Boundary conforming mesh to T-NURCC surface conversion

• Published in: Computers & graphics Vol. 82; pp. 95 - 105
• Main Authors: Marinov, Martin, Amagliani, Marco, Charrot, Peter
• Format: Journal Article
• Language: English
• Published: Oxford Elsevier Ltd 01.08.2019; Elsevier Science Ltd
• Subjects: Algorithms; Boundaries; Boundary curves and conditions; Conversion; Curves; Design optimization; Finite element method; Free form; Generative design; Interpolation; Intersections; Mesh conversion; Reverse engineering; Surface approximation; Surface geometry; Synthesis; T-spline and T-NURCC surfaces; Topology optimization; Transfinite interpolation; Triangles; T-spline and T-NURCC surfaces; Generative design; Boundary curves and conditions; Surface approximation; Mesh conversion; Transfinite interpolation
• ISSN: 0097-8493; 1873-7684
• DOI: 10.1016/j.cag.2019.05.012

•Mesh geometry integration in B-Rep CAD models by conversion to T-NURCC surfaces.•Transfinite interpolation patch network combines seamlessly mesh and smooth curves.•Boundary conforming approximation algorithm leads to low tolerance B-Rep models.•Enable synthesis of accurate generative design and topology optimization CAD models. [Display omitted] We present a method for converting an open triangle mesh, whose boundary is constrained to a set of smooth curves, to a T-NURCC surface approximating seamlessly both the mesh and the curve geometry. The curves represent boundaries of B-Rep faces adjacent to the mesh and include intersections, trim-curves, patch boundaries, etc. This conversion problem arises in generative design and topology optimization, where “organic” meshes are synthesized by a physics solver to complement an existing mechanical B-Rep model. It can also occur in reverse engineering, where a scanned mesh is converted to a collection of adjacent analytical and free-form surfaces. The core of our algorithm is a novel transfinite interpolation construction defining a C0 patch network interpolating the curves at the boundaries and coincident with the mesh in the interior. We convert this network to a T-NURCC surface by applying an approximation algorithm designed to produce a very accurate boundary fit and reproduce exactly all boundary corners. These properties allow a B-Rep modeling kernel to stitch the output T-NURCCs with adjacent B-Rep faces into a watertight, low tolerance B-Rep CAD model. We demonstrate our method’s results and applicability on several examples synthesized by topology optimization and generative design applications.