SBIR Phase I: T-Splines for Surface Intersection

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.