Free-form Implicit Haptic Rendering

Abstract

This paper presents a framework for haptic rendering in virtual environments based on distance maps over implicit support plane mappings. Initially, a rigid 3D object is modelled using support plane mappings so as to efficiently perform collision detection. Then, and after the collision queries are resolved, the surface of the 3D object can be directly reconstructed in constant time, using the equations of the support planes and the discrete distance map that encodes the distance of the object surface from the support plane. As a result analytical formulae can be extracted that provide the force feedback only as a function of the 3D object spatial transformation and position of the haptic probe. Experimental evaluation and computational complexity analysis demonstrates that the proposed approach can reduce significantly the computational cost when compared to existing collision detection and haptic rendering methods