PhysiJS: How to get linear velocity at a given point on a rotating object

How can I query the linear velocity (relative to world space) of a point of an object in PhysiJS, given the object's linear and angular velocity?

I was thinking of creating an invisible vertex on the object for this purpose, but I don't think the API even gives that capability. Do I need to calculate myself it based on translational and rotational velocity of the object? (And if so, does THREE.js or PhysiJS give a straight forward way of doing that?)

From first principles:

Given object.position (1)
Given position of point in world space object.localToWorld(point) (2)
Given object.getLinearVelocity() (3)
Given object.getAngularVelocity() (4)

So I need to:

Subtract (1) from (2) to give point's offset in world space (5)
Use (4) and (5) to get linear velocity of point relative to object (6)
Add (6) and (3) to get total linear velocity of point

For that first and third step I can use Three.js's Vector3's .sub(Vector3) and .add(Vector3) methods, but the middle operation is eluding me, although I'd guess a kind of multiplication. What sort of operation should I use, given that (4) can be a Euler angle or a Quaternion?

My knowledge of matrices is very limited (and rusty!) and of quaternions non-existent.

Three.js's API documentation is here

Thanks

Solution

Finally! Solved. Below is the more generic version which avoids PhysiJS. Just subsitute three's vectors with those of PhysiJS's.

scene.add(point2);
scene.add(pointAxis);
pointAxis.add(point);

angularVelocity = new THREE.Vector3( 0, 0, 0.01);

function animate(){

    // rotate point around pointAxis
    pointAxis.rotation = pointAxis.rotation.add(angularVelocity);

    // calculate position of point in world space
    var pointPosWorld = pointAxis.localToWorld(point.position.clone());

    // calculate position of point in world with respect to fulcrum
    var pointOffsetPos = new THREE.Vector3();
    pointOffsetPos = pointPosWorld.sub(pointAxis.position.clone());

    // Calculate tangential velocity
    tangentialVelocity = rotate.clone().cross(pointOffsetPos);

}

I arrived at the above thanks to answer here asked in the physics stack exchange site.