Haptic Rendering of Surfaces Defined by Implicit Functions
چکیده
This paper presents a method for computing the contact forces which must be imposed on a human (via a haptic interface) to evoke the sensation of touching surfaces described by implicit equations of the form S(p) = 0. The algorithm computes in real-time the forces of interaction which would arise from a point interacting with a real surface of the given shape. It models the forces of interaction which would arise when contacting linearly elastic material with surface friction. At each instant, a tangent plane to the surface at the contact point is computed and used to track the contact point's motion and prevent it from passing though the surface. A method using cutting planes to limit the extent of these surfaces is described. Though the rendering techniques are presented in the context of implicit surfaces, they can be applied to other classes of surfaces. NOMENCLATURE S, S(p) implicit function de ning a surface T tangent plane to S N normal to S p point in 3D space, (x; y; z) p0 the haptic interface point p1 the surface contact point (SCP) p0 rst approximation to p0, on T Sname a named surface or cutting plane pi;k point i at time k Tk tangent plane at time k