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G 1 -smooth splines on quad meshes with 4-split macro-patch elements

Ahmed Blidia, Bernard Mourrain, Nelly Villamizar Orcid Logo

Computer Aided Geometric Design, Volume: 52-53, Pages: 106 - 125

Swansea University Author: Nelly Villamizar Orcid Logo

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DOI (Published version): 10.1016/j.cagd.2017.03.003

Abstract

We analyze the space of smooth spline functions on quad-meshes. These functions are composed of 4-split spline macro-patch elements on each quadrangular face. We describe explicit transition maps across shared edges so that the space of smooth splines is ample on a quad-mesh of arbitrary topology. T...

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Published in: Computer Aided Geometric Design
ISSN: 01678396
Published: 2017
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URI: https://cronfa.swan.ac.uk/Record/cronfa32862
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Abstract: We analyze the space of smooth spline functions on quad-meshes. These functions are composed of 4-split spline macro-patch elements on each quadrangular face. We describe explicit transition maps across shared edges so that the space of smooth splines is ample on a quad-mesh of arbitrary topology. These transition maps define a finite dimensional vector space of G1 spline functions on each quadrangular face of the mesh. We determine the dimension of this space of G1 spline functions for degree big enough and provide explicit constructions of basis functions attached respectively to vertices, edges and faces. This construction requires the analysis of the module of syzygies of univariate b-spline functions with b-spline function coefficients. We provide new results on their generators and the dimension of the graded pieces.Examples of bases of G1 splines of small degree for simple topological surfaces are detailed and illustrated by parametric surface constructions.
Keywords: Geometrically continuous splines, Multivariate spline approximation, B-splines, surfaces with arbitrary topology, quad meshes, macro patch elements
College: Faculty of Science and Engineering
Start Page: 106
End Page: 125

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