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  • 1
    Electronic Resource
    Electronic Resource
    Surface Reconstruction by Voronoi Filtering (1999)
    Springer
    Discrete & computational geometry 22 (1999), S. 481-504 
    Details
    ISSN: 1432-0444
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract. We give a simple combinatorial algorithm that computes a piecewise-linear approximation of a smooth surface from a finite set of sample points. The algorithm uses Voronoi vertices to remove triangles from the Delaunay triangulation. We prove the algorithm correct by showing that for densely sampled surfaces, where density depends on a local feature size function, the output is topologically valid and convergent (both pointwise and in surface normals) to the original surface. We briefly describe an implementation of the algorithm and show example outputs.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/PL00009475
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Largest Placement of One Convex Polygon Inside Another (1998)
    Springer
    Discrete & computational geometry 19 (1998), S. 95-104 
    Details
    ISSN: 1432-0444
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract. We show that the largest similar copy of a convex polygon P with m edges inside a convex polygon Q with n edges can be computed in O(mn 2 log n) time. We also show that the combinatorial complexity of the space of all similar copies of P inside Q is O(mn 2 ) , and that it can also be computed in O(mn 2 log n) time.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/PL00009337
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    Regression Depth and Center Points (2000)
    Springer
    Discrete & computational geometry 23 (2000), S. 305-323 
    Details
    ISSN: 1432-0444
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract. We show that, for any set of n points in d dimensions, there exists a hyperplane with regression depth at least $\lceil n/(d+1)\rceil$ , as had been conjectured by Rousseeuw and Hubert. Dually, for any arrangement of n hyperplanes in d dimensions there exists a point that cannot escape to infinity without crossing at least $\lceil n/(d+1)\rceil$ hyperplanes. We also apply our approach to related questions on the existence of partitions of the data into subsets such that a common plane has nonzero regression depth in each subset, and to the computational complexity of regression depth problems.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/PL00009502
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    Paper (German National Licenses)
    Fulltext
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