begin live server support

src/scene/coordinates.ts

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+import { Matrix4, Quaternion } from "three";
+import type { MatrixF, Vec3 } from "./types";
+
+/**
+ * Convert a Torque Vec3 (X-right, Y-forward, Z-up) to Three.js (X-right, Y-up, Z-backward).
+ * Swizzle: three.x = torque.y, three.y = torque.z, three.z = torque.x
+ *
+ * Note: this is the same swizzle used by getPosition() in mission.ts.
+ */
+export function torqueToThree(v: Vec3): [number, number, number] {
+  return [v.y, v.z, v.x];
+}
+
+/** Convert a Torque scale Vec3 to Three.js axis order. */
+export function torqueScaleToThree(v: Vec3): [number, number, number] {
+  return [v.y, v.z, v.x];
+}
+
+/**
+ * Convert a Torque MatrixF to a Three.js Quaternion.
+ *
+ * Torque MatrixF layout (row-major, idx = row*4 + col):
+ *   [0]  [1]  [2]  [3]      m00 m01 m02 tx
+ *   [4]  [5]  [6]  [7]   =  m10 m11 m12 ty
+ *   [8]  [9]  [10] [11]     m20 m21 m22 tz
+ *   [12] [13] [14] [15]     0   0   0   1
+ *
+ * Three.js Matrix4 is column-major, with elements in the same index layout
+ * but interpreted differently. We extract the 3×3 rotation, apply the
+ * Torque→Three.js coordinate transform, then decompose to quaternion.
+ */
+export function matrixFToQuaternion(m: MatrixF): Quaternion {
+  const e = m.elements;
+
+  // Extract the Torque 3×3 rotation columns (row-major storage)
+  // Column 0: e[0], e[1], e[2]
+  // Column 1: e[4], e[5], e[6]
+  // Column 2: e[8], e[9], e[10]
+
+  // Apply Torque→Three.js coordinate transform to the rotation matrix.
+  // Torque (X,Y,Z) → Three.js (Y,Z,X) means:
+  //   Three.js row i, col j = Torque row swizzle[i], col swizzle[j]
+  // where swizzle maps Three axis → Torque axis: X→Y(1), Y→Z(2), Z→X(0)
+  //
+  // Build a Three.js column-major Matrix4 from the transformed rotation.
+  const mat4 = new Matrix4();
+  // Three.js Matrix4.elements is column-major:
+  // [m11, m21, m31, m41, m12, m22, m32, m42, m13, m23, m33, m43, m14, m24, m34, m44]
+  const t = mat4.elements;
+
+  // Torque col 0 (X-axis) maps to Three.js col 2 (Z-axis after swizzle)
+  // Torque col 1 (Y-axis) maps to Three.js col 0 (X-axis after swizzle)
+  // Torque col 2 (Z-axis) maps to Three.js col 1 (Y-axis after swizzle)
+  //
+  // Within each column, rows are also swizzled:
+  // Torque row 0 (X) → Three.js row 2 (Z)
+  // Torque row 1 (Y) → Three.js row 0 (X)
+  // Torque row 2 (Z) → Three.js row 1 (Y)
+
+  // Three.js column 0 ← Torque column 1 (Y→X), rows swizzled
+  t[0] = e[5]; // T_Y_Y → Three X_X
+  t[1] = e[6]; // T_Z_Y → Three Y_X
+  t[2] = e[4]; // T_X_Y → Three Z_X
+  t[3] = 0;
+
+  // Three.js column 1 ← Torque column 2 (Z→Y), rows swizzled
+  t[4] = e[9]; // T_Y_Z → Three X_Y
+  t[5] = e[10]; // T_Z_Z → Three Y_Y
+  t[6] = e[8]; // T_X_Z → Three Z_Y
+  t[7] = 0;
+
+  // Three.js column 2 ← Torque column 0 (X→Z), rows swizzled
+  t[8] = e[1]; // T_Y_X → Three X_Z
+  t[9] = e[2]; // T_Z_X → Three Y_Z
+  t[10] = e[0]; // T_X_X → Three Z_Z
+  t[11] = 0;
+
+  // Translation column (not used for quaternion, but set for completeness)
+  t[12] = 0;
+  t[13] = 0;
+  t[14] = 0;
+  t[15] = 1;
+
+  const q = new Quaternion();
+  q.setFromRotationMatrix(mat4);
+  // Torque uses row-vector convention (v * M), Three.js uses column-vector (M * v).
+  // The extracted rotation is the transpose, so conjugate to invert.
+  q.conjugate();
+  return q;
+}
+
+/**
+ * Convert a Torque axis-angle rotation string ("ax ay az angleDeg") to a Quaternion.
+ * This is the format used in .mis files. The axis is in Torque coordinates.
+ */
+export function torqueAxisAngleToQuaternion(
+  ax: number,
+  ay: number,
+  az: number,
+  angleDeg: number,
+): Quaternion {
+  // Swizzle axis: Torque (X,Y,Z) → Three.js (Y,Z,X)
+  const threeAx = ay;
+  const threeAy = az;
+  const threeAz = ax;
+  const len = Math.sqrt(threeAx * threeAx + threeAy * threeAy + threeAz * threeAz);
+  if (len < 1e-8) return new Quaternion();
+  const angleRad = -angleDeg * (Math.PI / 180);
+  return new Quaternion().setFromAxisAngle(
+    { x: threeAx / len, y: threeAy / len, z: threeAz / len } as any,
+    angleRad,
+  );
+}