ut tensio, sic vis

A simple, efficient spring animation library for smooth, natural motion.

Hooke is framework-agnostic and works well in 2D and 3D contexts. Simply call Spring.make with your settings to initialize and Spring.update on each frame to animate.

open Hooke

(* A thing we want to animate. *)
let sprite_x = Spring.zero_snapshot in

(* A spring to animate it with *)
let spring = Spring.make ~delta_time:0.016 ~angular_freq:6. ~damping_ratio:0.5 in

(* Where we want to animate it. *)
let target_pos = 50.0 in

(* Animate! *)
while true do
  let new_sprite_x = Spring.update spring sprite_x in
  (* throttle frames *)
  animate ()
done

...

Spring.make takes three values:

• delta_time: the time step to operate on. Game engines typically provide a way to determine the time delta, however if that's not available you can simply set the framerate with 1_000 /. fps. Make sure the framerate you set here matches your actual framerate.
• angular_freq: this translates roughly to the speed. Higher values are faster.
• damping_ratio: the springiness of the animation, generally between 0 and 1, though it can go higher. Lower values are springier. For details, see below.

The damping ratio affects the motion in one of three different ways depending on how it's set.

A spring is under-damped when its damping ratio is less than 1. An under-damped spring reaches equilibrium the fastest, but overshoots and will continue to oscillate as its amplitude decays over time.

A spring is critically-damped the damping ratio is exactly 1. A critically damped spring will reach equilibrium as fast as possible without oscillating.

A spring is over-damped the damping ratio is greater than 1. An over-damped spring will never oscillate, but reaches equilibrium at a slower rate than a critically damped spring.

This library is a fairly straightforward port of Charm's Harmonica, which is a port of Ryan Juckett’s excellent damped simple harmonic oscillator originally written in C++ in 2008 and published in 2012. Ryan’s writeup on the subject is fantastic.