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  • 1
    Electronic Resource
    Electronic Resource
    An improved technique for output-sensitive hidden surface removal (1994)
    Springer
    Algorithmica 11 (1994), S. 469-484 
    Details
    ISSN: 1432-0541
    Keywords: Computational geometry ; Hidden surface removal ; Ray shooting
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract We derive a new output-sensitive algorithm for hidden surface removal in a collection ofn triangles, viewed from a pointz such that they can be ordered in an acyclic fashion according to their nearness toz. Ifk is the combinatorial complexity of the outputvisibility map, then we obtain a sophisticated randomized algorithm that runs in (randomized) timeO(n4/3 log2.89 n +k 3/5 n 4/5 + δ for anyδ 〉 0. The method is based on a new technique for tracing the visible contours using ray shooting.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01293267
    Library Location Call Number Volume/Issue/Year Availability
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Triangles in space or building (and analyzing) castles in the air (1990)
    Springer
    Combinatorica 10 (1990), S. 137-173 
    Details
    ISSN: 1439-6912
    Keywords: 51-04 ; 52 A 37 ; 68 R 05
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We show that the total combinatorial complexity of all non-convex cells in an arrangement ofn (possibly intersecting) triangles in 3-space isO(n 7/3 logn) and that this bound is almost tight in the worst case. Our bound significantly improves a previous nearly cubic bound of Pach and Sharir. We also present a (nearly) worst-case optimal randomized algorithm for calculating a single cell of the arrangement and an alternative less efficient, but still subcubic algorithm for calculating all non-convex cells, analyze some special cases of the problem where improved bounds (and faster algorithms) can be obtained, and describe applications of our results to translational motion planning for polyhedra in 3-space.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02123007
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    Paper (German National Licenses)
    Fulltext
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