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Infimaximal frames: a technique for making lines look like segments

MPS-Authors
http://pubman.mpdl.mpg.de/cone/persons/resource/persons45446

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

http://pubman.mpdl.mpg.de/cone/persons/resource/persons45021

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

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2000-1-005
(Any fulltext), 11KB

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Citation

Seel, M., & Mehlhorn, K.(2000). Infimaximal frames: a technique for making lines look like segments (MPI-I-2000-1-005). Saarbrücken: Max-Planck-Institut für Informatik.


Cite as: http://hdl.handle.net/11858/00-001M-0000-0014-6D53-3
Abstract
Many geometric algorithms that are usually formulated for points and segments generalize easily to inputs also containing rays and lines. The sweep algorithm for segment intersection is a prototypical example. Implementations of such algorithms do, in general, not extend easily. For example, segment endpoints cause events in sweep line algorithms, but lines have no endpoints. We describe a general technique, which we call infimaximal frames, for extending implementations to inputs also containing rays and lines. The technique can also be used to extend implementations of planar subdivisions to subdivisions with many unbounded faces. We have used the technique successfully in generalizing a sweep algorithm designed for segments to rays and lines and also in an implementation of planar Nef polyhedra. Our implementation is based on concepts of generic programming in C++ and the geometric data types provided by the C++ Computational Geometry Algorithms Library (CGAL).