THB-splines multi-patch parameterization for multiply-connected planar domains via Template Segmentation

Given a planar multiply-connected domain Omega, we provide a multi-patch parameterization exploiting a segmentation algorithm and the construction of templates. The segmentation is a fundamental step which allows to split the input domain into patches topologically equivalent to quadrilaterals. Templates are prototypes of segmentation that will be chosen according to the shape of the given domain. We will compute a bijective harmonic mapping h defined between the input Omega and the chosen template (Omega) over cap. The segmentation will be transferred from the prototype template to the input Omega by approximating the inverse mapping. Templates are equipped with a multi-patch structure and each patch (Omega) over cap ((i)) is parametrized individually by a geometry mapping G(i). The final multi-patch parameterization of Omega is achieved exploiting the combination of each geometry mapping G(i) and the inverse of the mapping h obtained by projection into the THB-spline space. (C) 2018 Elsevier B.V. All rights reserved.