A Constraint Equation Algebra as a Basis for Haptic Rendering

Many haptic rendering problems can be expressed in terms of constraints on the motion of a proxy within a virtual environment. This principle is well established for surface rendering, and can also be applied to other types of haptic interaction. A key problem in general constraint based rendering is combining constraints from several sources into a single unified constraint. This paper describes some work in progress toward developing a mathematical framework for manipulating motion constraint equations, and in particular the derivation of a combination algebra for constraints. This work could lead to a system for 6DOF rendering involving non-trivial proxy shapes.