Texts in Computational Science and Engineering

Space-Filling Curves

An Introduction with Applications in Scientific Computing

Authors: Bader, Michael

  • Connects the different techniques to describe space-filling curves to corresponding algorithms
  • Connects space-filling curves and respective orders to regular and adaptive meshes for discretisation
  • Describes parallelisation and cache-efficient algorithms based on space-filling curves
  • Provides a section on references to both pioneering and current research on space-filling curves in scientific computing​
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  • ISBN 978-3-642-31046-1
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About this Textbook

­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.

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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.

About the authors

Michael Bader is professor for computer science at Technische Universität München, where he leads a research group on hardware-aware algorithms and software for high performance computing (located at the Leibniz Supercomputing Centre). His focus in research and teaching is on algorithmic challenges imposed by modern
computing platforms. A large part of his work is dedicated to exploiting locality properties of space-filling curves for simulation tasks in science and engineering.



Reviews

From the reviews:

“This book concentrates on low-dimensional, two or three at most, curves used for linearly ordering points on the 2D or 3D grid with applications in computer graphics and data structures. … Each section ends with indications for further reading and exercises. This is a new book in the field of computer science which should be a valuable resource for advanced undergraduate and graduate students as well as more experienced researchers.” (Ewa Skubalska-Rafajłowicz, Mathematical Reviews, January, 2014)

“Bader’s book … provides an introduction to the algorithmics of space-filling curves. … The book has many color illustrations and can be used as a textbook and as reference monograph for research.” (Luiz Henrique de Figueiredo, MAA Reviews, April, 2013)

“This is a gentle introduction to space filling curves. Emphasis is on the representation, implementation and application in computer science. … It is clear that the author has a long teaching experience with this subject. He had found the right balance between motivation, rigor, application, implementation, in just the right pace to take the reader/student along climbing up the hill towards of increasing complexity as academic examples are left and one approaches the real life applications.” (A. Bultheel, The European Mathematical Society, December, 2012)

Table of contents (15 chapters)

  • Two Motivating Examples: Sequential Orders on Quadtrees and Multidimensional Data Structures

    Bader, Michael

    Pages 1-14

  • How to Construct Space-Filling Curves

    Bader, Michael

    Pages 15-30

  • Grammar-Based Description of Space-Filling Curves

    Bader, Michael

    Pages 31-45

  • Arithmetic Representation of Space-Filling Curves

    Bader, Michael

    Pages 47-65

  • Approximating Polygons

    Bader, Michael

    Pages 67-76

Buy this book

eBook $69.99
price for USA (gross)
  • ISBN 978-3-642-31046-1
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $89.95
price for USA
  • ISBN 978-3-642-31045-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Space-Filling Curves
Book Subtitle
An Introduction with Applications in Scientific Computing
Authors
Series Title
Texts in Computational Science and Engineering
Series Volume
9
Copyright
2013
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-642-31046-1
DOI
10.1007/978-3-642-31046-1
Hardcover ISBN
978-3-642-31045-4
Series ISSN
1611-0994
Edition Number
1
Number of Pages
XIII, 285
Topics