A method for providing a haptic interface between a user held physical device and a computer generated parametric surface determines if a collision has occurred therebetween. If a collision has occurred, a force to apply to the physical device is determined and a force actuation mechanism is activated so as to produce the force at the physical device. If a collision has not occurred, the force actuation mechanism is deactivated. The method is repeated as the physical device is moved through a virtual space in which the parametric surface is modeled. The physical device is capable of transmitting forces in at least three degrees-of-freedom via the force actuation mechanism which is connected thereto. A human operator holding the physical device can thus interact with the surface, which may be a CAD generated surface.