Accelerating geometric queries using the GPU

We present practical algorithms for accelerating geometric queries on models made of NURBS surfaces using programmable Graphics Processing Units (GPUs). We provide a generalized framework for using GPUs as co-processors in accelerating CAD operations. By attaching the data corresponding to surface-normals to a surface bounding-box structure, we can calculate view-dependent geometric features such as silhouette curves in real time. We make use of additional surface data linked to surface bounding-box hierarchies on the GPU to answer queries such as finding the closest point on a curved NURBS surface given any point in space and evaluating the clearance between two solid models constructed using multiple NURBS surfaces. We simultaneously output the parameter values corresponding to the solution of these queries along with the model space values. Though our algorithms make use of the programmable fragment processor, the accuracy is based on the model space precision, unlike earlier graphics algorithms that were based only on image space precision. In addition, we provide theoretical bounds for both the computed minimum distance values as well as the location of the closest point. Our algorithms are at least an order of magnitude faster than the commercial solid modeling kernel ACIS.