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Easing

Based on game build 714014 | Last updated: 2026-03-10

Overview​

easing.lua is a utility module that exports a set of classic easing functions derived from Robert Penner's Easing Equations. These functions accept elapsed time (t), start value (b), change in value (c), and duration (d) as inputs and return interpolated intermediate values. The module is used by game systems to create smooth animations for visual effects, camera movements, UI transitions, and entity behaviors — not as a component attached to entities, but as a pure math library returned for direct consumption.

Usage example​

local Easing = require "easing"
local t = 0
local duration = 2
local start_val = 0
local end_val = 100
local change = end_val - start_val

t = t + 0.1
local value = Easing.outQuad(t, start_val, change, duration)

Dependencies & tags​

Components used: None identified
Tags: None identified

Properties​

No public properties.

Main functions​

linear(t, b, c, d)​

  • Description: Returns a linear interpolation from b to b + c over duration d.
  • Parameters:
    • t (number) – elapsed time (must be 0 <= t <= d).
    • b (number) – starting value.
    • c (number) – total change in value (ending - beginning).
    • d (number) – total duration (time to complete the transition).
  • Returns: (number) interpolated value at time t.

inQuad(t, b, c, d)​

  • Description: Quadratic easing-in: starts slowly and accelerates.
  • Parameters: Same as linear.
  • Returns: (number) interpolated value.

outQuad(t, b, c, d)​

  • Description: Quadratic easing-out: starts quickly and decelerates.
  • Parameters: Same as linear.
  • Returns: (number) interpolated value.

inOutQuad(t, b, c, d)​

  • Description: Quadratic easing-in-out: starts slowly, accelerates, then decelerates smoothly.
  • Parameters: Same as linear.
  • Returns: (number) interpolated value.

outInQuad(t, b, c, d)​

  • Description: Quadratic easing-out-in: starts by decelerating, then accelerates.
  • Parameters: Same as linear.
  • Returns: (number) interpolated value.

inCubic(t, b, c, d)​

  • Description: Cubic easing-in: starts very slowly, accelerates rapidly.
  • Parameters: Same as linear.
  • Returns: (number) interpolated value.

outCubic(t, b, c, d)​

  • Description: Cubic easing-out: starts quickly, slows down.
  • Parameters: Same as linear.
  • Returns: (number) interpolated value.

inOutCubic(t, b, c, d)​

  • Description: Cubic easing-in-out.
  • Parameters: Same as linear.
  • Returns: (number) interpolated value.

outInCubic(t, b, c, d)​

  • Description: Cubic easing-out-in.
  • Parameters: Same as linear.
  • Returns: (number) interpolated value.

inQuart(t, b, c, d)​

  • Description: Quartic easing-in.
  • Parameters: Same as linear.
  • Returns: (number) interpolated value.

outQuart(t, b, c, d)​

  • Description: Quartic easing-out.
  • Parameters: Same as linear.
  • Returns: (number) interpolated value.

inOutQuart(t, b, c, d)​

  • Description: Quartic easing-in-out.
  • Parameters: Same as linear.
  • Returns: (number) interpolated value.

outInQuart(t, b, c, d)​

  • Description: Quartic easing-out-in.
  • Parameters: Same as linear.
  • Returns: (number) interpolated value.

inQuint(t, b, c, d)​

  • Description: Quintic easing-in.
  • Parameters: Same as linear.
  • Returns: (number) interpolated value.

outQuint(t, b, c, d)​

  • Description: Quintic easing-out.
  • Parameters: Same as linear.
  • Returns: (number) interpolated value.

inOutQuint(t, b, c, d)​

  • Description: Quintic easing-in-out.
  • Parameters: Same as linear.
  • Returns: (number) interpolated value.

outInQuint(t, b, c, d)​

  • Description: Quintic easing-out-in.
  • Parameters: Same as linear.
  • Returns: (number) interpolated value.

inSine(t, b, c, d)​

  • Description: Sine-based easing-in (quarter-wave).
  • Parameters: Same as linear.
  • Returns: (number) interpolated value.

outSine(t, b, c, d)​

  • Description: Sine-based easing-out.
  • Parameters: Same as linear.
  • Returns: (number) interpolated value.

inOutSine(t, b, c, d)​

  • Description: Sine-based easing-in-out.
  • Parameters: Same as linear.
  • Returns: (number) interpolated value.

outInSine(t, b, c, d)​

  • Description: Sine-based easing-out-in.
  • Parameters: Same as linear.
  • Returns: (number) interpolated value.

inExpo(t, b, c, d)​

  • Description: Exponential easing-in (doubles speed at each step).
  • Parameters: Same as linear.
  • Returns: (number) interpolated value.
  • Error states: Returns b exactly when t == 0.

outExpo(t, b, c, d)​

  • Description: Exponential easing-out.
  • Parameters: Same as linear.
  • Returns: (number) interpolated value.
  • Error states: Returns b + c exactly when t == d.

inOutExpo(t, b, c, d)​

  • Description: Exponential easing-in-out.
  • Parameters: Same as linear.
  • Returns: (number) interpolated value.
  • Error states: Returns b when t == 0, b + c when t == d.

outInExpo(t, b, c, d)​

  • Description: Exponential easing-out-in.
  • Parameters: Same as linear.
  • Returns: (number) interpolated value.

inCirc(t, b, c, d)​

  • Description: Circular easing-in.
  • Parameters: Same as linear.
  • Returns: (number) interpolated value.

outCirc(t, b, c, d)​

  • Description: Circular easing-out.
  • Parameters: Same as linear.
  • Returns: (number) interpolated value.

inOutCirc(t, b, c, d)​

  • Description: Circular easing-in-out.
  • Parameters: Same as linear.
  • Returns: (number) interpolated value.

outInCirc(t, b, c, d)​

  • Description: Circular easing-out-in.
  • Parameters: Same as linear.
  • Returns: (number) interpolated value.

inElastic(t, b, c, d, a, p)​

  • Description: Elastic easing-in (overshoots and oscillates before settling).
  • Parameters:
    • a (number, optional) – amplitude of the elastic oscillation. Defaults to abs(c) if not set or too small.
    • p (number, optional) – period of oscillation. Defaults to d * 0.3.
  • Parameters: Same as linear + a, p.
  • Returns: (number) interpolated value.
  • Error states: Returns b when t == 0, b + c when t == d.

outElastic(t, b, c, d, a, p)​

  • Description: Elastic easing-out.
  • Parameters: Same as inElastic.
  • Returns: (number) interpolated value.
  • Error states: Returns b when t == 0, b + c when t == d.

inOutElastic(t, b, c, d, a, p)​

  • Description: Elastic easing-in-out (symmetric oscillation).
  • Parameters: Same as inElastic.
  • Returns: (number) interpolated value.
  • Error states: Returns b when t == 0, b + c when t == d.

outInElastic(t, b, c, d, a, p)​

  • Description: Elastic easing-out-in.
  • Parameters: Same as inElastic.
  • Returns: (number) interpolated value.

inBack(t, b, c, d, s)​

  • Description: Back easing-in (retracts slightly before moving forward).
  • Parameters:
    • s (number, optional) – overshoot strength. Defaults to 1.70158.
  • Parameters: Same as linear + s.
  • Returns: (number) interpolated value.

outBack(t, b, c, d, s)​

  • Description: Back easing-out (overshoots and settles).
  • Parameters: Same as inBack.
  • Returns: (number) interpolated value.

inOutBack(t, b, c, d, s)​

  • Description: Back easing-in-out (symmetric overshoot).
  • Parameters: Same as inBack.
  • Returns: (number) interpolated value.

outInBack(t, b, c, d, s)​

  • Description: Back easing-out-in.
  • Parameters: Same as inBack.
  • Returns: (number) interpolated value.

outBounce(t, b, c, d)​

  • Description: Bounce easing-out (mimics a bouncing ball settling).
  • Parameters: Same as linear.
  • Returns: (number) interpolated value.

inBounce(t, b, c, d)​

  • Description: Bounce easing-in.
  • Parameters: Same as linear.
  • Returns: (number) interpolated value.

inOutBounce(t, b, c, d)​

  • Description: Bounce easing-in-out.
  • Parameters: Same as linear.
  • Returns: (number) interpolated value.

outInBounce(t, b, c, d)​

  • Description: Bounce easing-out-in.
  • Parameters: Same as linear.
  • Returns: (number) interpolated value.

Events & listeners​

None identified.