À. Gauche, le schéma interpolant 4 points avec un ordre d'approximation optimal mais une mauvaise continuité Au milieu, le schéma 4 points approximant . À droite, le schéma approximant B-spline quadratique avec une continuité optimale mais un mauvais ordre d'approximation, p.71

.. En-haut-À-gauche, En haut à droite les points qui génèrent la fonction limite du schéma B-spline cubique En bas, les points qui générent la fonction limite des schémas quasi-linéaires univariés (les schémas qui unifient le schéma 4- point pour i < 0 et le schéma B-spline cubique pour i > 0) Le point rouge représente le point de contrôle Qp 0 pour ? = 1, le point bleu représente le point de contrôle Qp 0 pour ? = 1, p.121

. Comparaison-entre-le-schéma-de-butterfly, schéma de Catmull- Clark (au centre) et le schéma quasi-linéaire qui unifie le schéma interpolant de Butterfly et le schéma approximant de Catmull-Clark sur un maillage triangle/quad (en bas) De gauche à droite : les mailles de contrôle, les surfaces limites, des mailles de couleur (jaune pour les triangles, et les lignes de réflexion. . . . . . . . . . . . . 139

. Les-cinq-cas-d......, application d'un schéma quasi-linéaire sur une grille 6?régulière (les zones d'application d'un schéma interpolant en bleu et les zones d'application d'un schéma approximant en jaune), p.158

]. A. Ball and D. J. Storry, Conditions for tangent plane continuity over recursively generated B-spline surfaces, ACM Transactions on Graphics, vol.7, issue.2, p.83102, 1988.
DOI : 10.1145/42458.42459

]. E. Catmull and J. Clark, Recursively generated b-spline surfaces on arbitrary topological surfaces, Computer Aided Geometric Design, vol.10, issue.6, p.350355, 1978.
DOI : 10.1016/0010-4485(78)90110-0

]. A. Cavaretta, W. Dahmen, and C. A. Micchelli, Stationary subdivision. Memoirsof the, 1991.
DOI : 10.1090/memo/0453

[. C. Gérot-]-c, L. Gérot, N. Barthe, M. Dodgson, and . Sabin, Subdivision as a sequence of sampled C p surfaces Advances in Multiresolution for Geometric Modelling, pp.259-270, 2005.

]. R. Chen, X. Chen, G. Luo, R. Zheng, and . Ling, Multi-resolution compression of meshes based on reverse interpolatory ? 3 subdivision scheme, International Journal of Computer Science and Network Security

]. C. Chui and Q. T. Jiang, Surface subdivision schemes generated by refinable bivariate spline function vectors, Applied and Computational Harmonic Analysis, vol.15, issue.2, pp.147-162, 2003.
DOI : 10.1016/S1063-5203(03)00062-9

]. C. Chui and Q. T. Jiang, Matrix-valued subdivision schemes for generating surfaces with extraordinary vertices, Computer Aided Geometric Design, vol.23, issue.5, pp.419-438, 2006.
DOI : 10.1016/j.cagd.2006.02.001

]. C. Chui and Q. T. Jiang, From extension of Loop's approximation scheme to interpolatory subdivisions, Computer Aided Geometric Design, vol.25, issue.2, pp.96-115, 2008.
DOI : 10.1016/j.cagd.2007.05.004

[. D. Zorin-1996a-]-p, D. Schroder, W. Zorin, and . Sweldens, Interpolating Subdivision for Meshes with Arbitrary Topology, Computer Graphics Proceedings (SIGGRAPH 96), pp.189-192, 1996.

[. D. Zorin-1996b-]-p, D. Schröder, W. Zorin, and . Sweldens, Interpolating subdivision for meshes with arbitrary topology, Proceedings of the 23rd annual conference on Computer graphics and interactive techniques ACM Press, p.189192, 1996.

]. C. Deboor and A. Ron, The exponentials in the span of the multiinteger translates of a compactly supported function : quasiinterpolation and approximation order, Journal of London Mathematical Society, vol.45, issue.2, pp.519-535, 1992.

M. Lounsbery and J. Warren, Multiresolution analysis for surfaces of arbitrary topological type, ACM Transactions on Graphics, vol.16, issue.1, pp.77-85, 1997.
DOI : 10.1145/237748.237750

]. F. Destelle, Adaptation de schémas de subdivision pour la reconstruction d'objet sans artefact, 2010.

]. N. Dyn, J. A. Gregory, and D. Levin, A 4-point interpolatory subdivision scheme for curve design, Computer Aided Geometric Design, vol.4, issue.4, pp.257-268, 1987.
DOI : 10.1016/0167-8396(87)90001-X

]. N. Dyn, J. A. Gregory, and D. Levin, Analysis of uniform binary subdivision schemes for curve design, Constructive Approximation, vol.39, issue.115, pp.127-147, 1991.
DOI : 10.1007/BF01888150

N. Dyn, M. S. Floater, and K. Hormann, A C2 four-point subdivision scheme with fourth order accuracy and its extensions, Mathematical Methods for Curves and Surfaces : Troms?gTroms? Troms?g, pp.145-156, 2004.

]. T. Goodman, C. A. Micchelli, and J. D. Ward, Spectral radius formulas for subdivisionoperators, in Recent Advances in Wavelet Analysis, pp.335-360, 1994.

[. H. Hoppe, M. Halstead, H. Jin, J. Mcdonald, J. Schweitzer et al., Piecewise Smooth Surface Reconsruction, Computer Graphics Proceedings, Annual Conference Series, pp.295-302, 1994.

]. M. Hassan and N. A. Dodgson, Reverse subdivision Advances in Multiresolution for Geometric Modelling, pp.271-283, 2005.

]. L. Kobbelt, A variational approach to subdivision, Computer Aided Geometric Design, vol.13, issue.8, p.743761, 1996.
DOI : 10.1016/0167-8396(96)00007-6

]. F. Kuijt, Convexity Preserving Interpolation, Stationary Nonlinear Subdivision and Splines, 1998.

]. S. Lanquetin and M. Neveu, Reverse Catmull-Clark subdivison, The 14-th International Conference in Central Europe on Computer Graphics, Visualization and Computer (WSCG), 2006.

]. A. Levin, Combined Subdivision schemes, 2000.

]. A. Levin, Polynomial generation and quasi-interpolation in stationary non-uniform subdivision, Computer Aided Geometric Design, vol.20, issue.1, pp.41-60, 2003.
DOI : 10.1016/S0167-8396(03)00006-2

]. A. Levin and D. Levin, Analysis of quasi-uniform subdivision, Applied and Computational Harmonic Analysis, vol.15, issue.1, pp.18-32, 2003.
DOI : 10.1016/S1063-5203(03)00031-9

]. D. Levin, N. Dyn, and J. Gregory, A butterfy subdivision scheme for surface interpolation with tension control, ACM Trans. Graph, vol.9, issue.2, p.160169, 1990.

]. J. Peters and U. Reif, Analysis of generalized B-spline subdivision algorithms, SIAM Jornal of Numerical Analysis, 1997.

]. H. Prautzsch, Smoothness of subdivision surfaces at extraordinary points, Advances in Computational Mathematics, vol.9, issue.3/4, pp.377-389, 1998.
DOI : 10.1023/A:1018945708536

[. Q. Li, Q. T. Jiang, and W. W. Zhu, Interpolatory quad/triangle subdivision schemes for surface design, Computer Aided Geometric Design, vol.26, pp.904-922, 2009.

]. M. Sabin and L. Barthe, Artifacts in Recursive Subdivision Surfaces. curves and Surfaces Fitting : St Malo, pp.353-362, 2002.

]. F. Samavati and R. Bartels, Multiresolution Curve and Surface Representation: Reversing Subdivision Rules by Least-Squares Data Fitting, Computer Graphics Forum, vol.18, issue.2, pp.97-120, 1999.
DOI : 10.1111/1467-8659.00361

]. F. Samavati, M. A. Nezam, and R. Bartels, Multiresolution Surfaces having Arbitrary Topologies by a Reverse Doo Subdivision Method, Computer Graphics Forum, vol.4, issue.2, pp.121-134, 2002.
DOI : 10.1111/1467-8659.00361
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.37.1048

]. F. Samavati and R. Bartels, DIAGRAMMATIC TOOLS FOR GENERATING BIORTHOGONAL MULTIRESOLUTIONS, International Journal of Shape Modeling, vol.12, issue.01, pp.47-73, 2006.
DOI : 10.1142/S0218654306000834

]. F. Samavati, H. Pakdel, and C. Smith, Reverse of Loop subdivision, Iranian Journal of Mathematical Sciences and Informatics, vol.2, issue.1, 2007.

]. S. Schaefer and J. Warren, triangle/quad subdivision, ACM Transactions on Graphics, vol.24, issue.1, pp.28-36, 2005.
DOI : 10.1145/1037957.1037959
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.91.7247

]. J. Stam and C. Loop, Quad/Triangle Subdivision, Computer Graphics Forum, vol.10, issue.6, pp.79-85, 2003.
DOI : 10.1016/S0167-8396(01)00038-3

]. J. Warren and H. Weimer, Subdivision Methods for Geometric design, 2002.

]. D. Zorin and P. Schröder, Subdivision for modeling and animation, SIG- GRAPH Courses Notes, 2000.