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  • 1
    Electronic Resource
    Electronic Resource
    Computing the volume of the union of spheres (1988)
    Springer
    The visual computer 3 (1988), S. 323-328 
    Details
    ISSN: 1432-2315
    Keywords: Union of Spheres ; Volumes ; Laguerre Voronoid diagram ; Power diagram
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract OnO(n 2) exact algorithm is given for computing the volume of a set ofn spheres in space. The algorithm employs the Laguerre Voronoi (power) diagram and a method for computing the volume of the intersection of a simplex and a sphere exactly. We give a new proof of a special case of a conjecture, popularized by Klee, concerning the change in volume as the centres of the spheres become further apart.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01901190
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Visibility of disjoint polygons (1986)
    Springer
    Algorithmica 1 (1986), S. 49-63 
    Details
    ISSN: 1432-0541
    Keywords: Computational geometry ; Computer graphics ; Robotics ; Visibility ; Hidden-line Elimination ; Visibility graph ; Shortest path
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract Consider a collection of disjoint polygons in the plane containing a total ofn edges. We show how to build, inO(n 2) time and space, a data structure from which inO(n) time we can compute the visibility polygon of a given point with respect to the polygon collection. As an application of this structure, the visibility graph of the given polygons can be constructed inO(n 2) time and space. This implies that the shortest path that connects two points in the plane and avoids the polygons in our collection can be computed inO(n 2) time, improving earlierO(n 2 logn) results.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01840436
    Library Location Call Number Volume/Issue/Year Availability
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    Paper (German National Licenses)
    Fulltext
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