3D Physics Engine

type Id = Ball | Floor


bodies : List ( Id, Body )
bodies =
    [ ( Ball
      , Physics.sphere
            (Sphere3d.atOrigin (Length.meters 0.5))
            Material.rubber
            |> Physics.moveTo (Point3d.meters 0 0 5)
      )
    , ( Floor, Physics.plane Plane3d.xy Material.wood )
    ]


step model =
    let
        ( newBodies, newContacts ) =
            Physics.simulate
                { onEarth | contacts = model.contacts }
                model.bodies
    in
    { model | bodies = newBodies, contacts = newContacts }

Features

• Pure — simulate is a function, not a stateful world; deterministic, replayable, time-travel friendly.
• Your list is the world — bodies live in List ( id, Body ); add with (::), remove with List.filter.
• Type-safe coordinates and units — built on elm-geometry and elm-units; phantom types keep WorldCoordinates and BodyCoordinates apart, and forces, masses, velocities, and durations all carry units.
• Shapes — block, sphere, cylinder, cone, capsule, and arbitrary convex polyhedra.
• Compound bodies — combine shapes with Shape.plus / minus / sum and per-shape materials; mass, center of mass, and the full inertia tensor are derived for you.
• Declarative constraints and collisions — pass constrain and collide as functions to simulate; the engine asks per body-pair what applies, so there's no constraint registry and no filter-group API.
• Sequential-impulse solver — a Projected Gauss-Seidel velocity solver with Spook soft-constraint stabilization for resting contacts; warm-start it by feeding last frame’s contacts back into simulate.
• Simulation islands — bodies connected by contacts and constraints are grouped into islands and solved independently, so unrelated parts of a large scene don’t slow each other down.

Examples

• Lack (source, demo)
• Duckling (source, demo)
• Raycast (source, demo)
• RaycastCar (source, demo)

Prior Work

Inspired by Cannon.js and Bullet — this project is an experiment in what a purely functional 3D physics engine can look like.