19
Views
2
CrossRef citations to date
0
Altmetric
Original Articles

An Algorithm for C 1 Surface Approximation with Large Variations

Pages 111-131 | Published online: 15 Sep 2010

  • Apprato , D. 1987 . Approximation de surfaces paramétrées par éléments finis , Université de Pau et des Pays de l'Adour . Thèse d'Etat
  • Apprato , D. and Gout , C. 2000 . A result about scale transformation families in approximation: application to surface fitting from rapidly varying data . Numerical Algorithms , 23 (2,3} ) : 263 – 279 .
  • Arcangéli , R. 1986 . D"-splines sur un domaine borné de R” . Publication URA 1204 CNRS numéro , 1986/2
  • Arcangéli , R. 1989 . “ Some Applications of Discrete D" Splines ” . In Mathematical Methods in Computer Aided Geometric Design, Lyche , Edited by: Schumaker , L. L. 35 – 44 . Academic Press .
  • Aronsajn , N. 1950 . Theory of reproducing kernels . Trans. Amer. Math. Soc. ,
  • Atteia , M. 1968 . Fonctions "spline" définies sur un ensemble convexe . Numer. Math. , 12 : 192 – 210 .
  • Bézier , P. 1968 . Procédé de définition numérique des courbes et des surfaces non mathématiques, Système Unisurf . Automatisme , : 13
  • Bouhamidi , A. 1992 . Interpolation et approximation par des fonctions splines radiales à plusieurs variables , Université de Nantes . Thèse
  • Carlson , R. E. and Fritsch , F. N. 1985 . Monotone piecewise bicubic interpolation . SIAM J. Numer. Anal , 22 : 386 – 400 .
  • Chui , C. K. 1987 . Lectures on multivariate spline: Theory and applications, Center of Approximation Theory . Dpt. of Mathematics, Texas A&M, College Station Texas ,
  • Ciarlet , P. G. 1978 . The Finite Element Method for Elliptic Problems , Amsterdam : North Holland .
  • Cohen , E. and Lyche , T. 1980 . Discrete B-Splines and subdivision techniques in computer-aided geometric design and computer graphics, Comput . Graphics Image Process. , 14 : 87 – 111 .
  • de Boor , C . 1978 . A Practical Guide to Splines , Berlin-Heidelberg : Springer Verlag .
  • De Casteljau , P. 1959 . Outillage méthodes de calcul , Paris, , S.A. : André Citroën Automobiles .
  • DeRose , T. D. and Barsky , B. A. 1988 . Geometrie continuity, shape parameters, and geometric constructions for Catmull-Roms splines . ACM Treats. Graphics , 7 : 1 – 41 .
  • Duchon , J. 1977 . Splines Minimizing Rotation- Invariant Semi- Norms in Sobolev Spaces , Lecture Notes in Math., 571 85 – 100 . Springer .
  • Farin , G. 1988 . “ Curves and Surfaces for Computer Aided Geometric Design ” . In A Practical Guide , Academic Press .
  • Farin , G. , Rein , G. , Sapidis , N. and Worsey , A. J. 1987 . Fairing cubic B-spline curves . Computer Aided Geometric Design , 6 : 97 – 109 .
  • Foley , T. A. 1987 . Weighted bicubic spline interpolation to rapidly varying data . ACM Trans. Graphics , 6 : 1 – 18 .
  • Foley , T. A. and Ely , H. S. 1989 . Surface interpolation with tension controls using cardinal bases, Comput . Aided Geometric Design , 6 : 97 – 109 .
  • Forrest , A. R. 1980 . The twisted cubic curve: a computer-aided geometric design approach . Computer Aided Design , 12 : 165 – 172 .
  • Franke , R. 1985 . Thin plate spline with tension . Computer Aided Geometric Design , 2 : 87 – 95 .
  • Franke , R. 1982 . Smooth interpolation of scattered data by local thin plate splines . Comp. and Maths, with Appls. , 8 (4} ) : 273 – 281 .
  • Gout , C. 1998 . Approximation of curves and surfaces from rapidly varying data, preprint, Center for Pure and Applied Mathematics , PAM No. 729 Berkeley : University of California at Berkeley .
  • Gout , C. and Guessab , A. 2001 . A new family of Extended Gauss Quadratures with an Interior Constraint, accepted for publication . Journal of Computational and Applied Mathematics , in press
  • Gout , C. 1997 . Etude de changements d'échelle en Approximation - Adjustment spline sur des morceaux de surfaces , Université de Pau . Ph.D. Dissertation
  • Gout , C. and Komatitsch , D. 2000 . Surface fitting of rapidly varying data using rank coding: application to geophysical surfaces . Mathematical Geology , 32 (7} ) : 873 – 888 .
  • Gout , C. and Komatitsch , D. C1-Approximation of Seafloor Surfaces with large variations . IEEE International Geoscience and Remote Sensing Symposium . Vol. 5 , pp. 1836 – 1838 . Honolulu : IEEE Press .
  • Hou , H. S. and Andrews , H. C. 1981 . Cubic splines for image interpolation and digital filtering . IEEE Trans. Acoust., Speech, Signal Process. , 29 : 508 – 517 .
  • Hsieh , H. C. and Chang , W. T. 1994 . Virtual knot technique for curve fitting of rapidly varying data . Computer Aided Geometric Design , 11 : 71 – 95 .
  • Keys , R. G. 1981 . Cubic convolution interpolation for digital image processing . IEEE Trans. Acoust., Speech, Signal Process. , 29 : 1153 – 1160 .
  • Lancaster , P. and Salkauskas , K. 1986 . Curve and Surface fitting , New York : Academic press .
  • Lane , J. M. and Riesenfield , R. F. 1980 . A theoretical development for the generation and display of piecewise polynomial surfaces . IEEE Trans. Pattern Anal. Mach. Intell. , 2 : 35 – 46 .
  • Laurent , P. J. 1972 . Approximation et optimisation , Paris : Hermann .
  • Medioni , G. and Yasumoto , Y. 1987 . Corner detection and curve representation using cubic B-Splines . Comput. Vision Graphics Image Process. , 38 : 267 – 278 .
  • Namane , A. and Sid-Ahmed , M. A. 1990 . Character scaling by contour method . IEEE Trans. Pattern Anal. Math. Intell. , 12 : 600 – 606 .
  • Nielson , G. M. 1983 . A method for interpolating scattered data based upon a minimum norm network . Math, of Cony. , 40 : 253 – 271 .
  • Nielson , G. M. and Franke , R. 1984 . A method for construction of surfaces under tension . Rocky Mountain J. Math. , 14 : 203 – 221 .
  • Nielson , G. M. and Franke , R. 1983 . “ Surface construction based upon triangulations ” . In Surfaces in Computer Aided Geometric Design , Edited by: Barnhill , R. E. and Boehm , W. North Holland Publ. Co. .
  • Prenter , P. M. and Westwater , E. R. 1986 . Three adaptative discrete least squares cubic spline procedures for the compression of data, Comput . Vision Graphics Image Process. , 33 : 327 – 345 .
  • Salkauskas , K. 1974 . C1 splines for interpolation of rapidly varying data . Rocky Mountain J. Math. , 14 : 239 – 250 .
  • Schoenberg , I. J. 1960 . Contribution to the problem of approximation of equidistant data by analytic functions . Quart. of Appl. Math. , 4 : 45 – 99 . 112 – 141 .
  • Schumaker , L. L. 1976 . “ Fitting surfaces to scattered data ” . In Approximation Théorie II , Edited by: Lorentz , G. G. , Chui , C. K. and Schumaker , L. L. 203 – 269 . Academic Press . (éditeurs}
  • Schwarz , L. 1964 . Sous espaces hilbertiens d'espaces vectoriels topologiques et noyaux associés (noyaux reproduisants} . J. Anal. Math., Paris ,
  • Torrens , J. J. 1991 . Interpolation de superficies parametricas con discontinuidades mediante, Elementes Finîtes, Aplicaciones , Universidad de Zaragoza . Thèse
  • Wu , S. C. , Abel , J. F. and Greenberg , D. P. 1977 . An interactive computer graphics approach to surface representation . Comm. ACM , 20 : 703 – 712 .
  • Yang , M. C. K. , Kim , C. K. , Yang , C. C. and Liu , S. S. 1986 . Automatic curve fitting with quadratic B-spline functions and its applications to computer-assisted animation, Comput . Vision Graphics Image Process , 33 : 346 – 363 .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.