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  • Computational geometry  (3)
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  • 1
    Digitale Medien
    Digitale Medien
    Lines in space: Combinatorics and algorithms (1996)
    Springer
    Algorithmica 15 (1996), S. 428-447 
    Details
    ISSN: 1432-0541
    Schlagwort(e): Computational geometry ; Lines in space ; Plücker coordinates ; ε-Nets
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Informatik , Mathematik
    Notizen: Abstract Questions about lines in space arise frequently as subproblems in three-dimensional computational geometry. In this paper we study a number of fundamental combinatorial and algorithmic problems involving arrangements ofn lines in three-dimensional space. Our main results include: 1. A tight Θ(n 2) bound on the maximum combinatorial description complexity of the set of all oriented lines that have specified orientations relative to then given lines. 2. A similar bound of Θ(n 3) for the complexity of the set of all lines passing above then given lines. 3. A preprocessing procedure usingO(n 2+ɛ) time and storage, for anyε〉0, that builds a structure supportingO(logn)-time queries for testing if a line lies above all the given lines. 4. An algorithm that tests the “towering property” inO(n 2+ɛ) time, for anyε〉0; don given red lines lie all aboven given blue lines? The tools used to obtain these and other results include Plücker coordinates for lines in space andε-nets for various geometric range spaces.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01955043
    Bibliothek Standort Signatur Band/Heft/Jahr Verfügbarkeit
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  • 2
    Digitale Medien
    Digitale Medien
    Ray shooting in polygons using geodesic triangulations (1994)
    Springer
    Algorithmica 12 (1994), S. 54-68 
    Details
    ISSN: 1432-0541
    Schlagwort(e): Computational geometry ; Ray-shooting ; Triangulation
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Informatik , Mathematik
    Notizen: Abstract LetP be a simple polygon withn vertices. We present a simple decomposition scheme that partitions the interior ofP intoO(n) so-called geodesic triangles, so that any line segment interior toP crosses at most 2 logn of these triangles. This decomposition can be used to preprocessP in a very simple manner, so that any ray-shooting query can be answered in timeO(logn). The data structure requiresO(n) storage andO(n logn) preprocessing time. By using more sophisticated techniques, we can reduce the preprocessing time toO(n). We also extend our general technique to the case of ray shooting amidstk polygonal obstacles with a total ofn edges, so that a query can be answered inO(√ logn) time.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01377183
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  • 3
    Digitale Medien
    Digitale Medien
    Parallel computational geometry (1988)
    Springer
    Algorithmica 3 (1988), S. 293-327 
    Details
    ISSN: 1432-0541
    Schlagwort(e): Parallel algorithms ; Computational geometry ; Data structures
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Informatik , Mathematik
    Notizen: Abstract We present efficient parallel algorithms for several basic problems in computational geometry: convex hulls, Voronoi diagrams, detecting line segment intersections, triangulating simple polygons, minimizing a circumscribing triangle, and recursive data-structures for three-dimensional queries.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01762120
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