Pseudo-tensor product interpolation and blending with families of univariate schemes

Bos, Len; Grabenstetter, James E.; Šalkauskas, K.

doi:10.1016/0167-8396(95)00036-4

Cited by 6 publications

(9 citation statements)

References 8 publications

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“…For instance a classical one is based on blending-function methods (Barnhill, 1976;Bos et al, 1996;Delvos and Schempp, 1989;Gordon, 1969Gordon, , 1971Gordon, , 1993. Some other ones consist in the interpolation of the curve mesh either by a smooth regularly parametrized surface with one polynomial piece per facet (Peters, 1991) or by subdivision schemes (Conti and Dyn, 2005).…”

Section: Introductionmentioning

confidence: 99%

Curve network interpolation by C 1 quadratic B-spline surfaces

Dagnino

Lamberti

Remogna

2015

Computer Aided Geometric Design

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Please cite this article in press as: Dagnino, C., et al. Curve network interpolation by C 1 quadratic B-spline surfaces. Comput. Aided Geom. Des. (2015), http://dx. Highlights• Interpolation of a B-spline curve network by a surface based on C 1 quadratic B-splines on criss-cross triangulations.• Proof of the existence and uniqueness of the surface and constructive algorithm for its generation.• Numerical and graphical results and comparisons with other spline methods. AbstractIn this paper we investigate the problem of interpolating a B-spline curve network, in order to create a surface satisfying such a constraint and defined by blending functions spanning the space of bivariate C 1 quadratic splines on criss-cross triangulations. We prove the existence and uniqueness of the surface, providing a constructive algorithm for its generation. We also present numerical and graphical results and comparisons with other methods.

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Section: Introductionmentioning

confidence: 99%

Curve network interpolation by C 1 quadratic B-spline surfaces

Dagnino

Lamberti

Remogna

2015

Computer Aided Geometric Design

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“…In the two-dimensional (2-D) case, the transfinite interpolant is given by (18) and the interpolation errors are (19) The second-level interpolant can now be written as (20) where the second-level interpolation must satisfy (21) in the version and (22) in the version.…”

Section: Transfinite Methods Of Momentsmentioning

confidence: 99%

“…Let be the interpolation error of this method. Since is in this case a zero-order polynomial approximation, for a cell of size the order of is thus given asymptotically when by (see (19)):…”

Section: Application To the Scattering By A Dielectric Cylindermentioning

confidence: 99%

“…Thanks to the first equation of (19), with the order of accuracy of the first-level interpolation is The second-level projectors have to be chosen to not degrade this accuracy.…”

Section: B Transfinite Versionsmentioning

confidence: 99%

“…Rapidly it has been adapted and applied to the problem of curvilinear mesh generation for finite element analysis [15] and it is now become a standard method for surface and volume modeling (see [17] for an introduction to this technique or [19], [20] and references therein for its last developments). But the use of the TFI has not been restricted to CAD.…”

Section: Introductionmentioning

confidence: 99%

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The use of the transfinite interpolation in the method of moments applied to electromagnetic scattering by dielectric cylinders

Doncker

2000

IEEE Trans. Antennas Propagat.

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The method of moments (MoM) solution of electromagnetic scattering presents two major numerical difficulties: the number of unknowns and the computation time necessary to calculate the matrix elements. To circumvent these problems, a MoM using the transfinite interpolation and a reduced integration scheme is presented here. The so-called and versions of the new method are applied to the scattering of an electromagnetic wave by an infinite dielectric cylinder (TM case) in the Richmond's formulation. The transfinite and classical methods are compared in terms of the convergence rates of the radar cross section and of the total electric field inside the dielectric. The results confirm the superiority of the new schemes as predicted by the theory.

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