Dynamic implicit solids with constraints for haptic sculpting

We present a novel, interactive shape modeling technique: dynamic implicit solid modeling, which unifies volumetric implicit functions and powerful physics-based modeling. Although implicit functions are extremely powerful in graphics, geometric design, and shape modeling, the full potential of implicit functions is yet to be fully realized due to the lack of flexible and interactive design techniques. In order to broaden the accessibility of implicit functions in geometric modeling, we marry the implicit solids, which are semi-algebraic sets of volumetric implicit functions, with the principle of physics-based models and formulate dynamic implicit solids. By using "density springs" to connect the scalar values of implicit functions, we offer a viable solution to introduce the elasticity into implicit representations. As a result, our dynamic implicit solids respond to sculpting forces in a natural and predictive manner. The geometric and physical behaviors are tightly coupled in our modeling system. The flexibility of our modeling technique allows users to easily modify the geometry and topology of sculpted objects, while the inherent physical properties can provide a natural interface for direct, force-based free-form deformation. The additional constraints provide users more control on the dynamic implicit solids. We have developed a sculpting system equipped with a large variety of physics-based toolkits and an intuitive haptic interface to facilitate the direct, natural editing of implicit functions in real-time. Our experiments demonstrate many attractive advantages of our dynamic approach for implicit modeling such as intuitive control, direct manipulation, real-time haptic feedback, and capability to model complicated geometry and arbitrary topology.