SBIR-STTR Award

This Small Business Innovative Research Phase I research project will investigate the application of T-splines to the problem of computing a topologically consistent surface intersection for geometric modeling applications. In the CAD/CAM industry, most free-form geometric modeling is done using NURBS surfaces. The intersection between two NURBS surfaces is traditionally represented using trimmed-NURBS format, but trimmed-NURBS cannot express the intersection of two NURBS surfaces without error, and hence a gap occurs. T-splines are a dramatically new surface formulation that allows local refinement, which means that a single control point can be inserted into a T-spline control grid without changing the surface. The objective of the proposed research is to study algorithms for computing the intersection of two NURBS surfaces represented as T-splines. The anticipated result will be a robust algorithm for representing the intersection of two NURBS surfaces using a single gap-free T-spline model. The gaps that occur in NURBS intersection algorithms mean that the resulting models are not topologically consistent. This lack of topological consistency is regarded as the single most serious unsolved problem in CAD/CAM. This problem is estimated to cost the industry a billion dollars per year. A successful solution to this problem will greatly reduce the design/analysis cycle time. T-splines seem ideally suited to solve this problem. Furthermore, NURBS are a special case of T-splines, and any T-spline can be converted without error into a NURBS. This means that a T-spline-based solution to the surface intersection problem will be forward and backward compatible with existing CAD/CAM software

This SBIR Phase II project addresses what is considered to be a significant unsolved problem in the Computer-Aided Design (CAD) industry; the fact that many CAD models contain numerous small, unwanted holes or gaps. These gaps occur most often along the seams where two surfaces in a CAD model meet, such as where a wing meets the fuselage of an airplane, and result from fundamental mathematical limitations. Software for analyzing a CAD model for physical properties such as aerodynamics, deflection, or stress cannot work unless those holes are repaired; a time consuming process that causes a significant bottleneck in the CAD workflow. Under Phase I funding, a solution to this gap problem was devised that uses a new surface formulation called T-Splines. Tasks to be performed in Phase II include extending the algorithms to work in arbitrary cases, designing and implementing algorithms for converting trimmed-NURBS models into gap-free T-Splines, adding fillets to the surface intersection, and incorporating the core software into two existing CAD packages using the idea of a "plugin."

The gap problem has vexed the CAD industry for over 25 years. The solution to the gap problem conceived in previous efforts involves a new technology called T-Splines, which some researchers in the CAD community believe represents a significant advance in the field of surface modeling theory. This project will help the T-Splines technology to mature and will hasten its adoption into the CAD industry