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Subdivision and G-Spline Hybrid Constructions for High-Quality Geometric and Analysis-Suitable Surfaces

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Geometric Challenges in Isogeometric Analysis

Part of the book series: Springer INdAM Series ((SINDAMS,volume 49))

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Abstract

This survey of piecewise polynomial surface constructions for filling multi-sided holes in a smooth spline complex focusses on a class of hybrid constructions that, while heterogeneous, combines all the practical advantages of state-of-the-art for modelling and analysis: good shape, easy implementation and simple refinability up a pre-defined level. After reviewing the three ingredients—subdivision, G-spline and guided surfaces—the hybrid is defined to consist essentially of one macro-patch for each of n sectors, leaving just a tiny n-sided central hole to be filled by a G-spline construction. Here tiny means both geometrically small, e.g., two orders of magnitude smaller than pieces of the spline complex, and small in its contribution to engineering analysis, i.e., it is unlikely to require further refinement to express additional geometric detail or resolve a function on the surface, such as the solution of a partial differential equation. Each macro-patch has the local structure of a subdivision surface near, but excluding the central, extraordinary point: all internal transitions are the identity or scale according to contraction speed toward the extraordinary point. Both the number of pieces of the macro-patches and the speed can be chosen application-dependent and adaptively.

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  1. University of Florida, Gainesville, FL, USA

    Jörg Peters

  2. Vilnius University, Vilnius, Lithuania

    Kȩstutis Karčiauskas

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  1. Jörg Peters
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  1. Department of Mathematics, University of Rome Tor Vergata, Rome, Italy

    Carla Manni

  2. Department of Mathematics, University of Rome Tor Vergata, Rome, Italy

    Hendrik Speleers

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Peters, J., Karčiauskas, K. (2022). Subdivision and G-Spline Hybrid Constructions for High-Quality Geometric and Analysis-Suitable Surfaces. In: Manni, C., Speleers, H. (eds) Geometric Challenges in Isogeometric Analysis. Springer INdAM Series, vol 49. Springer, Cham. https://doi.org/10.1007/978-3-030-92313-6_8

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