Reconstruction of Trimmed NURBS Surfaces for Gap-Free Intersections

The modern engineering technologies of computer-aided design (CAD), computer-aided engineering (CAE), and computer-aided manufacturing (CAM) are ubiquitous in engineering practice. They are focused on creating, analyzing, and fabricating engineering artifacts represented as geometric models. Historically, these technologies developed independently, with different geometric representations that are customized to the needs of the technology. As a result, the combined use of these technologies has led to differences in data structures, file formats, 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.

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.

MATEC Web of Conferences – General and efficient algorithms for handling intricate situations in trimmed surface rendering

Trimmed surfaces have been widely used in complicated product design in mechanical engineering especially in complex free form surface models of CAD/CAM/CAE. Focusing on the deficiencies of the algorithms available in published literatures when handling some intricate situations, this paper proposes a more general and efficient algorithm of trimmed surface rendering (ATSR). The ATSR is a general algorithm that can deal with most intricate situations, which frequently occur in practical engineering that no special attention has been paid to in references at hand, as well as common situations. Furthermore, this paper presents a new algorithm for the nodes of polygon connecting into elements (ANCE). The ANCE can handle most tricky polygons appearing in the process of rendering and achieve successful triangulation for the to-be-rendered surface. Preferable results are obtained in the case studies, which indicate that the algorithms (ATSR and ANCE) are efficient and effective in handling complicated as well as common trimmed surface models in real engineering industry.