Space-Filling Curves

An Introduction with Applications in Scientific Computing

  • Michael Bader

Part of the Texts in Computational Science and Engineering book series (TCSE, volume 9)

Table of contents

About this book


­The present book provides an introduction to using space-filling curves (SFC) as tools in scientific computing. Special focus is laid on the representation of SFC and on resulting algorithms. For example, grammar-based techniques are introduced for traversals of Cartesian and octree-type meshes, and arithmetisation of SFC is explained to compute SFC mappings and indexings.

­The locality properties of SFC are discussed in detail, together with their importance for algorithms. Templates for parallelisation and cache-efficient algorithms are presented to reflect the most important applications of SFC in scientific computing. Special attention is also given to the interplay of adaptive mesh refinement and SFC, including the structured refinement of triangular and tetrahedral grids. For each topic, a short overview is given on the most important publications and recent research activities.


Hilbert curve, Peano curve, Sierpinski curve adaptive meshes algorithms in scientific computing octrees parallelisation space-filling curves

Authors and affiliations

  • Michael Bader
    • 1
  1. 1., Department of InformaticsMunich Center of Advanced ComputingGarchingGermany

Bibliographic information