A Computational Basis for Conic Arcs and Boolean Operations on Conic Polygons

  • Eric Berberich
  • Arno Eigenwillig
  • Michael Hemmer
  • Susan Hert
  • Kurt Mehlhorn
  • Elmar Schömer
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2461)

Abstract

We give an exact geometry kernel for conic arcs, algorithms for exact computation with low-degree algebraic numbers, and an algorithm for computing the arrangement of conic arcs that immediately leads to a realization of regularized boolean operations on conic polygons. A conic polygon, or polygon for short, is anything that can be obtained from linear or conic halfspaces (= the set of points where a linear or quadratic function is non-negative) by regularized boolean operations. The algorithm and its implementation are complete (they can handle all cases), exact (they give the mathematically correct result), and efficient (they can handle inputs with several hundred primitives).

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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Eric Berberich
    • 1
  • Arno Eigenwillig
    • 1
  • Michael Hemmer
    • 1
  • Susan Hert
    • 1
  • Kurt Mehlhorn
    • 1
  • Elmar Schömer
    • 1
  1. 1.Max-Planck-Institut für InformatikSaarbrückenGermany

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