I am using PhysX-transform matrices and I want to simulate dynamic acceleration and velocity-changes around a center, to make it seem like a static world is moving, when in fact all the dynamic objects in it are being moved, as if the world was moving/rotating. It's working very well as long as I am using the origin as center. But now I want to rotate everything around a center of mass. I don't know how to combine this point with my "world movement and rotation matrix" to transform all the postions and velocities of world objects the right way.

The obvious solution is to translate the world so the origin is now at the desired center of rotation, then rotate, then translate back.

Are the direction vectors affected as well? Or do I just need the rotation center to determine the shift in position? That part was easy, but I'm not sure about the directions of linear and angular velocity... It looks right, but it doesn't feel like it's supposed to be working like this. Can you tell me, if this is correct?

Ignore the cnv()-functions, that's just converting types between PhysX and the graphics engine, "sp" is the secondsPassed-float and worldShift is the transformation-matrix describing this frame's world-movement, with q being the rotation-quaternion part.

vector3df newLin = object->getLinVel();
vector3df newAng = object->getAngVel();

newLin -= object->linComp;// // negate last frames "compensation"-velocity
newAng -= object->angComp;

newLin = cnv(worldShift.q.rotate(cnv(newLin)));// should this be affected by rotation-center???
newAng = cnv(worldShift.q.rotate(cnv(newAng)));

vector3df oPos = object->getPos();
vector3df oDest = cnv(worldShift.transform(cnv(oPos - COR)) + COR);// COR: center of rotation
vector3df linShift = oDest - oPos;
vector3df angShift;
cnv(worldShift.q).toEuler(angShift);

newLin += linShift/sp;// what if frame-rate changes?
newAng += angShift/sp;

object->accelLin(newLin-object->getLinVel(), false, PxForceMode::eVELOCITY_CHANGE);
object->accelAng(newAng-object->getAngVel(), false, PxForceMode::eVELOCITY_CHANGE);

object->linComp = linShift/sp;// to be negated next frame
object->angComp = angShift/sp;

I don't feel like trying to figure out what that code does. A proper vector (as opposed to a position) is not affected by translations.

I don't know if you care, but this code is called per frame and physical object and applies velocity changes to every object in a world as if the world was moving and rotating itself... only it isn't, you just get the impression.

The way I see it (and I can't state it often enough: I am not a mathematician) there are two things to consider:

- each object gets a shift in position & rotation caused by the (imaginary) world movement, applied as velocity changes for the current frame

-> so instead of rotating a point, I give an object a velocity (angular and linear) in order to reach the point without bypassing the physics engine

- this "compensation"-velocity is remembered and subtracted in the next frame

- each objects' actual velocity vectors (the ones NOT artificially applied and subtracted to make it seem like the world is moving) need to be rotated, to be confirm with the imaginary world orientation. So, if I want to create the illusion that the world rotated 180° around the Y-axis, all the objects' velocities need to do the same.

I just wasn't sure wether the center of rotation is relevant for the second part or just needed for the "position shift".

It seems to work great and it's very fast compared to moving the world in actuality. It still felt like the "actual" velocities should be affected by the center of rotation as well, that's why I was asking. Anyway, I guess being proper vectors, they don't. Thank you.