Convert global coordinates to local - matrix

Question

A particle system based on three.js' Points.
Internally I am treating the particles as global (with position and velocity vectors) and update the Points geometry accordingly.
It works nicely if the Points object is global (and static).
I need to change this so the Points object moves through the Scene (as child of the "particle emitter"). That requires converting global coordinates for each particle to local coordinates for the Points object geometry.
I have attempted the following:
local = globalParticle.position.clone().applyMatrix4( movingPointsObject.matrixWorld.invert() );
and
local = movingPointsObject.worldToLocal( globalParticle.position );
with different results.
The former seems to work in principle, but the particles appear to have duplicates depending on the Z-rotation of the Points object (they align when rotation is PI).
The latter causes the particles to rotate quickly, giving the appearance of a ring.
What's going on?
https://jsfiddle.net/b7nLorvf/
or
const renderer = new THREE.WebGLRenderer();
renderer.setPixelRatio(window.devicePixelRatio);
renderer.setSize(480, 480);
document.body.appendChild(renderer.domElement);
const scene = new THREE.Scene();
scene.background = new THREE.Color("gray");
const camera = new THREE.OrthographicCamera(-2, 2, 2, -2, 1, 2);
camera.position.set(0, 0, 2);
scene.add(camera);
const light = new THREE.AmbientLight(0xffffff, 0.75); // soft white light
scene.add(light);
const bgeometry = new THREE.BoxGeometry(0.1, 0.1, 0.1);
const bmaterial = new THREE.MeshBasicMaterial({
color: 0xff00ff
});
const cube = new THREE.Mesh(bgeometry, bmaterial);
scene.add(cube);
let pgeometry = new THREE.BufferGeometry();
//pgeometry.setAttribute("position", new THREE.Float32BufferAttribute([], 3));
const pmaterial = new THREE.PointsMaterial({
color: 0xff0000,
size: 2
}); //, depthTest:true } );
let points = new THREE.Points(pgeometry, pmaterial);
const axesHelper = new THREE.AxesHelper(1);
points.add(axesHelper);
//const global = true;
const global = false;
if (global) {
scene.add(points); // global
} else {
cube.add(points); // local
}
let particles = [];
let lt = 0,
dt = 0;
function animate(ms) {
dt = (ms - lt) / 1000;
lt = ms;
// move emitter
const a = ms / 1000;
cube.position.x = Math.cos(a) * 1;
cube.position.y = Math.sin(a) * 1;
cube.rotation.z = a;
// particles
particles.push({
position: cube.position.clone(),
velocity: new THREE.Vector3(2, 0, 0).applyEuler(cube.rotation),
life: 1
});
for (let p of particles) {
p.life -= dt;
}
particles = particles.filter(p => {
return p.life > 0.0;
});
let v = [];
for (let p of particles) {
p.position.add(p.velocity.clone().multiplyScalar(dt));
let vertex;
if (global) {
vertex = p.position;
} else {
//vertex = p.position.clone().applyMatrix4( points.matrixWorld.invert() );
vertex = points.worldToLocal( p.position );
}
v.push(vertex.x, vertex.y, vertex.z);
}
pgeometry.setAttribute("position", new THREE.Float32BufferAttribute(v, 3));
renderer.render(scene, camera);
requestAnimationFrame(animate);
}
requestAnimationFrame(animate);
<script src="https://cdnjs.cloudflare.com/ajax/libs/three.js/0.148.0/three.min.js"></script>

Answer 1

The former works in conjunction with
movingPointsObject.updateWorldMatrix(true, true);
Inspired by worldToLocal, see three.js/Object3D.js#L256.