Isogeometric Segmentation via Midpoint Subdivision Suitable Solids. (September 2019) - Haberleitner, Michael; Jüttler, Bert; Masson, Yannick
Abstract: The framework of Isogeometric Analysis (IgA) makes frequent use of trivariate NURBS parameterizations (representing topological cuboids) of the computational domain. Several recent publications [1–6] describe methodologies that decompose a given three-dimensional solid in boundary representation into a collection of topological cuboids, or generate trivariate NURBS parameterizations for each of them in a subsequent step. The decomposition can be derived via a segmentation into sufficiently simple "base solids", for which cuboidal multi-patch representations are readily available. Based on midpoint subdivision, we propose a new class of base solids. In addition, we establish the pre-processing step of face pre-segmentation, which simplifies the splitting operations and improves the shape of the resulting topological cuboids. Finally, we show how to realize the midpoint subdivision by a template mapping approach, which simultaneously generates parameterizations of the base solids as trivariate multi-patch NURBS volumes. Highlights: Segmentation of 3D solids into topological cuboids, suitable for NURBS parameterization. Pre-segmentation is used to improve the shape of the topological cuboids. Segmentation produces base solids that are suitable for midpoint subdivision. Subdivision of these base solids is realized by a template mapping approach.