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  • Centroid  (1)
  • Triangulation  (1)
  • 1
    Electronic Resource
    Electronic Resource
    An optimal algorithm for the on-line closest-pair problem (1994)
    Springer
    Algorithmica 12 (1994), S. 18-29 
    Details
    ISSN: 1432-0541
    Keywords: Computational geometry ; Closest pair ; Point location ; Centroid ; Amortization
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract We give an algorithm that computes the closest pair in a set ofn points ink-dimensional space on-line, inO(n logn) time. The algorithm only uses algebraic functions and, therefore, is optimal. The algorithm maintains a hierarchical subdivision ofk-space into hyperrectangles, which is stored in a binary tree. Centroids are used to maintain a balanced decomposition of this tree.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01377181
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Ray shooting in polygons using geodesic triangulations (1994)
    Springer
    Algorithmica 12 (1994), S. 54-68 
    Details
    ISSN: 1432-0541
    Keywords: Computational geometry ; Ray-shooting ; Triangulation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: 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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01377183
    Library Location Call Number Volume/Issue/Year Availability
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    Paper (German National Licenses)
    Fulltext
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