Haptic rendering using support plane mappings

This paper presents a haptic rendering scheme based on distance maps over implicit surfaces. Using the successful concept of support planes and mappings, a support plane mapping formulation is used so as to generate a convex conservative representation and efficiently perform collision detection. The proposed scheme enables, under specific assumptions, the analytical reconstruction of the rigid 3D object´s surface, using the equations of the support planes and their respective distance map. As a direct consequence, the problem of calculating the force feedback can be analytically solved using only information about the 3D object´s spatial trasnformation and position of the haptic probe. Moreover, several haptic effects are derived by the proposed mesh-free haptic rendering formulation. Experimental evaluation and computational complexity analysis demonstrates that the proposed approach can reduce significantly the computational cost when compared to existing methods.