Encyclopedia of Parallel Computing

2011 Edition
| Editors: David Padua

Space-Filling Curves

  • Michael Bader
  • Hans-Joachim Bungartz
  • Miriam Mehl
Reference work entry
DOI: https://doi.org/10.1007/978-0-387-09766-4_145

Synonyms

FASS (space-f illing, self-a voiding, s imple, and self-s imilar)-curves

Definition

A space-filling curve is a continuous and surjective mapping from a 1D parameter interval, say [0,1], onto a higher-dimensional domain, say the unit square in 2D or the unit cube in 3D. Although this, at first glance, seems to be of a purely mathematical interest, space-filling curves and their recursive construction process have obtained a broad impact on scientific computing in general and on the parallelization of numerical algorithms for spatially discretized problems in particular.

Discussion

Introduction

Space-filling curves (SFC) were presented at the end of the nineteenth century – first by Peano (1890) and Hilbert (1891), and later by Moore, Lebesgue, Sierpinski, and others. The idea that some curves (i.e., something actually one-dimensional) may completely cover an area or a volume sounds somewhat strange and formerly caused mathematicians to call them “topological monsters.” The...

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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  • Michael Bader
    • 1
  • Hans-Joachim Bungartz
    • 1
  • Miriam Mehl
    • 1
  1. 1.Institute of Parallel and Distributed SystemsUniversität StuttgartStuttgartGermany