Haptic sculpting of volumetric implicit functions

Implicit functions characterized by the zero-set of polynomial-based algebraic equations and other commonly-used analytic equations are extremely powerful in graphics, geometric design, and visualization. But the potential of implicit functions is yet to be fully realized due to the lack of flexible and interactive design techniques. This paper presents a haptic sculpting system founded upon scalar trivariate B-spline functions. All the solids sculpted in our environment are semi-algebraic sets of volumetric implicit functions. We develop a large variety of sculpting toolkits equipped with an intuitive haptic interface to facilitate the direct manipulation of implicit functions in real-time. To facilitate multiresolution editing and different levels of details, we employ three techniques: hierarchical B-splines, CSG-based functional composition, and knot insertion. Our experiments demonstrate that our algorithms and haptics-based techniques can greatly overcome the modeling difficulties associated with implicit functions. The novel modeling techniques and their haptics-based design principle are extensible to the design of arbitrary implicit functions.