PageScene: extract cameraMath + browserChecks modules

Pure-function helpers carved out of FreeCam in preparation for the
hook rewrite:

- engine/cameraMath.ts: HeldMoveKeys / HeldRotateKeys types,
  moveVectorFromKeys, rotationVectorFromKeys, panFromDrag,
  zoomFromWheel, lookAtFromCamera, lerpVelocity. No DOM access, no
  signals.
- engine/browserChecks.ts: isSafariOrWebKit, hasApplePay, isSafari,
  isPointerLockSupported. Unrelated to camera math; were just
  hitchhiking in free_cam.ts.

free_cam.ts re-exports the browser checks for back-compat with
keybinds_controls.ts; both consumers will switch to the direct
imports when free_cam.ts is deleted in the next commit.

frontend/apps/artcraft/app/src/pages/PageScene/engine/browserChecks.ts

@@ -0,0 +1,20 @@
+// Browser feature detection helpers used by the input subsystem.
+// Pointer Lock behaves differently on Safari/WebKit, so the input
+// hooks fall back to drag-based control there.
+
+export const isSafariOrWebKit = (): boolean => {
+  const ua = navigator.userAgent;
+  const isWebKit =
+    /AppleWebKit/i.test(ua) && !/Chrome|Chromium|Edg|OPR|CriOS|FxiOS/i.test(ua);
+  const isSafari = /^((?!chrome|android|crios|fxios).)*safari/i.test(ua);
+  return isSafari || isWebKit;
+};
+
+export const hasApplePay = (): boolean => {
+  // @ts-expect-error Apple Pay is not defined in TypeScript
+  return !!window.ApplePaySession;
+};
+
+export const isSafari = (): boolean => isSafariOrWebKit() || hasApplePay();
+
+export const isPointerLockSupported = (): boolean => !isSafari();

frontend/apps/artcraft/app/src/pages/PageScene/engine/cameraMath.ts

@@ -0,0 +1,109 @@
+import { MathUtils, Vector3 } from "three";
+import type { PerspectiveCamera } from "three";
+
+// Pure math used by the free-cam viewport controls.
+// No DOM access, no event listeners, no signals — every function
+// takes inputs and returns values. The input hooks own the listener
+// lifecycle and the per-frame loop; this module owns the formulas.
+
+// Held movement keys (WASD + QE). Stored as 0/1 so update steps can
+// just sum them in opposite directions.
+export interface HeldMoveKeys {
+  forward: 0 | 1;
+  back: 0 | 1;
+  left: 0 | 1;
+  right: 0 | 1;
+  up: 0 | 1;
+  down: 0 | 1;
+}
+
+// Held rotation keys (arrow keys + roll). Same encoding.
+export interface HeldRotateKeys {
+  pitchUp: 0 | 1;
+  pitchDown: 0 | 1;
+  yawLeft: 0 | 1;
+  yawRight: 0 | 1;
+  rollLeft: 0 | 1;
+  rollRight: 0 | 1;
+}
+
+export const emptyMoveKeys = (): HeldMoveKeys => ({
+  forward: 0,
+  back: 0,
+  left: 0,
+  right: 0,
+  up: 0,
+  down: 0,
+});
+
+export const emptyRotateKeys = (): HeldRotateKeys => ({
+  pitchUp: 0,
+  pitchDown: 0,
+  yawLeft: 0,
+  yawRight: 0,
+  rollLeft: 0,
+  rollRight: 0,
+});
+
+// Per-frame movement direction (in camera-local space). Multiply by
+// (delta * movementSpeed) before applying.
+export const moveVectorFromKeys = (
+  keys: HeldMoveKeys,
+  autoForward = false,
+): Vector3 => {
+  const forward = keys.forward || (autoForward && !keys.back) ? 1 : 0;
+  return new Vector3(
+    -keys.left + keys.right,
+    -keys.down + keys.up,
+    -forward + keys.back,
+  );
+};
+
+// Per-frame rotation deltas. Already pre-scaled by rollSpeed.
+export const rotationVectorFromKeys = (
+  keys: HeldRotateKeys,
+  rollSpeed: number,
+): Vector3 =>
+  new Vector3(
+    -keys.pitchDown + keys.pitchUp,
+    -keys.yawRight + keys.yawLeft,
+    -keys.rollRight + keys.rollLeft,
+  ).multiplyScalar(rollSpeed);
+
+// Mouse-drag pan amounts (in camera-local x/y, before applying).
+// dx/dy are pointer deltas in pixels; speed scales them.
+export const panFromDrag = (
+  dx: number,
+  dy: number,
+  speed: number,
+): { x: number; y: number } => ({
+  x: -dx * (speed * 0.01),
+  y: dy * (speed * 0.01),
+});
+
+// Wheel-event zoom amount along camera-local z.
+export const zoomFromWheel = (deltaY: number): number => deltaY / 120;
+
+// World-space lookAt point one unit ahead of the camera along its
+// current orientation. Used to update camera entries in the store
+// after a free-cam move so the camera entry's "lookAt" stays in
+// sync with the rendered orientation.
+export const lookAtFromCamera = (camera: PerspectiveCamera): Vector3 => {
+  const lookAt = new Vector3(0, 0, -1);
+  lookAt.applyQuaternion(camera.quaternion);
+  lookAt.add(camera.position);
+  return lookAt;
+};
+
+// Smooth a velocity vector toward a target with a per-component lerp.
+// Returns the same `velocity` instance for chaining.
+export const lerpVelocity = (
+  velocity: Vector3,
+  target: Vector3,
+  smoothing: number,
+): Vector3 => {
+  velocity.x = MathUtils.lerp(velocity.x, target.x, smoothing);
+  velocity.y = MathUtils.lerp(velocity.y, target.y, smoothing);
+  velocity.z = MathUtils.lerp(velocity.z, target.z, smoothing);
+  return velocity;
+};

frontend/apps/artcraft/app/src/pages/PageScene/engine/free_cam.ts

@@ -9,28 +9,15 @@ import * as THREE from "three";
 import { cameras, selectedCameraId } from "~/pages/PageScene/signals/camera";
 import { isPromptBoxFocused } from "~/pages/PageScene/signals/promptBox";
 
-
-export const isSafariOrWebKit = () => {
-  const ua = navigator.userAgent;
-
-  const isWebKit = /AppleWebKit/i.test(ua) && !/Chrome|Chromium|Edg|OPR|CriOS|FxiOS/i.test(ua);
-  const isSafari = /^((?!chrome|android|crios|fxios).)*safari/i.test(ua);
-
-  return isSafari || isWebKit;
-};
-
-export const hasApplePay = () => {
-  // @ts-expect-error Apple Pay is not defined in TypeScript
-  return !!window.ApplePaySession;
-}
-
-export const isSafari = () => {
-  return isSafariOrWebKit() || hasApplePay();
-}
-
-export const isPointerLockSupported = () => {
-  return !isSafari();
-}
+// Re-exported here for back-compat with keybinds_controls.ts; the
+// definitions live in browserChecks.ts and will be imported directly
+// once Phase 6 deletes this file.
+export {
+  isSafariOrWebKit,
+  hasApplePay,
+  isSafari,
+  isPointerLockSupported,
+} from "./browserChecks";
 
 class FreeCam extends EventDispatcher {
   object: THREE.PerspectiveCamera;