Recent Publications

Journals

  • Correction to: Fundamental functions for local interpolation of quadrilateral meshes with extraordinary vertices (with C.Beccari and L.Romani), Annali dell'Università di Ferrara, (2023).
  • Fundamental functions for local interpolation of quadrilateral meshes with extraordinary vertices (with C.Beccari and L.Romani), Annali dell'Università di Ferrara, 68, 369-383 (2022).
  • A practical method for computing with piecewise Chebyshevian splines (with C.Beccari and L.Romani), Journal of Computational and Applied Mathematics, Vol.406, 2022. DOI link
  • Stable numerical evaluation of multi-degree B-splines (with C.Beccari), Journal of Computational and Applied Mathematics, Vol.400, January 2022. DOI link
  • Matrix representations for multi-degree B-splines (with C.Beccari), Journal of Computational and Applied Mathematics, Vol.381, January 2021, pp.1-18. DOI link
  • Dimension elevation is not always corner-cutting (with C.Beccari and Marie-Laurance Mazure), Applied Mathematics Letters, Vol. 109, November 2020. DOI link
  • Critical Length: An alternative approach (with C.Beccari and Marie-Laurance Mazure), Journal of Computational and Applied Mathematics, Vol. 370, 15 May 2020. DOI link
  • A Cox-de Boor-type recurrence relation for C1 multi-degree splines (with C.Beccari), Computer Aided Geometric Design, Vol.75, November 2019, pp. DOI link
  • Design or not design? A numerical characterisation for piecewise Chebyshevian splines (with C.Beccari and Marie-Laurance Mazure), Numerical Algorithms, Vol. 81, (1) May 2019, pp.1-31. DOI link
  • An extended B-Rep solid modeling kernel integrating mesh and NURBS faces (with G.Ferrari, R.Raffaeli and S.Morigi), Computer-Aided Design and Applications, Vol.15, No. 5 2018, 697-706. DOI link
  • On multi-degree splines (with C.Beccari and S.Morigi), Computer Aided Geometric Design, Vol.58, November 2017, pp.8-23. DOI link
  • Piecewise Extended Chebyshev spaces: A numerical test for design (with C.Beccari and Marie-Laurance Mazure), Applied Mathematics and Computation, Vol.296, (2017), pp.239-256. DOI link
  • High quality local interpolation by composite parametric surfaces (with M.Antonelli,C.Beccari), Computer Aided Geometric Design, vol.46, pp.103-124 (August 2016). DOI link
  • A general framework for the construction of piecewise-polynomial local interpolants of minimum degree (with M.Antonelli,C.Beccari), Advances in Computational Mathematics, vol.40 no.4 (2014), pp.945-976. DOI link
  • Subdivision surfaces integrated in a CAD system (with M.Antonelli,C.Beccari,R.Ciarloni and S.Morigi), Computer Aided Design, no.45 (2013), pp. 1294-1311. DOI link
  • Non-uniform non-tensor product local interpolatory subdivision surfaces (with C.Beccari and L.Romani), Computer Aided Geometric Design, 30 (2013), pp.357-373. DOI link
  • Construction and characterization of non-uniform local interpolating polynomial splines (with C.Beccari and L.Romani), Journal of Computational and Applied Mathematics, Vol.240, (2013), pp.5-19. DOI link
  • Non-uniform interpolatory curve subdivision with edge parameters built upon compactly supported fundamental splines (with C.Beccari and L.Romani), BIT Numerical Mathematics, 51(4) (2011), pp. 781-808.
  • Polynomial-based non-uniform interpolatory subdivision with features control (with C.Beccari and L.Romani), Journal of Computational and Applied Mathematics, 25(16) (2011), pp.4754-4769.
  • A unified framework for interpolating and approximating univariate subdivision (with C.Beccari and L.Romani), Applied Mathematics and Computation, 216 (2010), pp.1169-1180.
  • Shape controlled interpolatory ternary subdivision (with C.Beccari and L.Romani), Applied Mathematics and Computation, 215 (2009), pp. 916-927.
  • Edge-driven image interpolation using Adaptive Anisotropic Radial basis Functions (with L.B.Montefusco and S.Morigi), Journal of Mathematical Imaging and Vision, vol. DOI 10.1007/s10851-009-0176-8. (2008). DOI link
  • A Newton-type method for constrained least-square data-fitting with easy-to-control rational curves (with L.Romani), Journal of Computational and Applied Mathematics, 223 (2009), pp. 672-692. DOI link
  • The regularizing properties of anisotropic Radial Basis Functions (with L.B.Montefusco, S.Morigi), Applied Mathematics and Computation, 190, 2, 1050-1062 (2007) DOI link
  • An interpolating 4-point C^2 ternary non stationary subdivision scheme with tension control (with C.Beccari and L.Romani), Computer Aided Geometric Design, 24, 210-219 (2007).
  • A non-stationary uniform tension controlled interpolating 4-point scheme reproducing conics (with C.Beccari and L.Romani), Computer Aided Geometric Design, 24, 1-9 (2007).
  • The mixed directional difference-summation algorithm for generating the Bezier net of a trivariate four-direction Box-spline (with E.Franchini and L.Romani)Numerical Algorithms, 43, 75-98 (2006).
  • A Fast Bivariate Function Rendering for Small Devices (with A.Amoroso)International Journal of Computers and Applications, (2006).
  • Shape Preserving Surface Reconstruction using Locally Anisotropic RBF Interpolants (with D.Lazzaro, L.B.Montefusco, S.Morigi), Computers and Mathematics with Applications, 51, 8, 1185-1198 (2006). pdf file
  • Inverse Spherical Surfaces (with S.Morigi) Journal of Computational and Applied Mathematics 176 (2005). pdf file
  • Fast surface reconstruction and hole filling using Radial Basis Functions (with D.Lazzaro, L.B.Montefusco, S.Morigi), Numerical AlgorithmsVol.39, No.1-3 (2005) ISSN: 1017-1398. pdf file
  • An Application of Fast Factorization Algorithms in Computer Aided Geometric Design (with F.Fabbri and L.B.Montefusco) Linear Algebra and its Applications 366 (2003). pdf file
  • Inverse Circular Curves (with S.Morigi) International Journal of Shape Modeling Vol.8, no.1 (2002). pdf file
  • The trimmed NURBS age (with S.Morigi) Advances in Theory of Computational Mathematics: Recent Trends in Numerical Analysis Vol.3, Ed. D.Trigiante, Nova Science Publishers, Inc., (2000). pdf file
  • xcmodel: an aCADemic system (with S.Morigi) Annali Universita` di Ferrara Sez. VII - Sc.Mat., Supplemento al Vol.XLV (2000). pdf file
  • Degree elevation for p-Bezier curves (with S.Morigi and J.Sanchez-Reyes)Computer Aided Geometric Design,Vol.15 (1998). pdf file
  • A recurrence relation for rational B-splines Computer Aided Geometric Design. Vol.14, (1997). pdf file
  • Reparametrization of NURBS curves (with S.Morigi) International Journal Shape Modelling Vol. 2, No.2&3, (1996). pdf file
  • Graphics in parallel computation for rendering 3D modelled scenes (with S.Morigi) Parallel Computing , 21 (1995).

    • Conferences

  • On the construction of compactly supported fundamental functions for interpolation via polynomial blends (with C.Beccari and L.Romani), International Conference on Approximation Theory and Applications 18-22 June 2023 Cetraro - Italy
  • Multi-degree B-splines and their stable evaluation (with C.Beccari), SMART 2022-Third International Conference on Subdivision Geometric and Algebraic Methods, Isogeometric Analysis and Refinability in Italy Rimini, September 20-24, 2022
  • Compactly supported fundamental functions for local interpolation over arbitrary topology meshes (with C.Beccari and L.Romani), MAIA 2019-Multivariate Approximation and Interpolation with Applications 26-30 August 2019 ESI - Vienna, AUSTRIA (Poster Session)
  • Critical Length an alternative approach (with C.Beccari and M.L.Mazure), Curves and Surfaces 2018 Arcachon, France June 28 - July 4, 2018
  • An extended solid modelling kernel for combined analytic and mesh B-Rep faces (with G.Ferrari, R.Raffaele, S.Morigi), Cad'17 Conference, Japan, August, 2017
  • Geometrically continuous piecewise (quasi) Chebyshevian splines (with C.Beccari), NETNA 2015 New Trends in Numerical Analysis Falerna (CZ) June 20, 2015
  • Computation and modeling in spaces of generalized splines (with M.Antonelli, C.Beccari and L.Romani), SMART 2014 Certosa di Pontignano September 28, 2014
  • A local method for the construction of high-quality interpolatory surfaces of arbitrary topology (with M.Antonelli and C.Beccari), eighth International Conference Curves and Surfaces, Paris (France) June 12-18, 2014.
  • Generalized B-spline bases for design: a simple and constructive approach, (with M.Antonelli, C.Beccari and L.Romani), eighth International Conference Curves and Surfaces, Paris (France) June 12-18, 2014.
  • Subdivision surfaces integrated in a CAD system through parameterization and local correction, (with M.Antonelli and C.Beccari), IMACS 2013 - Track Geometrical Computing and Modeling, San Lorenzo de El Escorial, Spagna, 26-30 agosto 2013.
  • An approach for the integration of subdivision surfaces in a hybrid CAD system., (with M.Antonelli, C.Beccari and S.Morigi), SGP 2013 (Symposium on Geometry Processing) (poster), Genova, 3-5 luglio, 2013
  • An effective integration of subdivision surfaces in a hybrid computer-aided design system., (with M.Antonelli, C.Beccari and S.Morigi), SGP 2013 (Symposium on Geometry Processing), Genova, 3-5 luglio, 2013
  • A local method for high-quality interpolation of arbitrary meshes and curve networks, (with M.Antonelli and C.Beccari), International Workshop Multivariate Approximation and Interpolation with Applications, Erice (Trapani) September 25, 2013.
  • Interpolatory subdivision surfaces with augmented parameterization and their analysis, (with C.Beccari and L.Romani), 3rd Dolomites Workshop on Constructive Approximation and Applications, Alba di Canazei (Trento, Italy), September 9-14, 2012.
  • Subdivision Surfaces for CAD: integration through parameterization and local correction, (with M.Antonelli, C.Beccari and S.Morigi), Workshop New trends in subdivision and related applications, Milan-Bicocca September 4-7-2012.
  • Interpolatory subdivision surfaces with augmented parameterization and their analysis, (with C.Beccari and L.Romani), Workshop New trends in subdivision and related applications, Milan-Bicocca September 4-7-2012.
  • A general framework for the construction of piecewise local interpolants, (with C.Beccari and M.Antonelli), eighth International Conference on Mathematical Methods for Curves and Surfaces, Oslo (Norway) June 28 - July 3, 2012.
  • Non-uniform local interpolatory subdivision surfaces for regular quadrilateral meshes (with C.Beccari and L.Romani), (2011) Seventh International Conference on Curves and Surfaces, International Symposium in Approximation Theory, Vanderbilt University, Nashville, Tennessee, may 17-21, 2011
  • A blending based approach to interpolatory subdivision with shape parameters, (with C.Beccari and L.Romani), (2010) Seventh International Conference on Curves and Surfaces, Avignon (France) June 24 - 30, 2010.
  • Polynomial-based non-uniform interpolatory subdivision with features control, (with C.Beccari and L.Romani), INdAM Meeting-New Frontiers in CAGD, Bertinoro (FO), Italy (May.17-21, 2010).
  • NULISS: Non Uniform Local Interpolatory Subdivision Surfaces, (with C.Beccari and L.Romani), 14th International Congress on Computational and Applied Mathematics, Antalya, Turkey (Sep.29-Oct.2, 2009).
  • Subdivision Surfaces for CAD, (with C.Beccari), Workshop on Innovative Technologies for Computer Aided Design Systems, Bologna, Italy (May.21, 2009).
  • Interpolatory Surface Subdivision based on Geometric-Driven Parameterizations (with C.Beccari and L.Romani), Minisymposium on New Trends in Numerical Approximation and Applications, SIMAI, (Rome) September 17 2008.
  • Non-Uniform Interpolatory Subdivision Designed from Splines (with C.Beccari and L.Romani), seventh International Conference on Mathematical Methods for Curves and Surfaces, Tonsberg (Norway) June 26 - July 2, 2008.
  • Tension-controlled ternary subdivision (with C. Beccari and L.Romani), (2007) 10th SIAM Conference in Geometric Design and Computing, San Antonio, USA (Nov.4-8, 2007).
  • A Vector Outline Descriptor Using Interpolatory Subdivision Curves (with C.Beccari and L.Romani), (2006) Proceedings of sixth International Conference on Curves and Surfaces, Avignon (France) June 29 - July 5, 2006.
  • Interpolatory Subdivion Curves with Local Shape Control (with C.Beccari and L.Romani), (2005). WSCG 2006 (Winter School of Computer Graphics), Plzen, Czech Republic, Jan. 30-Feb. 3, 2006.
  • Fast 3D Surfaces Rendering Techniques for Small Portable Devices (with A.Amoroso and M.Masotti), Proceeding of Internet and Multimedia Systems and Applications (IMSA 2004) , Acta Press; ISSN: 1482-7905; ISBN: 0-88986-420-9.
  • A piecewise rational quintic Hermite interpolant fou use in CAGD (with L.Romani), Proceeding of The Sixth International Conference on Mathematical Methods for Curves and Surfaces, Tromso (Norway) July 1-6, 2004, Nashboro Press. pdf file
  • Shape Preserving Surface Inpainting: an RBF Approach (with L.B.Montefusco, D.Lazzaro, S.Morigi), SIAM Conference on Geometric Design and Computing, Seattle (U.S.A.) November 9-13, 2003.
  • The conversion matrix between non-uniform B-spline and Bezier representation (with L.Romani), Multivariate Approximation: Theory and Applications, Cancun (Mexico) April 24 -29, 2003.
    also
    A generalized conversion matrix between non-uniform B-spline and Bezier representations with applications in CAGD (with L.Romani), ALMA-DL University of Bologna (2004) Eprint-00000853
  • Modellazione 3D Sculturata Elaborazione e Progettazione Tecnologica, Accademia delle Scienze di Bologna, Bologna, 26 marzo 2003.
  • XCMODEL 3.0 - An Academic Modeling/Rendering System (with R.Sottile), Proceedings of First National Conference of Eurographics Italian Chapter, Milano (Italy) July 11/12, 2002. pdf file
  • Exploting Matrix Structure in Curve Intersection Problems (with F.Fabbri and L.B. Montefusco), Fifth International Conference on Curves and Surfaces, Saint-Malo (France) June 27 - July 3, 2002.
  • Inverse Spherical Surfaces with Applications to Geometric Modelling (with S.Morigi), Fifth International Conference on Curves and Surfaces, Saint-Malo (France) June 27 - July 3, 2002.
  • Rational Interpolants with Tension Parameters (with L.Romani), Proceedings of Fifth International Conference on Curves and Surfaces: Curve and Surface Design, T.Lyche, M-L.Mazure and L.L.Schumaker (Eds.), Nashboro Press (2003). pdf file
  • Curves and Surfaces for Modelling(with S.Morigi), Minisimposium on Approximation of Curves and Surfaces, Firenze, 8-9 giugno 2000.
  • Presentazione del software xcmodel version 2.0, Mostra Matematica, Arte e Tecnologia: da Escher alla Computer Graphics, Bologna, 12/10-3/12 2000. pdf file
  • Ricostruzione di Superfici con Subdivision e Wavelets, Convegno GNIM, Bertinoro, 11-13 dicembre 2000.
  • xcmodel: a system to model and render NURBS curves and surfaces, User's Guide - Version 1.0 Analisi Numerica: Metodi e Software Matematico, Ferrara (2000). pdf file
  • xccurv: the 2D modeller, User's Guide - Version 1.0 Analisi Numerica: Metodi e Software Matematico, Ferrara (2000). pdf file
  • xcsurf: the 3D modeller, User's Guide - Version 1.0 Analisi Numerica: Metodi e Software Matematico, Ferrara (2000). pdf file
  • xcrayt: the scene descriptor, User's Guide - Version 1.0 Analisi Numerica: Metodi e Software Matematico, Ferrara (2000). pdf file
  • xcbool: the object composer, (with G.DeMarco) User's Guide - Version 1.0 Analisi Numerica: Metodi e Software Matematico, Ferrara (2000). pdf file
  • Spline in polar and in Cartesian coordinates (with S.Morigi) Proceedings of Cuves and Surfaces with applications in CAGD , A. LeMeahute, C. Rabut and L.L. Schumaker (Eds.) (1997). pdf file
  • Un Sistema Distribuito per la Modellazione Solida Sculturata Giornate di studio sul Calcolo Parallelo, Lucca 9-10 Dicembre 1996
  • Il problema SSI nella modellazione solida con superfici NURBS (with S.Morigi) Atti dell'Accademia delle Scienze dell'Istituto di Bologna Febbraio (1995). pdf file
  • L'algoritmo PAM nella modellazione con superfici spline in coordinate sferiche (with A.Amoroso) Atti dell'Accademia delle Scienze dell'Istituto di Bologna Febbraio (1995). pdf file
  • Riparametrizzazione di curve NURBS XV Cogresso U.M.I. Padova 11-16 Settembre(1995)
  • Una formula ricorrente per funzioni B-spline razionali Convegno Nazionale di Analisi Numerica Montecatini 27-29 Aprile 1994

    • Technical Reports

  • Stable numerical evaluation of multi-degree B-splines (with C.Beccari), arXiv:2102.03252 - 2021
  • Critical length: an alternative approach (with C.Beccari and M.L.Mazure), arXiv:1904.09253 - 2019
  • On multi-degree splines (with C.Beccari and S.Morigi), arXiv:1709.04998 - 2017
  • Computation and modeling in piecewise Chebyshevian spline spaces (with C.Beccari and L.Romani), arXiv:1611.02068 - 2017
  • Piecewise Extended Chebyshev Spaces: a numerical test for design (with C.Beccari and M.L.Mazure), arXiv:1606.07591 - 2016
  • High quality local interpolation by composite parametric surfaces (with M.Antonelli and C.Beccari), arXiv:1601.01436 - 2016
  • A practical criterion for the existence of optimal piecewise Chebyshevian spline bases (with C.Beccari), arXiv:1601.00380 - 2016
  • A general matrix representation for non-uniform B-spline subdivision with boundary control (with L.Romani), ALMA-DL University of Bologna (2007) Eprint-00002532
  • XCCurv: the 2D modeller, User's Guide - Version 4.0 (2007) xccurv_v4.pdf
  • XCRayt: the scene descriptor, User's Guide - Version 2.0 (2007) xcrayt_v2.pdf
  • trim library: Programming Guide - Version 2.0, (2007), trim_v2.pdf
  • descriptor library: Programming Guide - Version 3.0, (2007), descriptor_v3.pdf
  • XCSurf: the 3D modeller, User's Guide - Version 4.0 (2006) xcsurf_v4.pdf
  • Free Form Deformation: xcsurf (Version 3.0) plugin, (2005), (with E.Trevisan). ffd_guide_v3.pdf (662Kb) (in italian)
  • XCSurf: the 3D modeller, User's Guide - Version 3.0 (2005)
  • Free Form Deformation: xcsurf (Version 2.0) plugin, (2001), (with E.Trevisan).
  • xtools library: Programming Guide - Version 2.0, (2001), (with S.Bonetti). xtools_v2.pdf (142Kb)
  • MATRIX library: Programming Guide - Version 1.0, (1999), (with S.Bonetti). matrix_v1.pdf (91Kb)
  • descriptor library: Programming Guide - Version 1.0, (1999), (with S.Bonetti).
  • trim library: Programming Guide - Version 1.0, (1999), (with G.DeMarco).
  • xtools library: Programming Guide - Version 1.0, (1999), (with S.Bonetti).
  • A new approach to perspective views of spherical coordinate functions (with A.Amoroso) Department of Mathematics n.16, University of Bologna, Italy (1998) pdf file
  • Sulle Dynamic NURBS e la simulazione di processi dinamici (with G.L.Rubini) Rapporto Tecnico IAC-CNR, Roma (aprile 1998) pdf file
  • Circle as a p-spline curve (with S.Morigi) Department of Mathematics n.9, University of Bologna, Italy (1997) pdf file
  • Degree elevation for single-valued curves in polar coordinates (with S.Morigi and M.Lacchini), Department of Mathematics n.13, University of Bologna, Italy (1996). pdf file
  • Modelling of curves and surfaces in polar and Cartesian coordinates (with S.Morigi) Department of Mathematics n.12, University of Bologna, Italy (1996) pdf file
  • XCCURV: un sistema per la modellazione geometrica di curve NURBS; Manuale d'uso (with S.Morigi) Department of Mathematics, Bologna, Italy, novembre (1995) pdf file
  • Pseudopolar array mask algorithm for spherical coordinate grid surfaces(with A.Amoroso) Technical Report UBLCS-94-9, Laboratory for Computer Science, University of Bologna (1994) UBLCS Tech.Reports
  • Guida all'utilizzo e alle prestazioni dell'ipercubo Intel iPSC/860(with R.Rossi), N.1/138 (febbraio 1993), Progetto Finalizzato Sistemi Informatici e Calcolo Parallelo.
  • An inductive proof of the derivative B-spline recursion formula (with G.Valori) Department of Mathematics, Bologna, Italy, (1989) pdf file
    • Back to the Giulio Casciola's home page.