Matrix4

• compose(position, quaternion, scale) builds T * R * S and decompose() reverses it.
• multiply() applies its argument before the current matrix; premultiply() applies it after.
• set() takes row-major arguments and transposes internally.

const m = new THREE.Matrix4();

const T = new THREE.Matrix4().makeTranslation(10, 0, 5);
const R = new THREE.Matrix4().makeRotationY(Math.PI / 6);
const S = new THREE.Matrix4().makeScale(2, 2, 2);

m.multiplyMatrices(T, R).multiply(S);   // T · R · S
const position = new THREE.Vector3(10, 0, 5);
const quaternion = new THREE.Quaternion().setFromAxisAngle(
  new THREE.Vector3(0, 1, 0), Math.PI / 6
);
m.compose(position, quaternion, new THREE.Vector3(2, 2, 2));

mesh.updateMatrix();
const world = new THREE.Matrix4().multiplyMatrices(
  mesh.parent ? mesh.parent.matrixWorld : new THREE.Matrix4(),
  mesh.matrix
);
const clip = new THREE.Vector4(x, y, z, 1).applyMatrix4(camera.projectionMatrix);
const ndcX = clip.x / clip.w;

• makeTranslation() and makeScale() overwrite the matrix instead of accumulating onto it.
• Large world coordinates lose float precision; shift the scene toward the origin instead.