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A pluggable, graphics-agnostic 3D physics simulator in cross-platform Scala (JVM / Scala.js / Scala Native). It starts with gravitational N-body dynamics and a family of interchangeable time integrators, built so the quality of a good (symplectic) integrator is something you can see and measure. Rigid-body dynamics are planned on top of the same machinery.

Integrating x'' = a(x) naively (forward Euler) injects energy every step, so orbits spiral apart. Symplectic integrators preserve the geometric structure of Hamiltonian flow, so energy stays bounded for as long as you run them. Running the figure-eight three-body choreography to t = 60 shows the gap:

integrator |ΔE / E0| character
------------------------------------------------------------------------------
Explicit Euler 2.903e-01 1st order, non-symplectic — energy grows
Symplectic Euler 1.745e-04 1st order, symplectic — bounded but noisy
Velocity Verlet (leapfrog) 1.152e-07 2nd order, symplectic — the workhorse
Runge–Kutta 4 8.028e-12 4th order, non-symplectic — accurate, slow drift
Yoshida 4 (symplectic) 1.406e-12 4th order, symplectic — accurate AND bounded

Note that RK4 is accurate but not symplectic: over very long runs its energy drifts monotonically, while leapfrog and Yoshida only oscillate. Accuracy and conservation are different properties.

The physics and rendering are completely independent of any graphics toolkit. A platform backend implements one tiny interface — Canvas (clear, fill a circle, stroke a line) — and provides an animation loop. Everything else (3D projection, depth sorting, perspective sizing, trails) lives in shared.

shared/ Vec3, State, ForceField/GravityField, Integrator (+ 5 methods),
 Energy, Simulation, Scenarios, Camera/Projector, Trails, Scene, Demo
jvm/ SwingCanvas + interactive Swing window
js/ HtmlCanvas + requestAnimationFrame app (+ index.html)
native/ headless energy demo (GUI via macOS graphics is future work)

All integrators implement Integrator.step(state, dt, field) and are interchangeable at runtime (press 1–5 in the GUI):

• ExplicitEuler — 1st order, non-symplectic (the cautionary baseline)
• SymplecticEuler — 1st order, symplectic
• Leapfrog (velocity Verlet) — 2nd order, symplectic; the workhorse
• Rk4 — classic 4th-order Runge–Kutta, non-symplectic
• Yoshida4 — 4th-order symplectic via the triple-jump composition

• Figure-eight — the Chenciner–Montgomery three-body choreography
• Star + planets — inclined near-circular orbits, genuinely 3D
• Cluster — a self-gravitating, gently spinning cloud of bodies

sbt sim3dJVM/run # interactive 3D window
sbt "sim3dJVM/run --headless" # print the energy-comparison table

Controls: drag to orbit, wheel to zoom, 1–5 switch integrator, n next scenario, t toggle trails, space pause, r reset.

sbt sim3dJS/fastLinkJS
cd js && python3 -m http.server 8080 # ES modules need http://, not file://
# open http://localhost:8080/

sbt sim3dNative/run

The test suite runs on all three platforms — it covers vector math, gravity symmetry, momentum conservation, the energy-error ordering of the integrators, and camera projection.

sbt sim3dJVM/test
sbt sim3dJS/test
sbt sim3dNative/test