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Area Formulas

  • Herbert EdelsbrunnerEmail author
Chapter
Part of the SpringerBriefs in Applied Sciences and Technology book series (BRIEFSAPPLSCIENCES)

Abstract

Perhaps surprisingly, \(\alpha \)-complexes are useful in measuring a union of balls in two and higher dimensions.

Keywords

Geometric Structure Delaunay Triangulation Common Intersection Voronoi Region Letter Alphabet 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

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    Bryant R, Edelsbrunner H, Koehl P, Levitt M (2004) The area derivative of a space-filling diagram. Discrete Comput Geom 32:293–308CrossRefzbMATHMathSciNetGoogle Scholar
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    Kratky KW (1978) The area of intersection of \(n\) equal circular disks. J Phys A: Math Gen 11:1017–1024CrossRefzbMATHMathSciNetGoogle Scholar
  3. 3.
    Edelsbrunner H (1995) The union of balls and its dual shape. Discrete Comput Geom 13:415–440CrossRefzbMATHMathSciNetGoogle Scholar
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    Naiman DQ, Wynn HP (1992) Inclusion-exclusion Bonferroni identities and inequalities for discrete tube-like problems via Euler characteristics. Ann Statist 20:43–76CrossRefzbMATHMathSciNetGoogle Scholar

Copyright information

© The Author(s) 2014

Authors and Affiliations

  1. 1.Institute of Science and Technology AustriaKlosterneuburgAustria

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