Convex Hulls

  • Jakob Andreas Bærentzen
  • Jens Gravesen
  • François Anton
  • Henrik Aanæs

Abstract

An object is convex if any two points inside it can be connected via a straight line that is entirely inside the object. This chapter opens with a discussion of convexity and then defines the convex hull: The tightest fitting convex region of space that covers a given object.

Initially, several algorithms for computing 2D convex hulls are considered and then methods for 3D convex hulls. In particular, we discuss an incremental algorithm where one adds a triangle at a time and the divide and conquer approach where the object is recursively divided until the computations are trivial. The essential part of the divide and conquer approach is to recursively merge the convex hulls of the parts.

Keywords

Hull Pyramid Sorting 

References

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Copyright information

© Springer-Verlag London 2012

Authors and Affiliations

  • Jakob Andreas Bærentzen
    • 1
  • Jens Gravesen
    • 2
  • François Anton
    • 1
  • Henrik Aanæs
    • 1
  1. 1.Department of Informatics and Mathematical ModellingTechnical University of DenmarkKongens LyngbyDenmark
  2. 2.Department of MathematicsTechnical University of DenmarkKongens LyngbyDenmark

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