Using linked volumes to model object collisions, deformation, cutting, carving, and joining

In volume graphics, objects are represented by arrays or clusters of sampled 3D data. A volumetric object representation is necessary in computer modeling whenever interior structure affects an object's behavior or appearance. However, existing volumetric representations are not sufficient for modeling the behaviors expected in applications such as surgical simulation, where interactions between both rigid and deformable objects and the cutting, tearing, and repairing of soft tissues must be modeled in real time. Three-dimensional voxel arrays lack the sense of connectivity needed for complex object deformation, while finite element models and mass-spring systems require substantially reduced geometric resolution for interactivity and they can not be easily cut or carved interactively. This paper discusses a linked volume representation that enables physically realistic modeling of object interactions such as: collision detection, collision response, 3D object deformation, and interactive object modification by carving, cutting, tearing, and joining. The paper presents a set of algorithms that allow interactive manipulation of linked volumes that have more than an order of magnitude more elements and considerably more flexibility than existing methods. Implementation details, results from timing tests, and measurements of material behavior are presented.