000264945 001__ 264945
000264945 005__ 20190913111824.0
000264945 0247_ $$a10.5075/epfl-MATHICSE-264945$$2doi
000264945 037__ $$aREP_WORK
000264945 245__ $$aMATHICSE Technical Report: Volumetric Untrimming: Precise decomposition of trimmed trivariates into tensor products
000264945 269__ $$a2019-03-21
000264945 260__ $$c2019-03-21$$bMATHICSE$$aÉcublens
000264945 300__ $$a18
000264945 336__ $$aWorking Papers
000264945 500__ $$aThis project has received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme under grant agreement No 694515 - CHANGE.
000264945 520__ $$a3D objects, modeled using Computer Aided Geometric Design (CAGD) tools, are traditionally represented using a boundary representation (B-rep), and typically use spline functions to parameterize these boundary surfaces. However, recent development in physical analysis, in isogeometric analysis (IGA) in specic, necessitates a volumetric parametrization of the interior of the object. IGA is performed directly by integrating over the spline spaces of the volumetric spline representation of the object. Typically, tensor-product B-spline trivariates are used to parameterize the volumetric domain. A general 3D object, that can be modeled in contemporary B-rep CAD tools, is typically represented using trimmed B-spline surfaces. In order to capture the generality of the contemporary B-rep modeling space, while supporting IGA needs, Massarwi and Elber (2016) proposed the use of trimmed trivariates volumetric elements. However, the use of trimmed geometry makes the integration process more difficult since integration over trimmed B-spline basis functions is a highly challenging task Xu et al. (2017). In this work, we propose an algorithm that precisely decomposes a trimmed B-spline trivariate into a set of (singular only on the boundary) tensor-product B-spline trivariates, that can be utilized to simplify the integration process, in IGA. The trimmed B-spline trivariate is first subdivided into a set of trimmed B--spline trivariates, at all its internal knots. Then, each trimmed Bezier trivariate, is decomposed into a set of mutually exclusive tensor-product B-spline trivariates, that precisely cover the entire trimmed domain. This process, denoted untrimming, can be performed in either the Euclidean space or the parametric space of the trivariate. We present examples of the algorithm on complex trimmed trivariates' based geometry, and we demonstrate the effectiveness of the method by applying IGA over the (untrimmed) results.
000264945 6531_ $$aVolumetric representations
000264945 6531_ $$aV-rep
000264945 6531_ $$aV-model
000264945 6531_ $$aIsogeometric analysis
000264945 6531_ $$aIGA
000264945 6531_ $$aHeterogeneous materials
000264945 700__ $$aMassarwi, Fady
000264945 700__ $$g276526$$aAntolin Sanchez, Pablo$$0250510
000264945 700__ $$aElber, Gershon
000264945 710__ $$aMATHICSE-Group
000264945 8564_ $$uhttps://infoscience.epfl.ch/record/264945/files/Report%2010.2019_FM_PA_GE.pdf$$s797036
000264945 8560_ $$fjocelyne.blanc@epfl.ch
000264945 909CO $$pSB$$pDOI$$pworking$$ooai:infoscience.epfl.ch:264945
000264945 909C0 $$zJunod, Julien$$yApproved$$xU13308$$mpablo.antolin@epfl.ch$$0252586$$pMNS
000264945 960__ $$asamantha.bettschen@epfl.ch
000264945 961__ $$afantin.reichler@epfl.ch
000264945 973__ $$aEPFL
000264945 980__ $$aREP_WORK
000264945 981__ $$aoverwrite