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Coefficient–Based Spline Data Reduction by Hierarchical Spaces

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Mathematical Methods for Curves and Surfaces (MMCS 2016)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10521))

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Abstract

We present a data reduction scheme for efficient surface storage, by introducing a coefficient–based least squares spline operator that does not require any pointwise evaluation to approximate (in a lower dimension spline space) a given bivariate B–spline function. In order to define an accurate approximation of the target spline with a significant reduction of the space dimension, this operator is subsequently combined with the hierarchical spline framework to design an adaptive method that exploits the capabilities of truncated hierarchical B–splines (THB–splines). The resulting THB–spline simplification approach is validated by several numerical tests. The target B–spline surfaces include approximations of functions whose analytical expression is available, reconstructions of geographic data and parametric surfaces.

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Acknowledgements

The support by MIUR “Futuro in Ricerca” programme through the project DREAMS (RBFR13FBI3) and by the Istituto Nazionale di Alta Matematica (INdAM) through Gruppo Nazionale per il Calcolo Scientifico (GNCS)—“Finanziamento Giovani Ricercatori” and “Progetti di ricerca” programmes—and Finanziamenti Premiali SUNRISE are gratefully acknowledged.

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Authors and Affiliations

  1. Dipartimento di Matematica e Informatica “U. Dini”, Università di Firenze, Viale Morgagni 67/A, 50134, Firenze, Italy

    Cesare Bracco, Carlotta Giannelli & Alessandra Sestini

Authors
  1. Cesare Bracco
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  2. Carlotta Giannelli
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  3. Alessandra Sestini
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Corresponding author

Correspondence to Carlotta Giannelli .

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Editors and Affiliations

  1. University of Oslo, Oslo, Norway

    Michael Floater

  2. University of Oslo, Oslo, Norway

    Tom Lyche

  3. Université Joseph Fourier, Grenoble, France

    Marie-Laurence Mazure

  4. University of Oslo, Oslo, Norway

    Knut Mørken

  5. Vanderbilt University, Nashville, Tennessee, USA

    Larry L. Schumaker

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Bracco, C., Giannelli, C., Sestini, A. (2017). Coefficient–Based Spline Data Reduction by Hierarchical Spaces. In: Floater, M., Lyche, T., Mazure, ML., Mørken, K., Schumaker, L. (eds) Mathematical Methods for Curves and Surfaces. MMCS 2016. Lecture Notes in Computer Science(), vol 10521. Springer, Cham. https://doi.org/10.1007/978-3-319-67885-6_2

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  • DOI: https://doi.org/10.1007/978-3-319-67885-6_2

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-67884-9

  • Online ISBN: 978-3-319-67885-6

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