diff --git a/VR/client/math/matrix3.js b/VR/client/math/matrix3.js
new file mode 100644
index 0000000..e40c9c1
--- /dev/null
+++ b/VR/client/math/matrix3.js
@@ -0,0 +1,29 @@
+export function identity3x3() {
+  return [
+    [1.0, 0.0, 0.0],
+    [0.0, 1.0, 0.0],
+    [0.0, 0.0, 1.0],
+  ];
+}
+
+export function transpose3x3(rows) {
+  return [
+    [rows[0][0], rows[1][0], rows[2][0]],
+    [rows[0][1], rows[1][1], rows[2][1]],
+    [rows[0][2], rows[1][2], rows[2][2]],
+  ];
+}
+
+export function multiply3x3(a, b) {
+  const out = [
+    [0.0, 0.0, 0.0],
+    [0.0, 0.0, 0.0],
+    [0.0, 0.0, 0.0],
+  ];
+  for (let i = 0; i < 3; i += 1) {
+    for (let j = 0; j < 3; j += 1) {
+      out[i][j] = a[i][0] * b[0][j] + a[i][1] * b[1][j] + a[i][2] * b[2][j];
+    }
+  }
+  return out;
+}
diff --git a/VR/client/math/quaternions.js b/VR/client/math/quaternions.js
new file mode 100644
index 0000000..24af53b
--- /dev/null
+++ b/VR/client/math/quaternions.js
@@ -0,0 +1,43 @@
+import * as THREE from "three";
+
+import { transpose3x3 } from "./matrix3.js";
+
+export function quaternionFromRowwiseDirector(matrixRows) {
+  const m = new THREE.Matrix4();
+  m.set(
+    matrixRows[0][0], matrixRows[1][0], matrixRows[2][0], 0.0,
+    matrixRows[0][1], matrixRows[1][1], matrixRows[2][1], 0.0,
+    matrixRows[0][2], matrixRows[1][2], matrixRows[2][2], 0.0,
+    0.0, 0.0, 0.0, 1.0
+  );
+  return new THREE.Quaternion().setFromRotationMatrix(m);
+}
+
+export function columnwiseDirectorFromQuaternion(quaternion) {
+  // Convert quaternion to column-wise director for elastica representation.
+  // Maybe consider using three.js's conversion, but we just want 3x3 orientation.
+  const x = quaternion.x;
+  const y = quaternion.y;
+  const z = quaternion.z;
+  const w = quaternion.w;
+  const xx = x * x;
+  const yy = y * y;
+  const zz = z * z;
+  const xy = x * y;
+  const xz = x * z;
+  const yz = y * z;
+  const wx = w * x;
+  const wy = w * y;
+  const wz = w * z;
+  return [
+    [1.0 - 2.0 * (yy + zz), 2.0 * (xy - wz), 2.0 * (xz + wy)],
+    [2.0 * (xy + wz), 1.0 - 2.0 * (xx + zz), 2.0 * (yz - wx)],
+    [2.0 * (xz - wy), 2.0 * (yz + wx), 1.0 - 2.0 * (xx + yy)],
+  ];
+}
+
+export function rowwiseDirectorFromQuaternion(quaternion) {
+  // Typically quaternion from controller is in world space,
+  // We need to convert to row-wise director for elastica representation.
+  return transpose3x3(columnwiseDirectorFromQuaternion(quaternion));
+}