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Easing

Version History​

Build VersionChange DateChange TypeDescription
6760422025-06-21stableCurrent version

Overview​

The easing module provides a comprehensive collection of mathematical easing functions for creating smooth animations and transitions. These functions are adapted from Robert Penner's Easing Equations and are commonly used in tweening systems to control the rate of change of animated values over time.

Usage Example​

local easing = require("easing")

-- Basic linear interpolation
local result = easing.linear(50, 0, 100, 100) -- Returns 50

-- Smooth ease-in animation
local smoothResult = easing.inQuad(25, 0, 100, 100) -- Returns 6.25

-- Bounce effect at the end
local bounceResult = easing.outBounce(75, 0, 100, 100) -- Returns bounce curve value

Function Parameters​

All easing functions follow the same parameter structure:

Standard Parameters:

  • t (number): Elapsed time (current time in animation)
  • b (number): Beginning value (start value)
  • c (number): Change in value (ending value - beginning value)
  • d (number): Duration (total animation time)

Additional Parameters (for some functions):

  • a (number): Amplitude (for elastic and back functions)
  • p (number): Period (for elastic functions)
  • s (number): Overshoot factor (for back functions)

Linear Functions​

linear(t, b, c, d)​

Status: stable

Description: Provides linear interpolation with constant rate of change.

Parameters:

  • t (number): Elapsed time
  • b (number): Beginning value
  • c (number): Change in value
  • d (number): Duration

Returns:

  • (number): Interpolated value

Example:

-- Linear movement from 0 to 100 over 2 seconds
local value = easing.linear(1, 0, 100, 2) -- Returns 50

Quadratic Functions​

inQuad(t, b, c, d)​

Status: stable

Description: Quadratic ease-in function. Acceleration from zero velocity.

Parameters:

  • t (number): Elapsed time
  • b (number): Beginning value
  • c (number): Change in value
  • d (number): Duration

Returns:

  • (number): Interpolated value with quadratic ease-in curve

Example:

-- Slow start, then accelerating
local value = easing.inQuad(0.5, 0, 100, 1) -- Returns 25

outQuad(t, b, c, d)​

Status: stable

Description: Quadratic ease-out function. Deceleration to zero velocity.

Example:

-- Fast start, then slowing down
local value = easing.outQuad(0.5, 0, 100, 1) -- Returns 75

inOutQuad(t, b, c, d)​

Status: stable

Description: Quadratic ease-in-out function. Acceleration until halfway, then deceleration.

Example:

-- Smooth acceleration and deceleration
local value = easing.inOutQuad(0.5, 0, 100, 1) -- Returns 50

outInQuad(t, b, c, d)​

Status: stable

Description: Quadratic ease-out-in function. Deceleration until halfway, then acceleration.

Cubic Functions​

inCubic(t, b, c, d)​

Status: stable

Description: Cubic ease-in function. Stronger acceleration than quadratic.

outCubic(t, b, c, d)​

Status: stable

Description: Cubic ease-out function. Stronger deceleration than quadratic.

inOutCubic(t, b, c, d)​

Status: stable

Description: Cubic ease-in-out function.

outInCubic(t, b, c, d)​

Status: stable

Description: Cubic ease-out-in function.

Quartic Functions​

inQuart(t, b, c, d)​

Status: stable

Description: Quartic (4th power) ease-in function.

outQuart(t, b, c, d)​

Status: stable

Description: Quartic ease-out function.

inOutQuart(t, b, c, d)​

Status: stable

Description: Quartic ease-in-out function.

outInQuart(t, b, c, d)​

Status: stable

Description: Quartic ease-out-in function.

Quintic Functions​

inQuint(t, b, c, d)​

Status: stable

Description: Quintic (5th power) ease-in function.

outQuint(t, b, c, d)​

Status: stable

Description: Quintic ease-out function.

inOutQuint(t, b, c, d)​

Status: stable

Description: Quintic ease-in-out function.

outInQuint(t, b, c, d)​

Status: stable

Description: Quintic ease-out-in function.

Sinusoidal Functions​

inSine(t, b, c, d)​

Status: stable

Description: Sinusoidal ease-in function. Smooth curved acceleration.

Example:

-- Gentle curved acceleration
local value = easing.inSine(0.5, 0, 100, 1) -- Returns ~29.3

outSine(t, b, c, d)​

Status: stable

Description: Sinusoidal ease-out function. Smooth curved deceleration.

inOutSine(t, b, c, d)​

Status: stable

Description: Sinusoidal ease-in-out function. Very smooth acceleration and deceleration.

outInSine(t, b, c, d)​

Status: stable

Description: Sinusoidal ease-out-in function.

Exponential Functions​

inExpo(t, b, c, d)​

Status: stable

Description: Exponential ease-in function. Very slow start with dramatic acceleration.

Example:

-- Very slow start, then rapid acceleration
local value = easing.inExpo(0, 0, 100, 1) -- Returns 0 (special case)
local value2 = easing.inExpo(0.5, 0, 100, 1) -- Returns ~3.1

outExpo(t, b, c, d)​

Status: stable

Description: Exponential ease-out function. Fast start with dramatic deceleration.

inOutExpo(t, b, c, d)​

Status: stable

Description: Exponential ease-in-out function.

outInExpo(t, b, c, d)​

Status: stable

Description: Exponential ease-out-in function.

Circular Functions​

inCirc(t, b, c, d)​

Status: stable

Description: Circular ease-in function. Based on quarter circle arc.

outCirc(t, b, c, d)​

Status: stable

Description: Circular ease-out function.

inOutCirc(t, b, c, d)​

Status: stable

Description: Circular ease-in-out function.

outInCirc(t, b, c, d)​

Status: stable

Description: Circular ease-out-in function.

Elastic Functions​

inElastic(t, b, c, d, a, p)​

Status: stable

Description: Elastic ease-in function. Creates a spring-like effect with oscillation before reaching the target.

Parameters:

  • t (number): Elapsed time
  • b (number): Beginning value
  • c (number): Change in value
  • d (number): Duration
  • a (number, optional): Amplitude (defaults to change value)
  • p (number, optional): Period (defaults to duration * 0.3)

Example:

-- Spring effect with oscillation at start
local value = easing.inElastic(0.8, 0, 100, 1) -- Creates elastic spring effect

outElastic(t, b, c, d, a, p)​

Status: stable

Description: Elastic ease-out function. Creates oscillation at the end of the animation.

inOutElastic(t, b, c, d, a, p)​

Status: stable

Description: Elastic ease-in-out function.

outInElastic(t, b, c, d, a, p)​

Status: stable

Description: Elastic ease-out-in function.

Back Functions​

inBack(t, b, c, d, s)​

Status: stable

Description: Back ease-in function. Backs up slightly before moving forward.

Parameters:

  • t (number): Elapsed time
  • b (number): Beginning value
  • c (number): Change in value
  • d (number): Duration
  • s (number, optional): Overshoot factor (defaults to 1.70158)

Example:

-- Backs up before moving forward
local value = easing.inBack(0.3, 0, 100, 1) -- Returns negative value (backing up)

outBack(t, b, c, d, s)​

Status: stable

Description: Back ease-out function. Overshoots the target then settles back.

inOutBack(t, b, c, d, s)​

Status: stable

Description: Back ease-in-out function.

outInBack(t, b, c, d, s)​

Status: stable

Description: Back ease-out-in function.

Bounce Functions​

inBounce(t, b, c, d)​

Status: stable

Description: Bounce ease-in function. Creates bouncing effect at the start.

Example:

-- Bouncing effect at start of animation
local value = easing.inBounce(0.2, 0, 100, 1) -- Creates bounce effect

outBounce(t, b, c, d)​

Status: stable

Description: Bounce ease-out function. Creates bouncing effect at the end.

Example:

-- Classic bouncing ball effect
local value = easing.outBounce(0.8, 0, 100, 1) -- Bounces before settling

inOutBounce(t, b, c, d)​

Status: stable

Description: Bounce ease-in-out function.

outInBounce(t, b, c, d)​

Status: stable

Description: Bounce ease-out-in function.

Common Usage Patterns​

UI Animations​

-- Smooth button hover effect
local hoverScale = easing.outQuad(hoverTime, 1.0, 0.1, 0.2)

-- Menu slide-in animation
local menuPos = easing.outBack(animTime, -200, 200, 0.5)

Game Object Movement​

-- Projectile arc with gravity
local height = easing.outQuad(flightTime, startHeight, -startHeight, totalTime)

-- Spring-loaded platform
local platformPos = easing.outElastic(springTime, restPos, displacement, 1.0)

Visual Effects​

-- Pulsing glow effect
local glowIntensity = easing.inOutSine(pulseTime, 0.5, 0.5, 2.0)

-- Screen shake with decay
local shakeAmount = easing.outBounce(shakeTime, maxShake, -maxShake, duration)

Mathematical Foundation​

The easing functions are based on Robert Penner's Easing Equations, which provide smooth interpolation curves using various mathematical functions:

  • Polynomial: Power functions (quad, cubic, quart, quint)
  • Trigonometric: Sine and cosine functions
  • Exponential: Powers of 2
  • Circular: Quarter-circle arcs
  • Physical: Spring (elastic) and bounce simulations

License Information​

This implementation is adapted from Robert Penner's Easing Equations, released under the BSD License. The original equations are widely used in animation and tweening libraries across many programming languages.

  • Scheduler: Often used with easing functions for timed animations
  • EntityScript: Entity animation systems may use easing functions
  • Main Functions: Core game loop where animations are updated