		int16_t	b ,
		int16_t	c ,
		uint16_t	d
		)

Quadratic easing in/out: t^2.

Acceleration until halfway, then deceleration.

Parameters:

t	Time. The current time or step.
b	Beginning. The beginning value.
c	Change. The change between the beginning value and the destination value.
d	Duration. The total time or total number of steps.

Returns:

The current value as a function of the current time or step.

quadEaseOut

static int16_t quadEaseOut	(	uint16_t	t ,
		int16_t	b ,
		int16_t	c ,
		uint16_t	d
		)

Quadratic easing out: t^2.

Decelerating to zero velocity.

Parameters:

t	Time. The current time or step.
b	Beginning. The beginning value.
c	Change. The change between the beginning value and the destination value.
d	Duration. The total time or total number of steps.

Returns:

The current value as a function of the current time or step.

quartEaseIn

static int16_t quartEaseIn	(	uint16_t	t ,
		int16_t	b ,
		int16_t	c ,
		uint16_t	d
		)

Quartic easing in: t^4.

Accelerating from zero velocity.

Parameters:

t	Time. The current time or step.
b	Beginning. The beginning value.
c	Change. The change between the beginning value and the destination value.
d	Duration. The total time or total number of steps.

Returns:

The current value as a function of the current time or step.

quartEaseInOut

static int16_t quartEaseInOut	(	uint16_t	t ,
		int16_t	b ,
		int16_t	c ,
		uint16_t	d
		)

Quartic easing in/out: t^4.

Acceleration until halfway, then deceleration.

Parameters:

t	Time. The current time or step.
b	Beginning. The beginning value.
c	Change. The change between the beginning value and the destination value.
d	Duration. The total time or total number of steps.

Returns:

The current value as a function of the current time or step.

quartEaseOut

static int16_t quartEaseOut	(	uint16_t	t ,
		int16_t	b ,
		int16_t	c ,
		uint16_t	d
		)

Quartic easing out: t^4.

Decelerating to zero velocity.

Parameters:

t	Time. The current time or step.
b	Beginning. The beginning value.
c	Change. The change between the beginning value and the destination value.
d	Duration. The total time or total number of steps.

Returns:

The current value as a function of the current time or step.

quintEaseIn

static int16_t quintEaseIn	(	uint16_t	t ,
		int16_t	b ,
		int16_t	c ,
		uint16_t	d
		)

Quintic/strong easing in: t^5.

Accelerating from zero velocity.

Parameters:

t	Time. The current time or step.
b	Beginning. The beginning value.
c	Change. The change between the beginning value and the destination value.
d	Duration. The total time or total number of steps.

Returns:

The current value as a function of the current time or step.

quintEaseInOut

static int16_t quintEaseInOut	(	uint16_t	t ,
		int16_t	b ,
		int16_t	c ,
		uint16_t	d
		)

Quintic/strong easing in/out: t^5.

Acceleration until halfway, then deceleration.

Parameters:

t	Time. The current time or step.
b	Beginning. The beginning value.
c	Change. The change between the beginning value and the destination value.
d	Duration. The total time or total number of steps.

Returns:

The current value as a function of the current time or step.

quintEaseOut

static int16_t quintEaseOut	(	uint16_t	t ,
		int16_t	b ,
		int16_t	c ,
		uint16_t	d
		)

Quintic/strong easing out: t^5.

Decelerating to zero velocity.

Parameters:

t	Time. The current time or step.
b	Beginning. The beginning value.
c	Change. The change between the beginning value and the destination value.
d	Duration. The total time or total number of steps.

Returns:

The current value as a function of the current time or step.

sineEaseIn

static int16_t sineEaseIn	(	uint16_t	t ,
		int16_t	b ,
		int16_t	c ,
		uint16_t	d
		)

Sinusoidal easing in: sin(t).

Accelerating from zero velocity.

Parameters:

t	Time. The current time or step.
b	Beginning. The beginning value.
c	Change. The change between the beginning value and the destination value.
d	Duration. The total time or total number of steps.

Returns:

The current value as a function of the current time or step.

sineEaseInOut

static int16_t sineEaseInOut	(	uint16_t	t ,
		int16_t	b ,
		int16_t	c ,
		uint16_t	d
		)

Sinusoidal easing in/out: sin(t).

Acceleration until halfway, then deceleration.

Parameters:

t	Time. The current time or step.
b	Beginning. The beginning value.
c	Change. The change between the beginning value and the destination value.
d	Duration. The total time or total number of steps.

Returns:

The current value as a function of the current time or step.

sineEaseOut

static int16_t sineEaseOut	(	uint16_t	t ,
		int16_t	b ,
		int16_t	c ,
		uint16_t	d
		)

Sinusoidal easing out: sin(t).

Decelerating to zero velocity.

Parameters:

t	Time. The current time or step.
b	Beginning. The beginning value.
c	Change. The change between the beginning value and the destination value.
d	Duration. The total time or total number of steps.

Returns:

The current value as a function of the current time or step.