B-spline bases for unequally smooth quadratic spline spaces on non-uniform criss-cross triangulations

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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“…and B 0,j (u 0 , v) = B j (v|V ) (Dagnino et al, , 2012, from (14), (1) and (25), we get (20). Similarly, by setting u = u m in (13), (21) holds.…”

Section: Construction Of the C 1 Quadratic B-spline Surface Interpolamentioning

confidence: 85%

“…and it has been used in many applications (see Lamberti 2008, 2007;Dagnino et al 2012Dagnino et al , 2013Lamberti 2009;Sablonnière 2003a,b;Wang 2001; Li 2004a and references therein). This paper wants also to be a further contribution to the researches on the surface construction based on above blending functions spanning S 1 2 (T mn ).…”

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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“…and B 0,j (u 0 , v) = B j (v|V) [23,24], from ( 1), ( 5) and ( 16), we get (11). Similarly, by setting u = u m+1 in (4), since i R+1 = m + 1, ( 12) follows.…”

Section: S(umentioning

confidence: 94%

Quadratic B-Spline Surfaces with Free Parameters for the Interpolation of Curve Networks

Lamberti

Remogna

2022

Mathematics

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In this paper, we propose a method for constructing spline surfaces interpolating a B-spline curve network, allowing the presence of free parameters, in order to model the interpolating surface. We provide a constructive algorithm for its generation in the case of biquadratic tensor product B-spline surfaces and bivariate B-spline surfaces on criss-cross triangulations. Finally, we present graphical results.

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“…The properties of such spline spaces are studied in [29]. In particular, we recall that the dimension of…”

Section: Generalization To Unequally Smooth Bivariate Quadratic Splinmentioning

confidence: 99%

NURBS on Criss-cross Triangulations and Applications

Cravero¹,

Dagnino²,

Remogna³

2016

AAN

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In this paper we consider and analyse NURBS based on bivariate quadratic B-splines on criss-cross triangulations of the parametric domain Ω0 = [0, 1] × [0, 1], presenting their main properties, showing their performances to exactly construct quadric surfaces and reporting some applications related to the modeling of objects. Moreover, we propose applications to the numerical solution of partial differential equations, with mixed boundary conditions on a given physical domain Ω, by using three different spline methods to set the prescribed Dirichlet boundary conditions.

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B-spline bases for unequally smooth quadratic spline spaces on non-uniform criss-cross triangulations

Cited by 11 publications

References 6 publications

Curve network interpolation by C 1 quadratic B-spline surfaces

Curve network interpolation by C 1 quadratic B-spline surfaces

Quadratic B-Spline Surfaces with Free Parameters for the Interpolation of Curve Networks

NURBS on Criss-cross Triangulations and Applications

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