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Keywords
(5)
Approximation Scheme
Curves and Surfaces
Point of View
Satisfiability
Subdivision Scheme
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Solving Bezoutlike polynomial equations for the design of interpolatory subdivision schemes
Solving Bezoutlike polynomial equations for the design of interpolatory subdivision schemes,10.1145/1837934.1837983,Costanza Conti,Luca Gemignani,Luc
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Solving Bezoutlike polynomial equations for the design of interpolatory subdivision schemes
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Citations: 1
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Costanza Conti
,
Luca Gemignani
,
Lucia Romani
Subdivision schemes are nowadays customary in curve and surface modeling. In this paper the problem of designing interpolatory subdivision schemes is considered. The idea is to modify a given approximating
subdivision scheme
just enough to satisfy the interpolation requirement. From an algebraic
point of view
this leads to the solution of a generalized Bezout polynomial equation possibly involving more than two polynomials. By exploiting the matrix counterpart of this equation it is shown that smalldegree solutions can be generally found by inverting an associated structured matrix of Toeplitzlike form. If the approximating scheme is defined in terms of a free parameter, then the inversion can be performed by numericsymbolic methods.
Conference:
International Symposium on Symbolic and Algebraic Computation  ISSAC
, pp. 251256, 2010
DOI:
10.1145/1837934.1837983
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Citation Context
(1)
... order of the interpolatory scheme we construct is higher than the approximation order of the given noninterpolatory scheme (see [13] for more details on this matter and Fig. 1 for a numerical comparison of the limit curves obtained by the schemes presented in Section 5). Yet, in case of non binary schemes, due to the proposed construction the increment of the support size of the interpolatory masks is less significant as shown in [
8
]...
Costanza Conti
,
et al.
From approximating to interpolatory nonstationary subdivision schemes...
References
(12)
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(
Citations: 22
)
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,
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(
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)
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,
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Journal:
Constructive Approximation  CONSTR APPROX
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Subdivision schemes in geometric modelling
(
Citations: 95
)
Nira Dyn
,
David Levin
Journal:
Acta Numerica
, vol. 11, 2002
Subdivision of Boxsplines
(
Citations: 5
)
M. A. Sabin
Published in 2002.
A Method for Constructing Interpolatory Subdivision Schemes and Blending Subdivisions
(
Citations: 10
)
Guiqing Li
,
Weiyin Ma
Journal:
Computer Graphics Forum  CGF
, vol. 26, no. 2, pp. 185201, 2007
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Citations
(1)
From approximating to interpolatory nonstationary subdivision schemes with the same generation properties
(
Citations: 1
)
Costanza Conti
,
Luca Gemignani
,
Lucia Romani
Journal:
Advances in Computational Mathematics  Adv. Comput. Math.
, pp. 125