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  • subdivision  (2)
  • arbitrary topology  (1)
  • 1
    Electronic Resource
    Electronic Resource
    Smoothness of subdivision surfaces at extraordinary points (1998)
    Springer
    Advances in computational mathematics 9 (1998), S. 377-389 
    Details
    ISSN: 1572-9044
    Keywords: subdivision ; extraordinary points ; regular G k-surfaces ; matrix iteration
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A stationary subdivision scheme such as Catmull and Clark's is described by a matrix iteration around an extraordinary point. We show how higher order smoothness of a limiting surface obtained by a stationary subdivision algorithm for tri- or quadrilateral nets depends on the spectral properties of the matrix and give necessary and sufficient conditions. The results are also useful to construct subdivision algorithms for surfaces of any smoothness order at extraordinary points.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1018945708536
    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
    Degree estimates for C k‐piecewise polynomial subdivision surfaces (1999)
    Springer
    Advances in computational mathematics 10 (1999), S. 209-217 
    Details
    ISSN: 1572-9044
    Keywords: subdivision ; piecewise polynomial surface ; arbitrary topology ; extraordinary point
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Piecewise polynomial subdivision surfaces are considered which consist of tri‐ or quadrilateral patches in a mostly regular arrangement with finitely many irregularities. A sharp estimate on the lowest possible degree of the polynomial patches is given. It depends on the smoothness and flexibility of the underlying subdivision scheme.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1018922530826
    Library Location Call Number Volume/Issue/Year Availability
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    Paper (German National Licenses)
    Fulltext
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