Accurate GPU-accelerated surface integrals for moment computation

We present algorithms for computing accurate moments of solid models that are represented using multiple trimmed NURBS surfaces and triangles. Our algorithms make use of programmable Graphics Processing Units (GPUs) to accelerate the moment computations. For NURBS surfaces, 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. Since typical solid models also contain flat planes that are usually tessellated into triangles, our framework also includes GPU acceleration of the moment contributions of such flat faces. Using our framework, we can compute volume and moments of solid models with theoretical guarantees. Our algorithms support 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. Other applications of such real-time moment computation include deformation modeling, animation, and physically based simulations.

► GPU-accelerated numerical surface integration on trimmed NURBS surfaces and triangles.
► Computation of solid models’ moments without pre-tessellation of NURBS.
► GPU algorithm for midpoint, 2- or 3-point Gaussian quadrature integration.
► Error estimates for moment computations.
► Supports local geometry changes, providing interactive feedback to the designer.