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

MPS-Authors
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Berberich,  Eric
Algorithms and Complexity, MPI for Informatics, Max Planck Society;

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Eigenwillig,  Arno
Algorithms and Complexity, MPI for Informatics, Max Planck Society;

/persons/resource/persons44609

Hemmer,  Michael
Algorithms and Complexity, MPI for Informatics, Max Planck Society;

/persons/resource/persons44616

Hert,  Susan
Algorithms and Complexity, MPI for Informatics, Max Planck Society;

/persons/resource/persons45021

Mehlhorn,  Kurt
Algorithms and Complexity, MPI for Informatics, Max Planck Society;

/persons/resource/persons45414

Schömer,  Elmar
Algorithms and Complexity, MPI for Informatics, Max Planck Society;

/persons/resource/persons45250

Raman,  Rajeev
Algorithms and Complexity, MPI for Informatics, Max Planck Society;

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Citation

Berberich, E., Eigenwillig, A., Hemmer, M., Hert, S., Mehlhorn, K., & Schömer, E. (2002). A Computational Basis for Conic Arcs and Boolean Operations on Conic Polygons. In Algorithms - ESA 2002: 10th Annual European Symposium (pp. 174-186). Berlin, Germany: Springer.


Cite as: https://hdl.handle.net/11858/00-001M-0000-000F-2EDD-0
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).