Run behaviors on a fixed step with an On fixed update node

Adding up the frame's dt in On update makes anything that counts in
steps depend on the frame rate. A pitch sweep sounds a little
different on every run. On fixed update runs 60 times per second of
game time with dt exactly 1/60, so the same graph gives the same
result every time.

- fixedSteps in src/core/time.ts is the one rule for the fixed step:
  spend the frame in steps of 1/60, keep the rest, catch up 8 steps
  at most after a hitch.
- The physics now counts its steps with fixedSteps too. It behaves
  as before, and On fixed update runs exactly as often as the engine
  steps.
- The steps run after On mouse wheel and before On update, each as a
  kind of its own with the usual Order setting.
- Each step gets its own context, so a node inside that reads dt
  (Time, Move, Apply force) gets 1/60 rather than the frame.
- A paused game has no steps, also for a behavior that runs while
  paused.
- The engine still takes all of a frame's steps before the behaviors
  run. A force set in On fixed update acts from the next frame on.

Tests:
- fixed-update.test.ts (new): 5 tests. Step counting, uneven frames
  adding up to 60 steps a second, the hitch cap, two steps at 30 Hz
  before On update with dt 1/60 for the event and for Time, one step
  every other frame at 120 Hz, none while paused.
- event-order, node-catalog, physics-system, game-pause: 430 tests
  together with the new file, all green.
- Counter-check: with the frame's dt inside a step and without the
  pause guard both world tests fail.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>

src/runtime/physics/PhysicsSystem.ts

@@ -22,6 +22,7 @@ import {
   shapesOverlap,
 } from '../../core/properties/collider';
 import { hasTransformProps } from '../../core/properties/PropertySchema';
+import { FIXED_STEP, fixedSteps } from '../../core/time';
 import {
   type BodyType,
   colliderMaterial,
@@ -66,10 +67,8 @@ import { type Rapier, toMetres, toPixels } from './engine';
 import { type JointHost, JointSet, type JointState, type RigidOwner } from './joints';
 import { passesOneWay, reachOf } from './oneWay';
 
-/** The engine always steps this long, whatever the frame took. */
-export const PHYSICS_STEP = 1 / 60;
-/** After a hitch the world catches up this many steps at most, and forgets the rest. */
-const MAX_STEPS_PER_TICK = 8;
+/** The engine always steps this long, whatever the frame took – as often as `On fixed update` runs. */
+export const PHYSICS_STEP = FIXED_STEP;
 
 /**
  * One body in the engine. `rigid` is an object with a rigidbody child, carrying every collider below
@@ -217,19 +216,16 @@ export class PhysicsSystem implements System, CollisionSource {
     this.exits = [];
     this.sync(world);
     engine.gravity = this.gravity(world);
-    this.backlog += dt;
-    let steps = 0;
+    const { steps, backlog } = fixedSteps(this.backlog, dt);
+    this.backlog = backlog;
     const entered = new Set<string>();
-    while (this.backlog >= PHYSICS_STEP - 1e-9 && steps < MAX_STEPS_PER_TICK) {
+    for (let step = 0; step < steps; step++) {
       for (const body of this.bodies.values()) if (body.body.isDynamic()) body.previous = body.current;
       this.decideOneWay(world);
       engine.step(this.queue!, this.hooks ?? undefined);
       for (const body of this.bodies.values()) if (body.body.isDynamic()) body.current = poseOf(body.body);
       this.collect(world, entered);
-      this.backlog -= PHYSICS_STEP;
-      steps++;
     }
-    this.backlog = steps === MAX_STEPS_PER_TICK ? 0 : Math.max(0, this.backlog);
     this.writeBack(this.backlog / PHYSICS_STEP);
     this.stays = [...this.current].filter(([key]) => !entered.has(key)).map(([, pair]) => pair);
     this.triggers.update(world);

src/runtime/systems/BehaviorSystem.ts

@@ -31,6 +31,7 @@ import { type PropertyBag, textOf } from '../../core/model/Properties';
 import { treeOrder } from '../../core/model/hierarchy';
 import { resolveObjects } from '../../core/model/instance';
 import { findAssetOf, findScene, type Project } from '../../core/model/Project';
+import { FIXED_STEP, fixedSteps } from '../../core/time';
 import { type AudioSink, SILENT_AUDIO } from './Audio';
 import type { Entity } from '../Entity';
 import type { World } from '../World';
@@ -182,6 +183,8 @@ export class BehaviorSystem implements System {
   private restarted: ReadonlySet<string> = new Set();
   /** Moves whose events are still owed; drained by `flushStateChanges` between exec flows. */
   private pending: StateChange[] = [];
+  /** Game time not yet spent on a fixed step (see `fixedSteps`); counted like the physics' own. */
+  private fixedBacklog = 0;
   /** Set when the scene may have been edited, so the next sync puts the instances in order again. */
   private unranked = true;
   /** The declarations as last read; an edit is what differs from these (see `syncDeclarations`). */
@@ -630,14 +633,22 @@ export class BehaviorSystem implements System {
               y: pointer.y,
             })
           : [],
-      () => pulsesOf(ticking, 'OnUpdate', { dt }),
     ];
-    for (const kind of kinds) {
-      this.runPulses(kind(), contextOf, true);
+    const run = (pulses: Pulse[], context = contextOf) => {
+      this.runPulses(pulses, context, true);
       // After the kind, not inside it: a state entered halfway through `On update` must not push
       // its events between the nodes that are still to run.
       this.flushStateChanges();
+    };
+    for (const kind of kinds) run(kind());
+    if (!frozen) {
+      const fixed = fixedSteps(this.fixedBacklog, dt);
+      this.fixedBacklog = fixed.backlog;
+      // A context of its own per step: what a node reads as `dt` inside is the step, not the frame.
+      for (let step = 0; step < fixed.steps; step++)
+        run(pulsesOf(ticking, 'OnFixedUpdate', { dt: FIXED_STEP }), this.contexts(world, FIXED_STEP));
     }
+    run(pulsesOf(ticking, 'OnUpdate', { dt }));
     this.reap(world);
     this.flushStateChanges();
     this.persist();