Question

I have created a THREE.Scene, and within the scene there is an THREE.Object3D() that is a new ‘coordinate system’.
Inside this object there is a particle with a certain position.
I understand that getting a this particle’s position from the object’s ‘coordinate System’ into the Scene’s ‘coordinate systems’ requires the following

//Gives particle position in scene coordinates
particle.position.applyMatrix4(Object.matrixWorld) 

What would be the inverse transformation though?

(aka, the particle is in the Scene’s ‘coordinate system’ and I want to find its position in the objects ‘coordinate system’)

Answer 1

The inverse transformation of the transform you referred to can be calculated like so:

var mInverse = new THREE.Matrix4().getInverse( object.matrixWorld );
particle.position.applyMatrix4( mInverse );

three.js r.55