Reconstruction of Gap-Free Intersections for Trimmed NURBS Surfaces

The modern engineering technologies of Computer-Aided Design (CAD), Computer-Aided Engineering (CAE) and Computer-Aided Manufacturing (CAM) are ubiquitous in engineering design. They are focused on creating, analyzing, and fabricating objects represented as geometric models. Historically, these technologies developed independently, such that their geometric representations are customized to the needs of the technology. As a result, combined use of these technologies has led to differences in data structures, file formats, software constraints, and user knowledge and practice, requiring translation of representations between systems to support interoperability. Complicating this situation is the approximate nature of modeling operations in CAD systems, which can result in gaps at the boundary curves between mating trimmed surfaces of a model. The research presented here is aimed at removing the gaps between trimmed surfaces, resulting in a “watertight” model that is suitable for use directly by downstream applications. A three-step algorithm is presented that includes analysis of the parametric space of the trimming curves, reparameterization to create a global parameter space, and reconstruction of the intersecting surfaces to ensure continuity at the trimming curve.