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A Versatile Strategy for the Implementation of Adaptive Splines

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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))

Abstract

This paper presents an implementation framework for spline spaces over T-meshes (and their d-dimensional analogs). The aim is to share code between the implementations of several spline spaces. This is achieved by reducing evaluation to a generalized Bézier extraction.

The approach was tested by implementing hierarchical B-splines, truncated hierarchical B-splines, decoupled hierarchical B-splines (a novel variation presented here), truncated B-splines for partially nested refinement and hierarchical LR-splines.

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Notes

  1. 1.

    (Or, more generally, generating sets).

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Acknowledgments

The authors have been supported by the Austrian Science Fund (FWF, NFN S117 “Geometry + Simulation”) and by the Seventh Framework Programme of the EU (project EXAMPLE, GA No. 324340). This support is gratefully acknowledged. The authors would also like to thank Dr. Rafael Vázquez for commenting on an earlier version of this paper and to the reviewers for their valuable suggestions.

Author information

Authors and Affiliations

  1. Department of Mathematics, University of Oslo, Oslo, Norway

    Andrea Bressan

  2. Institute of Applied Geometry, Johannes Kepler University Linz, Linz, Austria

    Dominik Mokriš

Authors
  1. Andrea Bressan
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  2. Dominik Mokriš
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Correspondence to Andrea Bressan .

Editor information

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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Bressan, A., Mokriš, D. (2017). A Versatile Strategy for the Implementation of Adaptive Splines. 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_3

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  • DOI: https://doi.org/10.1007/978-3-319-67885-6_3

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