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 Giulio Casciola

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Average citations per article3.35
Citation Count77
Publication count23
Publication years1984-2017
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23 results found Export Results: bibtexendnoteacmrefcsv

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1
March 2017 Applied Mathematics and Computation: Volume 296 Issue C, March 2017
Publisher: Elsevier Science Inc.
Bibliometrics:
Citation Count: 0

Given a number of Extended Chebyshev (EC) spaces on adjacent intervals, all of the same dimension, we join them via convenient connection matrices of the maximum order. The global space is called a Piecewise Extended Chebyshev (PEC) space. In such a space one can count the total number of zeroes ...
Keywords: (Piecewise) generalised derivatives, 65D17, Geometric design, 65D05, Bernstein-type bases, Blossoms, Connection matrices, Extended Chebyshev (piecewise) spaces

2
August 2016 Computer Aided Geometric Design: Volume 46 Issue C, August 2016
Publisher: Elsevier Science Publishers B. V.
Bibliometrics:
Citation Count: 0

In CAGD the design of a surface that interpolates an arbitrary quadrilateral mesh is definitely a challenging task. The basic requirement is to satisfy both criteria concerning the regularity of the surface and aesthetic concepts.With regard to aesthetic quality, it is well known that interpolatory methods often produce shape artifacts ...
Keywords: Non-uniform parametrization, Surface, Arbitrary topology, Local interpolation, Quadrilateral mesh, Curve network

3
August 2014 Advances in Computational Mathematics: Volume 40 Issue 4, August 2014
Publisher: Springer-Verlag New York, Inc.
Bibliometrics:
Citation Count: 3

In this paper we consider the problem of designing piecewise polynomial local interpolants of non-uniformly spaced data. We provide a constructive approach that, for any assigned degree of polynomial reproduction, continuity order, and support width, allows for generating the fundamental spline functions of minimum degree having the desired properties. Finally, ...
Keywords: 65D17, 65D05, 65D07, Local interpolation, Minimum degree, Design parameters, Non-uniform knot partition, Spline

4
November 2013 Computer-Aided Design: Volume 45 Issue 11, November, 2013
Publisher: Butterworth-Heinemann
Bibliometrics:
Citation Count: 1

The main roadblock that has limited the usage of subdivision surfaces in computer-aided design (CAD) systems is the lack of quality and precision that a model must achieve for being suitable in the engineering and manufacturing phases of design. The second roadblock concerns the integration into the modeling workflows, that, ...
Keywords: B-rep representation, Local correction, Subdivision surfaces, Computer-aided design

5
May 2013 Computer Aided Geometric Design: Volume 30 Issue 4, May, 2013
Publisher: Elsevier Science Publishers B. V.
Bibliometrics:
Citation Count: 2

In this paper we exploit a class of univariate, C^1 interpolating four-point subdivision schemes featured by a piecewise uniform parameterization, to define non-tensor product subdivision schemes interpolating regular grids of control points and generating C^1 limit surfaces with a better behavior than the well-established tensor product subdivision and spline surfaces. ...
Keywords: Non-uniform parameterization, Interpolation, Non-tensor product surfaces, Subdivision

6
March 2013 Journal of Computational and Applied Mathematics: Volume 240, March, 2013
Publisher: Elsevier Science Publishers B. V.
Bibliometrics:
Citation Count: 5

This paper presents a general framework for the construction of piecewise-polynomial local interpolants with given smoothness and approximation order, defined on non-uniform knot partitions. We design such splines through a suitable combination of polynomial interpolants with either polynomial or rational, compactly supported blending functions. In particular, when the blending functions ...
Keywords: Blending, Local interpolation, Rational functions, Non-uniform knot partition, Polynomial splines

7
June 2011 Journal of Computational and Applied Mathematics: Volume 235 Issue 16, June, 2011
Publisher: Elsevier Science Publishers B. V.
Bibliometrics:
Citation Count: 5

Starting from a well-known construction of polynomial-based interpolatory 4-point schemes, in this paper we present an original affine combination of quadratic polynomial samples that leads to a non-uniform 4-point scheme with edge parameters. This blending-type formulation is then further generalized to provide a powerful subdivision algorithm that combines the fairing ...
Keywords: Features control, Interpolation, Subdivision, Non-uniform parameterization, Arbitrary point insertion

8
April 2010 Applied Mathematics and Computation: Volume 216 Issue 4, April, 2010
Publisher: Elsevier Science Inc.
Bibliometrics:
Citation Count: 0

In this paper we show that the refinement rules of interpolating and approximating univariate subdivision schemes with odd-width masks of finite support can be derived ones from the others by simple operations on the mask coefficients. These operations are formalized as multiplication/division of the associated generating functions by a proper ...
Keywords: Interpolation, Uniform univariate subdivision, Generating function, Link Polynomial Factorization (LPF), Approximation

9
February 2010 Journal of Mathematical Imaging and Vision: Volume 36 Issue 2, February 2010
Publisher: Kluwer Academic Publishers
Bibliometrics:
Citation Count: 1

This paper investigates the image interpolation problem, where the objective is to improve the resolution of an image by dilating it according to a given enlargement factor. We present a novel interpolation method based on Radial Basis Functions (RBF) which recovers a continuous intensity function from discrete image data samples. ...
Keywords: Radial basis function, Structure tensor, Image enlargement, Image interpolation

10
October 2009 Applied Mathematics and Computation: Volume 215 Issue 3, October, 2009
Publisher: Elsevier Science Inc.
Bibliometrics:
Citation Count: 3

Ternary subdivision schemes compare favorably with their binary analogues because they are able to generate limit functions with the same (or higher) smoothness but smaller support. In this work we consider the two issues of local tension control and conics reproduction in univariate interpolating ternary refinements. We show that both ...
Keywords: Combined subdivision scheme, Conic section, Non-stationarity, Tension control, Univariate ternary refinement, Interpolation

11
January 2009 Journal of Computational and Applied Mathematics: Volume 223 Issue 2, January, 2009
Publisher: Elsevier Science Publishers B. V.
Bibliometrics:
Citation Count: 0

While the mathematics of constrained least-squares data-fitting is neat and clear, implementing a rapid and fully automatic fitter that is able to generate a fair curve approximating the shape described by an ordered sequence of distinct data subject to certain interpolation requirements, is far more difficult. The novel idea presented ...
Keywords: 65D17, 90C30, 90C51, Automatic selection of weights, Constrained approximation, Least-squares data-fitting, 41A20, 41A29, 65D10, Interior-point Newton-type method, Rational Hermite interpolation

12
May 2007 Computer Aided Geometric Design: Volume 24 Issue 4, May, 2007
Publisher: Elsevier Science Publishers B. V.
Bibliometrics:
Citation Count: 16

In this paper we present a non-stationary 4-point ternary interpolatory subdivision scheme which provides the user with a tension parameter that, when increased within its range of definition, can generate C^2-continuous limit curves showing considerable variations of shape. As a generalization we additionally propose a locally-controlled C^2-continuous subdivision scheme, which ...
Keywords: Interpolation, Curves, Locality, Subdivision, Tension control, Ternary

13
January 2007 Computer Aided Geometric Design: Volume 24 Issue 1, January, 2007
Publisher: Elsevier Science Publishers B. V.
Bibliometrics:
Citation Count: 28

In this paper we propose a non-stationary C^1-continuous interpolating 4-point scheme which provides users with a single tension parameter that can be either arbitrarily increased, to tighten the limit curve towards the piecewise linear interpolant between the data points, or appropriately chosen in order to represent elements of the linear ...
Keywords: Conics reproduction, Interpolation, Curves, Locality, Subdivision, Tension control

14
April 2006 Computers & Mathematics with Applications: Volume 51 Issue 8, April, 2006
Publisher: Pergamon Press, Inc.
Bibliometrics:
Citation Count: 7

In this paper we deal with the problem of reconstructing surfaces from unorganized sets of points, while capturing the significant geometry details of the modelled surface, such as edges, flat regions, and corners. This is obtained by exploiting the good approximation capabilities of the radial basis functions (RBF), the local ...

15
April 2005 Journal of Computational and Applied Mathematics: Volume 176 Issue 2, 15 April 2005
Publisher: Elsevier Science Publishers B. V.
Bibliometrics:
Citation Count: 0

In this paper we describe a new way to design rational parametric surfaces defined on spherical triangles which are useful for modelling in a spherical environment. These surfaces can be seen as single-valued functions in spherical coordinates.
Keywords: rational triangular Bézier patch, single-valued surfaces, spherical coordinates, geometric modelling

16
April 2005 Journal of Computational and Applied Mathematics: Volume 176 Issue 2, 15 April 2005
Publisher: Elsevier Science Publishers B. V.
Bibliometrics:
Citation Count: 1

In this paper we describe a new way to design rational parametric surfaces defined on spherical triangles which are useful for modelling in a spherical environment. These surfaces can be seen as single-valued functions in spherical coordinates.
Keywords: Rational triangular Bézier patch, Single-valued surfaces, Spherical coordinates, Geometric modelling

17
December 2000 Recent trends in numerical analysis
Publisher: Nova Science Publishers, Inc.
Bibliometrics:
Citation Count: 0

Keywords: rendering, solid modeling, trimmed NURBS, surface modeling

18
April 1998 Computer Aided Geometric Design: Volume 15 Issue 4, April 1998
Publisher: Elsevier Science Publishers B. V.
Bibliometrics:
Citation Count: 2

Keywords: degree elevation, curves in polar coordinates, rational curves

19
February 1997 Computer Aided Geometric Design: Volume 14 Issue 2, Feb. 1997
Publisher: Elsevier Science Publishers B. V.
Bibliometrics:
Citation Count: 0

Keywords: recurrence relation, rational B-splines

20
August 1995 Parallel Computing: Volume 21 Issue 8, Aug. 1995
Publisher: Elsevier Science Publishers B. V.
Bibliometrics:
Citation Count: 0

Keywords: geometric modelling, parallel graphics, performance evaluation



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