refactor: extract matrix, moveMapping, easing, cubeProjection utils from SmartCube

src/utils/cubeProjection.js

@@ -0,0 +1,58 @@
+// 3D geometry helpers for cube face/axis operations and screen projection
+
+export const getFaceNormal = (face, FACES) => {
+    const map = {
+        [FACES.FRONT]: { x: 0, y: 0, z: 1 },
+        [FACES.BACK]: { x: 0, y: 0, z: -1 },
+        [FACES.RIGHT]: { x: 1, y: 0, z: 0 },
+        [FACES.LEFT]: { x: -1, y: 0, z: 0 },
+        [FACES.UP]: { x: 0, y: 1, z: 0 },
+        [FACES.DOWN]: { x: 0, y: -1, z: 0 },
+    };
+    return map[face] || { x: 0, y: 0, z: 1 };
+};
+
+// Which axes can this face physically rotate along?
+export const getAllowedAxes = (face, FACES) => {
+    switch (face) {
+        case FACES.FRONT:
+        case FACES.BACK:
+            return ["x", "y"];
+        case FACES.RIGHT:
+        case FACES.LEFT:
+            return ["z", "y"];
+        case FACES.UP:
+        case FACES.DOWN:
+            return ["x", "z"];
+    }
+    return [];
+};
+
+export const getAxisVector = (axis) => {
+    if (axis === "x") return { x: 1, y: 0, z: 0 };
+    if (axis === "y") return { x: 0, y: 1, z: 0 };
+    if (axis === "z") return { x: 0, y: 0, z: 1 };
+    return { x: 0, y: 0, z: 0 };
+};
+
+// Cross product: a × b
+export const cross = (a, b) => ({
+    x: a.y * b.z - a.z * b.y,
+    y: a.z * b.x - a.x * b.z,
+    z: a.x * b.y - a.y * b.x,
+});
+
+// Project 3D vector to 2D screen space using a viewMatrix (column-major 4x4).
+// Input v is in Right-Handed Math Coordinates (Y up).
+// viewMatrix operates in CSS Coordinates (Y down).
+// Applies T⁻¹ * M * T to maintain correct projection chirality.
+export const project = (v, viewMatrix) => {
+    const m = viewMatrix;
+    const cssY = -v.y;
+
+    const x = v.x * m[0] + cssY * m[4] + v.z * m[8];
+    const projY = v.x * m[1] + cssY * m[5] + v.z * m[9];
+    const mathY = -projY;
+
+    return { x, y: mathY };
+};