Boundary conforming mesh to T-NURCC surface conversion

摘要

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 C-0 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. (C) 2019 Elsevier Ltd. All rights reserved.