Accurate moment computation using the GPU

Abstract

We present algorithms for computing accurate moments of solid models that are represented using multiple trimmed NURBS surfaces. Our algorithms make use of programmable Graphics Processing Units (GPUs) to accelerate the computations. We evaluate the surface coordinates and normals accurately, with theoretical bounds, using our GPU NURBS evaluator. We have developed a framework that makes use of this data to evaluate surface integrals of trimmed NURBS surfaces in real time. With our framework, we can compute volume and moments of solid models with theoretical guarantees. The framework also supports local geometry changes, which is useful for providing interactive feedback to the designer while the solid model is being designed. We can compute the center of mass and check for stability of the solid model interactively. Applications of such real-time moment computation include deformation modeling, animation, and physically based simulations.