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  • subdivision  (2)
  • Triangular splines  (1)
  • 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
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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
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    On triangular splines (1987)
    Springer
    Constructive approximation 3 (1987), S. 157-167 
    Details
    ISSN: 1432-0940
    Keywords: Splines ; Triangular splines ; Multivariate splines ; Algorithms ; 65D07 (14J25,41A15+63)
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This paper is concerned with some efficient algorithms for the calculation of triangular splines. Their development is based on some different interpretations of a construction given by Malcolm Sabin in 1977 [Sabin 1977].
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01890561
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    Paper (German National Licenses)
    Fulltext
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