@STRING{j-CAGD = {Computer-Aided Geometric Design}} @String{j-CAD = {Computer Aided Design}} @STRING{j-CGF = {Com{\-}pu{\-}ter Graphics Forum}} @STRING{j-SIAM-J-NUM-ANAL = {SIAM Journal on Numerical Analysis}} @STRING{j-TOG = {ACM Transactions on Graphics}} @BOOK{Boor:1993:BS, title = {Box splines}, publisher = {Springer-Verlag}, year = {1993}, author = {C.~{de Boor} and K.~H{\"o}llig and S.~Riemenschneider}, volume = {98}, pages = {xviii+200}, series = {Applied Mathematical Sciences}, address = {New York} } @MISC{DeRo98, author = {T.~DeRose et al.}, title = {Texture Mapping and Other Uses of Scalar Fields on Subdivision Surfaces in Computer Graphics and Animation}, year = {1998}, journal = {US Patent }, number = {6,037,949} } @ARTICLE{AkChErSr01, author = {E.~Akleman and J.~Chen and F.~Eryoldas and V.~Srinivasan}, title = {Handle and Hole Improvement by Using new corner cutting subdivision scheme with tension.}, journal = {SMI 2001 International Conference on Shape Modeling and Applications, IEEE}, year = {2001}, } @ARTICLE{AkSr03, author = {E.~Akleman and V.~Srinivasan}, title = {Honeycomb subdivision}, journal = {Preprint}, year = {2003}, } @ARTICLE{Alexa:2002:ROT, author = {M.~Alexa }, title = {Refinement operators for triangle meshes.}, journal = j-CAGD, year = {2002}, volume = {19}, pages = {169--172}, number = {4}, } @INPROCEEDINGS{Al04, author = {N.~Alkalai }, title = {Optimising 3D triangulations: {I}mproving the initial triangulation for the {B}utterfly subdivision scheme.}, editor = {N.A.~Dodgson and M.S.~Floater and M.A.~Sabin}, booktitle = {Advances in Multiresolution for Geometric Modelling}, year = {2005}, publisher = {Springer}, pages = {231--244},} } @ARTICLE{Augs:2006:TSM, author = {U.H.~Augsd{\"o}rfer and N.A.~Dodgson and M.A.~Sabin}, title = {Tuning subdivision by minimising {G}aussian curvature variation near extraordinary vertices}, journal = {Computer Graphics Forum (Proc. Eurographics)}, year = {2006}, volume = {25}, pages = {263--272}, number = {3} } @ARTICLE{BaScWaXu02, author = {C.~Bajaj and S.~Schaefer and J.~Warren and G.~Xu }, title = {A Subdivision Scheme for Hexahedral Meshes.}, journal = {The Visual Computer}, year = {2002}, volume = {18}, pages = {343--356}, number = {5--6} } @ARTICLE{BaXuHoNe02, author = {C.~Bajaj and G.~Xu and R.~Holt and A.~Netravali }, title = {Hierarchical multiresolution reconstruction of shell surfaces}, journal = j-CAGD, year = {2002}, volume = {19}, pages = {89--112}, number = {2}, } @INPROCEEDINGS{Ball:1984:RGB, author = {A.~Ball and D.~Storry }, title = {Recursively generated {B}-spline surfaces.}, booktitle = {Proc. CAD84}, year = {1984}, pages = {112--119}, } @TECHREPORT{Ball-Storry:1990, author = {A.A.~Ball and D.J.T.~Storry}, title = {An investigation of curvature variations over recursively generated {B}-spline surfaces}, institution = {Loughborough University of Technology}, year = {1990} } @ARTICLE{Ball:1988:CTC, author = {A.A.~Ball and D.J.T.~Storry}, title = {Conditions for tangent plane continuity over recursively generated {B}-spline surfaces}, journal = {ACM Trans.~ on Graphics}, year = {1988}, volume = {7}, pages = {83--102} } @ARTICLE{Ball:1986:MAA, author = {A.A.~Ball and D.J.T.~Storry}, title = {A matrix approach to the analysis of recursively generated {B}-spline surfaces}, journal = {Computer Aided Design}, year = {1986}, volume = {18}, pages = {437--442} } @ARTICLE{BaSa01, author = {R.~Bartels and F.~Samavati }, title = {Reversing subdivision rules: local linear conditions and observations on inner products.}, journal = {J. Comp. and Appl. Math.}, year = {2001}, volume = {119}, pages = {29--67}, number = {1-2} } @INPROCEEDINGS{BaGeSaKo04, author = {L.~Barthe and C.~G{\'e}rot and M.~Sabin and L.~Kobbelt }, title = {Simple computation of the eigencomponents of a subdivision matrix in the {F}ourier domain.}, editor = {N.A.~Dodgson and M.S.~Floater and M.A.~Sabin}, booktitle = {Advances in Multiresolution for Geometric Modelling}, year = {2005}, publisher = {Springer}, pages = {245--257}, } @INPROCEEDINGS{BiLeZo00, author = {H.~Biermann and A.~Levin and D.~Zorin }, title = {Piecewise smooth subdivision surfaces with normal control}, booktitle = {SIGGRAPH 2000 Conference Proceedings: Computer Graphics Annual Conference Series}, year = {2000}, pages = {113--120}, } @ARTICLE{Bohl:1997:DBP, author = {H.~Bohl and U.~Reif}, title = {Degenerate {B}e\'zier patches with continuous curvature}, journal = j-CAGD, year = {1997}, volume = {14}, pages = {749--761}, number = {8}, address = {Amsterdam, The Netherlands, The Netherlands}, doi = {http://dx.doi.org/10.1016/S0167-8396(97)00005-8}, issn = {0167-8396}, publisher = {Elsevier Science Publishers B. V.} } @INPROCEEDINGS{Boier:2004:DPC, author = {I.~Boier-Martin and D.~Zorin}, title = {Differentiable parameterization of {C}atmull-{C}lark subdivision surfaces}, booktitle = {SGP '04: Proceedings of the 2004 Eurographics/ACM SIGGRAPH symposium on Geometry processing}, year = {2004}, pages = {155--164}, address = {New York, NY, USA}, publisher = {ACM Press}, } @INPROCEEDINGS{Bolz:2002:RECC, author = {J.~Bolz and P.~Schr{\"o}der}, title = {Rapid Evaluation of {C}atmull-{C}lark Subdivision Surfaces}, booktitle = {Proceedings of the Web3{D} 2002 Symposium}, year = {2002}, pages = {11--18}, publisher = {ACM Press}, notes = {This paper tesselates the basis function and the C-C surface can be evaluated as the linear combination of those tesselations. Each basis function is defined as 1 at one coefficient and 0 elsewere.} } @ARTICLE{Bo83, author = {W.~B{\"o}hm}, title = {Subdividing multivariate splines}, journal = {Computer Aided Design}, year = {1983}, volume = {15}, pages = {345--352}, number = {6}, } @ARTICLE{Catmull:1978:RGB, author = {E.~Catmull and J.~Clark}, title = {Recursively generated {B}-spline surfaces on arbitrary topological meshes}, journal = {Computer Aided Design}, year = {1978}, volume = {10}, pages = {350--355} } @ARTICLE{Cavaretta:1991:SS, author = {A.S.~Cavaretta and W.~Dahmen and C.A.~Micchelli}, title = {Stationary subdivision}, journal = {Memoirs of the American Mathematical Society}, year = {1991}, volume = {93}, pages = {1--186}, number = {453} } @inproceedings{schaefer07exact, author = {S.~Schaefer and J.~Warren}, title = {Exact Evaluation of Non-Polynomial Subdivision Schemes at Rational Parameter Values}, booktitle = {PG '07: 15th Pacific Conference on Computer Graphics and Applications}, year = {2007}, pages = {321--330}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, } @article{Ni:2007:TSQ, author = "T.~Ni and A.H.~Nasri and J.~Peters", title = "Ternary Subdivision for Quadrilateral Meshes", journal = j-CAGD, volume = "24", number = "6", pages = "361--370", year = "Aug 2007", } @ARTICLE{Chaikin:1974:AHS, author = {G.~Chaikin }, title = {An Algorithm for High Speed Curve Generation}, journal = {Computer Graphics and Image Processing}, year = {1974}, volume = {3}, pages = {346--349}, } @INPROCEEDINGS{ChMcDoQi02, author = {Y.~Chang and K.~McDonnell and H.~Qin }, title = {A new solid subdivision scheme based on box splines.}, booktitle = {Proceedings of the Seventh ACM Symposium on Solid Modeling and Applications}, year = {2002}, pages = {226--233} } @ARTICLE{CiScAnOrSc02, author = {F.~Cirak and M.J.~Scott and E.K.~Antonsson and M.~Ortiz and P.~Schr{\"o}der}, title = {Integrated modeling, finite element analysis and engineering design for thin-shell structures using subdivision.}, journal = {Computer Aided Design}, year = {2002}, volume = {34}, pages = {137--148}, } @ARTICLE{Cirak:2000:SSP, author = {F.~Cirak and M.~Ortiz and P.~Schr{\"o}der }, title = {Subdivision surfaces: A new paradigm for thin-shell finite element analysis.}, journal = {Int. J. Numer. Meth. Eng.}, year = {2000}, volume = {47}, pages = {2039--2072}, number = {12}, } @INPROCEEDINGS{ClBeReIoKr01, author = {J.~Claes and K.~Beets and F.~van Reeth and I.~Iones and A.~Krupkin}, title = {Turning the Approximating {C}atmull-{C}lark Subdivision Scheme into an Locally Interpolating Surface Modelling Tool}, booktitle = {SMI 2001 International Conference on Shape Modeling and Applications}, year = {2001}, pages = {42--48}, } @ARTICLE{CoDyKaPo00, author = {A.~Cohen and N.~Dyn and K.~Kaber and M.~Postel }, title = {Multiresolution schemes on triangles for scalar conservation laws.}, journal = {Journal of Computational Physics}, year = {2000}, volume = {161}, pages = {264--286} } @ARTICLE{CoDyMa04, author = {A.~Cohen and N.~Dyn and B.~Matei}, title = {Quasilinear subdivision schemes with applications to {ENO} interpolation.}, journal = {Applied and Computational Harmonic Analysis}, year = {2004} } @ARTICLE{CoZi04, author = {C.~Conti and G.~Zimmermann }, title = {Interpolatory rank-1 vector subdivision schemes}, journal = j-CAGD, year = {2004}, volume = {21}, pages = {341--351}, } @ARTICLE{Da97, author = {R.~van Damme }, title = {Bivariate {H}ermite Subdivision.}, journal = j-CAGD, year = {1997}, volume = {14}, pages = {847--875}, } @ARTICLE{DaGuScSw99, author = {I.~Daubechies and I.~Guskov and P.~Schr{\"o}der and W.~Sweldens }, title = {Wavelets on irregular point sets.}, journal = {Phil. Trans. Roy. Soc. Lond A}, year = {1999}, volume = {357}, pages = {2397--2413}, number = {1760}, } @ARTICLE{DaGu98, author = {I.~Daubechies and I.~Guskov and W.~Sweldens}, title = {Commutation for Irregular subdivision}, journal = {Constructive Approximation}, year = {2001}, volume = {17}, pages = {479--514}, number = {4}, } @ARTICLE{DaGuSw99, author = {I.~Daubechies and I.~Guskov and W.~Sweldens }, title = {Regularity of irregular subdivision.}, journal = {Constructive Approximation}, year = {1999}, volume = {15}, pages = {381--426}, number = {3}, } @ARTICLE{DeRose:1993:EFI, author = {M.~Halstead and M.~Kass and T.~DeRose}, title = {Efficient, Fair Interpolation Using {C}atmull-{C}lark Surfaces}, journal = {Proceedings of SIGGRAPH 93}, year = {1993}, pages = {35--44}, editor = {James T.~Kajiya}, series = {Computer Graphics Proceedings, Annual Conference Series} } @INPROCEEDINGS{DeRose:1998:SSI, author = {T.~DeRose and M.~Kass and T.~Truong}, title = {Subdivision surfaces in character animation}, booktitle = {SIGGRAPH '98: Proceedings of the 25th annual conference on Computer graphics and interactive techniques}, year = {1998}, pages = {85--94}, address = {New York, NY, USA}, publisher = {ACM Press}, doi = {http://doi.acm.org/10.1145/280814.280826}, isbn = {0-89791-999-8} } @ARTICLE{DeDu92, author = {G.~Deslauriers and S.~Dubuc}, title = {Erratum:Symmetric Iterative Interpolation Processes}, journal = {Constructive Approximation}, year = {1992}, volume = {8}, pages = {125--126}, } @ARTICLE{Deslauriers:1989:SII, author = {G.~Deslauriers and S.~Dubuc }, title = {Symmetric iterative interpolation processes}, journal = {Constructive Approximation}, year = {1989}, volume = {5}, pages = {49--68}, } @INPROCEEDINGS{DoIvSa03, author = {N.~Dodgson and I.~Ivrissimtzis and M.~Sabin }, title = {Characteristics of dual triangular $\sqrt3$ subdivision.}, booktitle = {Curve and Surface fitting: St Malo 2002}, year = {2003}, pages = {119--128}, } @TechReport{DoSaBaHa02, author = "N.~A.~Dodgson and M.~A.~Sabin and L.~Barthe and M.F.~Hassan", title = "Towards a Ternary Interpolating Subdivision Scheme for the Triangular Mesh", type = "Technical Report", number = "UCAM-CL-TR-539", institution = "University of Cambridge, Computer Laboratory", year = "2002", ISSN = "1476-2986", pdf-url = "http://www.cl.cam.ac.uk/TechReports/UCAM-CL-TR-539.pdf", } @INPROCEEDINGS{doo78, author = {D.~Doo}, title = {A subdivision algorithm for smoothing down irregularly shaped polyhedrons}, booktitle = {Int'l Conf. Ineractive Techniques in Computer Aided Design}, year = {1978}, pages = {157--165}, address = {Bologna, Italy}, publisher = {IEEE Computer Soc.} } @ARTICLE{Doo:1978:BRD, author = {D.~Doo and M.~Sabin}, title = {Behaviour of recursive division surfaces near extraordinary points}, journal = {Computer Aided Design}, year = {1978}, volume = {10}, number = {6}, pages = {356--360} } @ARTICLE{DrGrSc, author = {A.~Dreger and M.~Gross and J.~Schlegel}, title = {Construction of Multiresolution triangular {B}-spline surfaces using hexagonal filters}, journal = {The visual computer}, year = {2000}, volume = {16}, number = {6}, } @ARTICLE{Du86, author = {S.~Dubuc}, title = {Interpolation through an iterative scheme}, journal = {J. Math Anal. and Appl.}, year = {1986}, volume = {114}, pages = {185--204}, } @INPROCEEDINGS{Dy92, author = {N.~Dyn }, title = {Subdivision Schemes in {C}omputer {A}ided {G}eometric {D}esign.}, booktitle = {Advances in Numerical Analysis -- Volume II, Wavelets, Subdivision Algorithms and Radial Basis Functions}, year = {1992}, editor = {W.~Light}, publisher = {Clarendon Press, Oxford}, pages = {36--104}, } @INPROCEEDINGS{Dyn02a, author = {N.~Dyn }, title = {Analysis of Convergence and Smoothness by the formalism of {L}aurent Polynomials.}, booktitle = {Primus Workshop Proceedings}, year = {2002}, pages = {51--68} } @INPROCEEDINGS{Dy02b, author = {N.~Dyn }, title = {Interpolatory Subdivision Schemes.}, booktitle = {Primus Workshop Proceedings}, year = {2002}, pages = {25--50} } @ARTICLE{Levin:1999:ULP, author = {D.~Levin }, title = {Using {L}aurent polynomial representation for the analysis of non-uniform binary subdivision schemes.}, journal = {Advances in Computational Mathematics}, year = {1999}, volume = {11}, pages = {41--54} } @ARTICLE{DyFa00, author = {N.~Dyn and E.~Farkhi }, title = {Spline Subdivision Schemes for Convex Compact Sets.}, journal = {Journal of Computational and Applied Mathematics}, year = {2000}, volume = {119}, pages = {133--144}, } @INPROCEEDINGS{DyGrLe95, author = {N.~Dyn and J.~Gregory and D.~Levin }, title = {Piecewise uniform subdivision schemes.}, booktitle = {Mathematical Methods for Curves and Surfaces: Ulvik 1996}, year = {1995}, editor = {M.~Dahlen, T.~Lyche and L.L.~Schumaker}, pages = {111--119}, } @ARTICLE{Dyn:1991:AUB, author = {N.~Dyn and J.A.~Gregory and D.~Levin}, title = {Analysis of Uniform Binary Subdivision Schemes for Curve Design}, journal = {Constructive Approximation}, year = {1991}, volume = {7}, number = {2}, pages = {127--148} } @ARTICLE{Dyn:1987:FPI, author = {N.~Dyn and J.A.~Gregory and D.~Levin}, title = {A four-point interpolatory subdivision scheme for curve design}, journal = j-CAGD, year = {1987}, volume = {4}, pages = {257--268} } @INPROCEEDINGS{DyLe99, author = {N.~Dyn and D.~Levin }, title = {Analysis of {H}ermite interpolatory subdivision schemes.}, booktitle = {Spline Functions and the Theory of Wavelets}, year = {1999}, editor = {S.~Dubuc}, pages = {105--113} } @INPROCEEDINGS{DyLe92, author = {N.~Dyn and D.~Levin }, title = {Stationary and non-stationary binary subdivision schemes.}, booktitle = {Mathematical Methods in Computer Aided Geometric Design II}, year = {1992}, editor = {T.~Lyche and L.L.~Schumaker}, publisher = {Academic Press}, pages = {209--216} } @ARTICLE{DyLe02, author = {N.~Dyn and D.~Levin }, title = {Subdivision schemes in geometric modelling.}, journal = {Acta Numerica}, year = {2002}, pages = {73--144}, } @ARTICLE{DyLe95, author = {N.~Dyn and D.~Levin }, title = {Analysis of asymptotically equivalent binary subdivision schemes.}, journal = {Journal of Math.~Anal.~Appl.}, year = {1995}, volume = {193}, pages = {594--621} } @ARTICLE{Dyn:1990:BSS, author = {N.~Dyn and D.~Levin and J.A.~Gregory}, title = {A {B}utterfly Subdivision Scheme for Surface Interpolation with Tension Control}, journal = {ACM Transactions on Graphics}, year = {1990}, number = "2", volume = {9}, pages = {160--169} } @ARTICLE{Dyn:1992-1, author = {N.~Dyn and D.~Levin and D.~Liu }, title = {Interpolatory convexity-preserving subdivision schemes for curves and surfaces }, journal = {Computer Aided Design }, year = {1992 }, volume = {24 }, pages = {211--216 } } @ARTICLE{DyLeLu03, author = {N.~Dyn and D.~Levin and A.~Luzzatto }, title = {Non-stationary interpolatory subdivision schemes reproducing spaces of exponential polynomials.}, journal = {Found. Comput. Math}, year = {2003}, pages = {187--206} } @INPROCEEDINGS{DyLeSi03, author = {N.~Dyn and D.~Levin and J.~Simoens }, title = {Face value subdivision schemes on triangulations by repeated averaging.}, booktitle = {Curve and Surface Fitting: St Malo 2002}, year = {2003}, editor = {A.~Cohen, J.-L.~Merrien and L.L.~Schumaker}, pages = {129--138}, } @BOOK{Farin:1997:CSC, title = {Curves and Surfaces for Computer-Aided Geometric Design: {A} Practical Guide}, publisher = {Academic Press}, year = {1997}, author = {Gerald Farin}, pages = {xvii + 429}, address = {pub-ACADEMIC:adr}, edition = {Fourth}, isbn = {0-12-249054-1}, } @BOOK{FlMi98, title = {Nonlinear Stationary Subdivision}, publisher = {Marcel Dekker, New York}, year = {1998}, author = {M.S.~Floater and C.A.~Micchelli}, pages = {209--224}, booktitle = {Approximation Theory}, editors = {N.K.~Govil and R.N.~Mohapatra and Z.~Nashed and A.~Sharma and J.~Szabados}, } @TECHREPORT{Forest:1974:NCA, author = {A.R.~Forrest }, title = {Notes on {C}haikin's algorithm}, institution = {University of East Anglia Computational Geometry Project Memo}, year = {1974}, number = {CGP74/1} } @INPROCEEDINGS{FrMuSc03, author = {I.~Friedel and P.~Mullen and P.~Schr{\"o}der}, title = {Data-dependent fairing of subdivision surfaces}, booktitle = {Proceedings of the eighth ACM symposium on Solid modeling and applications}, year = {2003}, pages = {185--195}, publisher = {ACM Press}, } @TECHREPORT{Ge03a, author = {C.~G\'erot}, title = {Rereading a subdivision scheme as the computation of ${C}^p$ Surfaces Series Samplings}, institution = {Laboratoire des Images et des Signaux}, year = {2003}, } @TECHREPORT{Ge03b, author = {C.~G\'erot}, title = {Analyzing a subdivision scheme with the eigenanalysis of a new subdivision matrix}, institution = {Laboratoire des Images et des Signaux}, year = {2003}, } @INPROCEEDINGS{GeBaDoSa04, author = {C.~G\'erot and L.~Barthe and N.~Dodgson and M.~Sabin }, title = {Subdivision as a sequence of sampled ${C}^p$ surfaces.}, editor = {N.A.~Dodgson and M.S.~Floater and M.A.~Sabin}, booktitle = {Advances in Multiresolution for Geometric Modelling}, year = {2005}, publisher = {Springer}, pages = {259--270}, } @ARTICLE{Ginkel:200x:SSC, author = {I.~Ginkel and G.~Umlauf}, title = {Symmetry of shape charts}, journal = j-CAGD, year = {2008}, note = {to appear} } @ARTICLE{Ginkel:2006:NSS, author = {I.~Ginkel and J.~Peters and G.~Umlauf}, title = {Normals of Subdivision Surfaces and their Control Polyhedra}, journal = j-CAGD, year = {2007}, volume = {24}, pages = {112--116}, number = {2}, } @INPROCEEDINGS{Ginkel:2006:PJS, author = {I.~Ginkel and G.~Umlauf}, title = {Loop subdivision with curvature control}, booktitle = {Proceedings of Symposium on Geometry Processing, June 26-28 2006, Cagliari, Italy}, year = {2006}, editor = {A.~Scheffer and K.~Polthier}, pages = {163--172}, publisher = {ACM Press} } @article{Ginkel:2007:AGL, author = {I.~Ginkel and G.~Umlauf}, title = {Analyzing a generalized {L}oop subdivision scheme}, journal = {Computing}, volume = {79}, number = {(2-4)}, pages = {353--363}, year = {2007} } @ARTICLE{GrQu96, author = {J.~Gregory and R.~Qu }, title = {Non-uniform corner cutting.}, journal = j-CAGD, year = {1996}, volume = {13}, pages = {763--772}, } @ARTICLE{gregory89, author = {J.N.~Gregory and J.M.~Hahn}, title = {A {$C^2$} polygonal surface patch}, journal = j-CAGD, year = {1989}, volume = {6}, pages = {69--75}, number = {1}, address = {Amsterdam, The Netherlands, The Netherlands}, publisher = {Elsevier Science Publishers B. V.} } @INPROCEEDINGS{Grinspun:2001:NBS, author = {E.~Grinspun and P.~Schr{\"o}der}, title = {Normal bounds for subdivision-surface interference detection}, booktitle = {Proc Visualization}, year = {2001}, editor = {T.~Ertl and K.~Joy and A.~Varshney}, pages = {333--340}, publisher = {IEEE} } @ARTICLE{Halstead:1993:EFI, author = {M.~Halstead and M.~Kass and T.~DeRose}, title = {Efficient, Fair Interpolation Using {C}atmull-{C}lark Surfaces}, journal = {Proceedings of SIGGRAPH 93}, year = {1993}, pages = {35--44}, editor = {J.T.~Kajiya}, series = {Computer Graphics Proceedings, Annual Conference Series} } @ARTICLE{Ha03a, author = {B.~Han }, title = {Computing the smoothness exponent of a symmetric multivariate refinable function.}, journal = {SIAM Journal on Matrix Analysis and its Applications}, year = {2003}, volume = {24}, pages = {693--714} } @INPROCEEDINGS{Ha03b, author = {B.~Han }, title = {Classification and construction of bivariate subdivision schemes.}, booktitle = {Curve and Surface fitting: St Malo 2002}, year = {2003}, pages = {187--198}, } @ARTICLE{HaJi98, author = {B.~Han and R.-Q.~Jia }, title = {Multivariate refinement equations and convergence of subdivision schemes.}, journal = {SIAM Journal on Math. Analysis}, year = {1998}, volume = {29}, pages = {1177--1199}, number = {5}, } @ARTICLE{HaYuYo03, author = {B.~Han and T.~Yu and Y.-G.~Xue }, title = {Non-interpolatory {H}ermite subdivision schemes.}, journal = {Mathematics of Computation}, year = {2003}, volume = {to appear} } @INPROCEEDINGS{HaDo03a, author = {M.~Hassan and N.~Dodgson }, title = {Ternary and Three-point univariate subdivision schemes.}, booktitle = {Curve and Surface fitting: St Malo 2002}, year = {2003}, pages = {199--208}, } @ARTICLE{HaDo03b, author = {M.~Hassan and N.~Dodgson}, title = {Reverse Subdivision (Draft)}, journal = {unpublished}, year = {2003}, } @ARTICLE{HaIvDoSa02, author = {M.~Hassan and I.P.~Ivrissimtzis and N.~Dodgson and M.~Sabin }, title = {An interpolating 4-point ${C}^2$ ternary stationary subdivision scheme.}, journal = j-CAGD, year = {2002}, volume = {19}, pages = {1--18}, } @ARTICLE{Holt:1996:TCC, author = {F.~Holt}, title = {Towards a curvature-continuous stationary subdivision algorithm}, journal = {{Z}.\ {A}ngew.\ {M}ath.\ {M}ech.}, year = {1996}, volume = {76}, page = {423--424} } @ARTICLE{IvDoHa02, author = { I.P.~Ivrissimtzis and N.~Dodgson and M.~Hassan}, title = {On the geometry of recursive subdivision}, journal = {International Journal of Shape Modeling}, year = { 2002}, volume = {8}, pages = {23--42}, number = {1}, } @ARTICLE{IvDoHaSa02, author = {I.P.~Ivrissimtzis and N.~Dodgson and M.~Hassan and M.~Sabin }, title = {The refinability of the four point scheme}, journal = j-CAGD, year = {2002}, volume = {19}, pages = {235--238}, number = {4} } @INPROCEEDINGS{IvDoSa04, author = {I.P.~Ivrissimtzis and N.~Dodgson and M.~Sabin }, title = {$\sqrt5$ Subdivision.}, editor = {N.A.~Dodgson and M.S.~Floater and M.A.~Sabin}, booktitle = {Advances in Multiresolution for Geometric Modelling}, year = {2005}, publisher = {Springer}, pages = {285--300} } @TECHREPORT{IvDoSa02, author = {I.P.~Ivrissimtzis and N.A.~Dodgson and and M.A.~Sabin}, title = {A generative classification of mesh refinement rules with lattice transformations.}, institution = {Computer Laboratory, University of Cambridge}, year = {2002}, number = {UCAM-CL-TR-542}, } @INPROCEEDINGS{IvShSe03, author = {I.P.~Ivrissimtzis and K.~Shrivastava and H.-P.~Seidel }, title = {Subdivision rules for general meshes.}, booktitle = {St Malo 2002}, year = {2003}, pages = {229--237} } @TECHREPORT{IvSaDo02, author = {I.P.~Ivrissimtzis and M.~Sabin and N.~Dodgson }, title = {On the support of recursive subdivision surfaces.}, institution = {Computer Laboratory, University of Cambridge}, year = {2002}, number = {UCAM-CL-TR-544}, } @ARTICLE{JeShDa03, author = {M.~Jena and P.~Shunmugaraj and P.~Das}, title = {A non-stationary subdivision scheme for generalizing trigonometric spline surfaces to arbitrary meshes}, journal = {CAGD}, year = {2003}, volume = {20}, pages = {61--77}, } @ARTICLE{JeShDa02, author = {M.~Jena and P.~Shunmugaraj and P.~Das}, title = {A subdivision algorithm for trigonometric spline curves}, journal = {CAGD}, year = {2002}, volume = {19}, pages = {71--88}, } @ARTICLE{JuSc02, author = {B.~J{\"u}ttler and U.~Schwanecke }, title = {Analysis and design of {H}ermite subdivision schemes}, journal = {The Visual Computer}, year = {2002}, volume = {18}, pages = {326--342}, number = {5-6} } @INPROCEEDINGS{KaSeHa01, author = {S.~Karbacher and S.~Seeger and G.~H{\"a}usler}, title = {Refining Triangle Meshes by Non-linear Subdivision}, booktitle = {Third International Conference on 3-D Digital Imaging and Modeling}, year = {2001}, pages = {xiii+408}, } @ARTICLE{Karciauskas:2004:SCS, author = {K.~Kar{\v c}iauskas and J.~Peters and U.~Reif}, title = {Shape Characterization of Subdivision Surfaces -- {C}ase Studies}, journal = j-CAGD, year = {2004}, volume = {21}, pages = {601--614}, number = {6}, } @INPROCEEDINGS{KKK:2006:PJS, author = {K.~Kar{\v c}iauskas and A.~Myles and J.~Peters}, title = {A {$C^2$} Polar Jet Subdivision}, booktitle = {Proceedings of Symposium on Geometry Processing, June 26-28 2006, Cagliari, Italy}, year = {2006}, editor = {A.~Scheffer and K.~Polthier}, pages = {173--180}, publisher = {ACM Press} } @Article{Karciauskas:2006:CTM, author = "K.~Kar{\v c}iauskas and J.~Peters", title = {Concentric Tessellation Maps and Curvature Continuous Guided Surfaces}, journal = j-CAGD, volume = "24", number = "2", year = "2007", pages= "99--111", } @Article{Karciauskas:2007:CGS, author = "K. Kar{\v c}iauskas and J. Peters", title = "On the curvature of guided surfaces", volume = "25", number = "2", journal = "Computer Aided Geometric Design", pages = "69--79", month = "feb", year = "2008", } @ARTICLE{KKK:2007:BPS, author = {K\c{e}stutis Kar\v{c}iauskas and J\"{o}rg Peters}, title = {Bicubic polar subdivision}, journal = {ACM Trans. Graph.}, volume = {26}, number = {4}, year = {2007}, pages = {14}, publisher = {ACM}, address = {New York, NY, USA}, } @Article{KP:2006:SPS, author = "K.~Kar{\v c}iauskas and J.~Peters", title = "Surfaces with Polar Structure", journal = "Computing", volume = "79", pages = "309--315", year = "2007" } @misc{KP:200a:GS, author = {K.~Kar{\v c}iauskas and J.~Peters}, title = {Guided Subdivision}, year = {2005}, note = {http://www.cise.ufl.edu/research/SurfLab/papers.shtml} } @INPROCEEDINGS{KhSc99, author = {A.~Khodakovsky and P.~Schr{\"o}der}, title = {Fine Level feature editing for subdivision surfaces}, booktitle = {ACM Solid Modeling 1999}, year = {1999}, } @INPROCEEDINGS{Kobbelt:1995-1, author = {L.~Kobbelt}, title = {Interpolatory refinement by variational methods}, booktitle = {Approximation Theory VIII, Vol. 2: Wavelets and Multilevel Approximation}, year = {1995}, editor = {C.~Chui and L.L.~Schumaker}, pages = {217--224}, publisher = {World Scientific Publishing Co.} } @INPROCEEDINGS{Kobbelt:2000:sqrt3, author = {L.~Kobbelt}, title = {$\sqrt{3}$-subdivision}, booktitle = {SIGGRAPH '00: Proceedings of the 27th annual conference on Computer Graphics and interactive techniques}, year = {2000}, pages = {103--112}, address = {New York, NY, USA}, publisher = {ACM Press/Addison-Wesley Publishing Co.}, doi = {http://doi.acm.org/10.1145/344779.344835}, isbn = {1-58113-208-5} } @ARTICLE{Kobbelt:1998, author = {L.~Kobbelt}, title = {Using the discrete {F}ourier-transform to analyze the convergence of subdivision schemes}, journal = {Appl.\ Comp.\ Harmonic Anal.}, year = {1998}, volume = {5}, pages = {68--91} } @INPROCEEDINGS{Kobbelt:1996:interp, author = {L.~Kobbelt}, title = {Interpolatory Subdivision on Open Quadrilateral Nets with Arbitrary Topology}, booktitle = {Computer Graphics Forum 15(3), Eurographics '96 Conference Issue}, year = {1996}, pages = {409--420}, } @ARTICLE{Kobbelt:1996, author = {L.~Kobbelt}, title = {A variational approach to subdivision}, journal = j-CAGD, year = {1996}, volume = {13}, pages = {743--761} } @InProceedings{Mathematical_Methods'94*281, author = "L.~Kobbelt", title = "Interpolatory Refinement as a Low Pass Filter", pages = "281--290", editor = "M.~D{\ae}hlen and T.~Lyche and L.L.~Schumaker", booktitle = "Proceedings of the first Conference on Mathematical Methods for Curves and Surfaces ({MMCS}-94)", publisher = "Vanderbilt University Press", address = "Nashville, USA", year = "1995", } @ARTICLE{Lane:1980:TDC, author = {J.M.~Lane and R.F.~Riesenfeld}, title = {A theoretical development for computer generation and display of piecewise polynomial surfaces}, journal = {IEEE Transactions on Pattern Analysis and Machine Intelligence}, year = {1980}, volume = {2}, pages = {35--46}, number = {1}, } @MASTERSTHESIS{Leber:1994, author = {M.~Leber}, title = {Interpolierende {U}nterteilungsalgorithmen}, school = {Universit\"at Stuttgart}, year = {1994} } @INPROCEEDINGS{LeMoHo00, author = {A.~Lee and H.~Moreton and H.~Hoppe}, title = { Displaced Subdivision surfaces}, booktitle = {SIGGRAPH 2000}, year = {2000}, pages = {85--94}, } @ARTICLE{Levin:MSS:2006, author = {A.~Levin}, title = {Modified subdivision surfaces with continuous curvature}, journal = {ACM Transactions on Graphics}, year = {2006}, volume = {25}, pages = {1035--1040}, number = {3}, address = {New York, NY, USA}, doi = {http://doi.acm.org/10.1145/1141911.1141990}, issn = {0730-0301}, publisher = {ACM Press} } @ARTICLE{Levin:2003:PGQ, author = {A.~Levin }, title = {Polynomial generation and quasi-interpolation in stationary non-uniform subdivision}, journal = j-CAGD, year = {2003}, volume = {20}, number = {1}, pages = {41--60}, } @ARTICLE{Levin:2000:SDL, author = {A.~Levin}, title = {Surface Design using Locally Interpolating Subdivision Schemes}, journal = {Journal of Approximation Theory}, year = {2000}, volume = {104}, pages = {98--120}, } @INPROCEEDINGS{Levin:1999:INC, author = {A.~Levin }, title = {Interpolating nets of curves by smooth subdivision surfaces.}, booktitle = {Proc ACM SIGGRAPH 1999}, year = {1999}, pages = {57--64}, } @ARTICLE{Levin:1999:CSS, author = {A.~Levin }, title = {Combined subdivision schemes for the design of surfaces satisfying boundary conditions.}, journal = {CAGD}, year = {1999}, volume = {16}, pages = {345--354} } @PHDTHESIS{Levin1999:thesis, author = {A.~Levin }, title = {Combined subdivision schemes.}, school = {Tel-Aviv University}, year = {1999} } @ARTICLE{Levin2:2003:AQU, author = {A.~Levin and D.~Levin}, title = {Analysis of quasi uniform subdivision}, journal = {Applied and Computational Harmonic Analysis}, year = {2003}, volume = {15(1)}, pages = {18--32} } @ARTICLE{LiLeSc01, author = {N.~Litke and A.~Levin and P.~Schr{\"o}der}, title = {Trimming for subdivision surfaces}, journal = {CAGD}, year = {2001}, volume = {18}, pages = {463--481}, } @ARTICLE{Loop:2002:BCT, author = {C.~Loop }, title = {Bounded curvature triangle mesh subdivision with the convex hull property.}, journal = {The Visual Computer}, year = {2002}, volume = {18}, pages = {316--325}, number = {5-6} } @INPROCEEDINGS{Loop:2002:STS, author = {C.~Loop}, title = {Smooth ternary subdivision of triangle meshes}, booktitle = {Proceedings of Curve and Surface Fitting}, year = {2002}, pages = {295--302}, address = {Saint-Malo, France} } @MASTERSTHESIS{Loop:1987:SSS, author = {C.~Loop }, title = {Smooth subdivision surfaces based on triangles.}, school = {Department of Mathematics, University of Utah}, year = {1987}, } @INPROCEEDINGS{MaMaTsPa02, author = {W.~Ma and X.~Ma and S.-K.~Tso and Z.~Pan }, title = {Subdivision Surface Fitting from a dense Triangle Mesh.}, booktitle = {Proc Geometric Modeling and Processing 2002}, year = {2002}, pages = {94--103} } @INPROCEEDINGS{MaZh00, author = {W.~Ma and N.~Zhao }, title = {{C}atmull-{C}lark surface fitting for reverse engineering applications.}, booktitle = {GMP 2000, IEEE}, year = {2000}, pages = {274--283} } @INPROCEEDINGS{MaCrJo96, author = {R.~MacCracken and K.~Joy }, title = {Free-form deformations with lattices of arbitrary topology}, booktitle = {Proc ACM. SIGGRAPH 1996}, year = {1996}, pages = {181--188}, } @ARTICLE{Maillot:2001:USS, author = {J.~Maillot and J.~Stam}, title = {A Unified Subdivision Scheme for Polygonal Modeling}, journal = {Computer Graphics Forum}, year = {2001}, volume = {20}, pages = {471--479}, number = {3}, } @Article{MaMaTsPa04, title = "A direct approach for subdivision surface fitting from a dense triangle mesh", author = "W.~Ma and X.~Ma and S.K.~Tso and Z.~Pan", journal = "Computer Aided Design", year = "2004", number = "6", volume = "36", pages = "525--536", URL = "http://dx.doi.org/10.1016/S0010-4485(03)00160-X", } @ARTICLE{Merrien:1994:DHI, author = {J.-L.~Merrien }, title = {Dyadic {H}ermite interpolation on a triangulation.}, journal = {Numerical Algorithms}, year = {1994}, volume = {7}, pages = {391--410} } @ARTICLE{MeUt94, author = {J.-L.~Merrien }, title = {Convexity-preserving interpolatory subdivision}, journal = j-CAGD, year = {1994}, volume = {11}, pages = {17--37}, } @ARTICLE{Merrien:1992:FHI, author = {J.-L~ Merrien }, title = {A family of {H}ermite interpolants by bisection algorithms.}, journal = {Numerical Algorithms}, year = {1992}, volume = {2}, pages = {187--200} } @ARTICLE{Micchelli:1987-1, author = {C.A.~Micchelli and H.~Prautzsch}, title = {Computing curves invariant under halving }, journal = j-CAGD, year = {1987 }, volume = {4 }, pages = {133--140 } } @ARTICLE{MiPr87, author = {C.~Micchelli and H.~Prautzsch}, title = {Computing surfaces invariant under subdivision}, journal = {CAGD}, year = {1987}, volume = {4}, pages = {321--328}, } @ARTICLE{MoGo00, author = {G.~Morin and R.~Goldman}, title = {A subdivision scheme for {P}oisson curves and surfaces}, journal = {CAGD}, year = {2000}, volume = {17}, pages = {813--833}, } @ARTICLE{Morin:2001:SSS, author = {G.~Morin and J.~Warren and H.~Weimer}, title = {A subdivision scheme for surfaces of revolution}, journal = j-CAGD, year = {2001}, volume = {18}, pages = {483--502}, number = {5} } @ARTICLE{Habib:2001:SSS, author = {A.W.~Habib and J.~Warren}, title = {Edge and vertex insertion for a class of $C^1$-subdivision surfaces}, journal = j-CAGD, year = {1999}, volume = {16}, pages = {223--247}, number = {4} } @ARTICLE{Nasri:2003:IUN, author = {A.~Nasri}, title = {Interpolating an unlimited number of curves meeting at extraordinary points on subdivision surfaces}, journal = {Computer Graphics Forum}, year = {2003}, volume = {22}, pages = {87--97}, number = {1}, } @ARTICLE{Na91, author = {A.~Nasri}, title = {Boundary-corner control in recursive subdivision surfaces}, journal = j-CAD, year = {1991}, volume = {23}, pages = {405--410}, number = {6}, } @ARTICLE{NaFa01, author = {A.~Nasri and G.~Farin }, title = {A subdivision algorithm for generating rational curves.}, journal = {Journal of Graphics Tools}, year = {2001}, volume = {6}, pages = {35--47}, number = {1} } @ARTICLE{NaOvWy01, author = {A.~Nasri and K.~van Overfeld and B.~Wyvill }, title = {A Recursive Subdivision Algorithm for Piecewise Circular Spline.}, journal = {Computer Graphics Forum}, year = {2001}, volume = {20}, pages = {35--45}, number = {1}, } @ARTICLE{NaSa02:1, author = {A.~Nasri and M.~Sabin }, title = {Taxonomy of interpolation constraints on recursive subdivision curves.}, journal = {The Visual Computer}, year = {2002}, volume = {18}, pages = {259--272}, } @ARTICLE{NaSa02:2, author = {A.~Nasri and M.~Sabin }, title = {A taxonomy of interpolation constraints on recursive subdivision surfaces.}, journal = {The Visual Computer}, year = {2002}, volume = {18}, pages = {382--403}, } @INPROCEEDINGS{NaKiLe01, author = {A.~Nasri and T.-W.~Kim and K.~Lee }, title = {Fairing recursive subdivision surfaces with curve interpolation constraints}, booktitle = {3rd International Conference on Shape Modeling and Applications (SMI 2001)}, year = {2001}, pages = {49--59}, } @ARTICLE{Neamtu:1994:degen, author = {M.~Neamtu and P.R.~Pfluger}, title = {Degenerate polynomial patches of degree 4 and 5 used for geometrically smooth interpolation in ${R}^3$ }, journal = j-CAGD, year = {1994}, volume = {11}, pages = {451--474}, number = {4}, address = {Amsterdam, The Netherlands, The Netherlands}, doi = {http://dx.doi.org/10.1016/0167-8396(94)90208-9}, issn = {0167-8396}, publisher = {Elsevier Science Publishers B. V.} } @INPROCEEDINGS{Os03, author = {P.~Oswald }, title = {Smoothness of a nonlinear subdivision scheme.}, booktitle = {St Malo 2002}, year = {2003}, pages = {323--332}, } @ARTICLE{OsSc03, author = {P.~Oswald and P.~Schr{\" o}der }, title = {Composite primal/dual $\sqrt{3}$ subdivision schemes}, journal = {CAGD}, year = {2003}, volume = {20}, pages = {135--164}, } @INPROCEEDINGS{PaXu04, author = {Q.~Pan and G.~Xu}, title = {Fast Evaluation of the Improved {L}oop's Subdivision Surfaces}, booktitle = {Proceedings of the Geometric Modeling and Processing 2004}, year = {2004}, publisher = {IEEE Computer Society}, isbn = {0-7695-2078-2}, page = {205} } @INPROCEEDINGS{Peters:2000:PCC, author = {J.~Peters}, title = {Patching {C}atmull-{C}lark Meshes}, booktitle = {Siggraph 2000, Computer Graphics Proceedings}, year = {2000}, editor = {Kurt Akeley}, series = {Annual Conference Series}, pages = {255--258}, publisher = {ACM Press / ACM SIGGRAPH / Addison Wesley Longman}, keywords = {CAD, Curves Surfaces, Geometric Modeling}, url = {http://visinfo.zib.de/EVlib/Show?EVL-2000-62} } @INPROCEEDINGS{Peters:1996:SBZ, author = {J.~Peters}, title = {${C}^2$ surfaces built from zero sets of the 7-direction box spline}, booktitle = {The Mathematics of surfaces {VI}}, year = {1996}, editor = {Glen Mullineux}, pages = {463--474}, address = {NY}, publisher = {Clarendon Press} } @ARTICLE{Peters:2002:CFF, author = {J.~Peters}, title = {${C}^2$ Free-Form Surfaces of degree (3,5)}, journal = j-CAGD, year = {2002}, volume = {19}, pages = {113--126}, number = {2} } @INPROCEEDINGS{Peters:2002:GC, author = {J.~Peters}, title = {Geometric Continuity}, booktitle = {Handbook of Computer Aided Geometric Design}, year = {2002}, pages = {193--229}, publisher = {Elsevier}, editors = {G.~Farin and J.~Hoschek and M.~Kim} } @INPROCEEDINGS{Peters:1998:PSS, author = {J.~Peters}, title = {Some properties of subdivision derived from splines}, booktitle = {Subdivision for modeling and animation}, year = {1998}, number = {36}, series = {Course notes of 25th International conference on Computer Graphics and Interactive Techniques}, pages = {83--90}, publisher = {ACM Siggraph} } @INPROCEEDINGS{Peters:1991:PSE, author = {J.~Peters}, title = {Parametrizing singularly to enclose vertices by a smooth parametric surface}, booktitle = {Graphics Interface '91}, editor = {S.~MacKay and E.M.~Kidd}, year = {1991}, pages = {1--7}, address = {Calgary, Alberta}, publisher = {Canadian Information Processing Society} } @INPROCEEDINGS{PeWi97, author = {J.~Peters and M.~Wittman }, title = {Smooth blending of basic surfaces using trivariate box splines.}, booktitle = {Mathematics of Surfaces VII}, year = {1997}, pages = {409--426}, } @ARTICLE{Peters:2004:SCS, author = {J.~Peters and U.~Reif}, title = {Shape characterization of subdivision surfaces -- {B}asic principles}, journal = j-CAGD, year = {2004}, volume = {21}, pages = {585--599}, number = {6}, address = {Amsterdam, The Netherlands, The Netherlands}, doi = {http://dx.doi.org/10.1016/j.cagd.2004.04.06}, issn = {0167-8396}, publisher = {Elsevier Science Publishers B. V.} } @ARTICLE{Peters:1998:AGB, author = {J.~Peters and U.~Reif}, title = {Analysis of algorithms generalizing {$B$}-spline subdivision}, journal = {SIAM Journal on Numerical Analysis}, year = {1998}, volume = {35}, pages = {728--748}, number = {2}, } @ARTICLE{Peters:1997:SSS, author = {J.~Peters and U.~Reif}, title = {The simplest subdivision scheme for smoothing polyhedra}, journal = j-TOG, year = {1997}, volume = {16}, pages = {420--431}, number = {4}, issn = {0730-0301} } @ARTICLE{Peters:2004:C43, author = {J.~Peters and L.~Shiue}, title = {Combining 4- and 3-direction subdivision}, journal = {ACM Transactions on Graphics}, year = {2004}, volume = {23}, pages = {980--1003}, number = {4} } @ARTICLE{Peters:2001:PCC, author = {J.~Peters and G.~Umlauf}, title = {Computing curvature bounds for bounded curvature subdivision}, journal = j-CAGD, year = {2001}, pages = {455--462} } @INPROCEEDINGS{Peters:2000:GMC, author = {J.~Peters and G.~Umlauf}, title = {Gaussian and Mean Curvature of Subdivision Surfaces}, booktitle = {Proceedings of the 9th IMA Conference on the Mathematics of Surfaces}, year = {2000}, pages = {59--69}, address = {London, UK}, publisher = {Springer-Verlag}, isbn = {1-85233-358-8} } @ARTICLE{Peters:2006:NSD, author = {J.~Peters and X.~Wu}, title = {Net-to-Surface Distance of Subdivision Functions}, journal = {JAT}, year = {2007}, note = {in revision} } @ARTICLE{Wu:2005:LLI, author = {J.~Peters and X.~Wu}, title = {On the Local Linear Independence of Generalized Subdivision Functions}, journal = {SIAM J. Numer.~Anal.}, year = {2006}, volume = {44}, pages = {2389--2407}, number = {6}, } @ARTICLE{Prautzsch:1998:SSS, author = {H.~Prautzsch }, title = {Smoothness of subdivision surfaces at extraordinary points.}, journal = {Advances in Computational Mathematics}, year = {1998}, volume = {9}, pages = {377--389}, } @ARTICLE{prautzsch97ff, author = {H.~Prautzsch}, title = {Freeform splines}, journal = j-CAGD, year = {1997}, volume = {14}, pages = {201--206}, number = {3}, } @ARTICLE{Prautzsch-Reif:1998, author = {H.~Prautzsch and U.~Reif}, title = {Degree estimates for {$C^k$}-piecewise polynomial subdivision surfaces}, journal = {Advances in Computational Mathematics}, year = {1999}, volume = {10}, number = {2}, pages = {209--217} } @ARTICLE{Prautzsch:2000:GGS, author = {H.~Prautzsch and G.~Umlauf}, title = {A ${G}^1$ and a ${G}^2$ subdivision scheme for triangular nets}, journal = {Int. J. Shape Modelling}, year = {2000}, volume = {6}, pages = {21--35}, number = {1} } @INPROCEEDINGS{Prautzsch:1998:ITS, author = {H.~Prautzsch and G.~Umlauf}, title = {Improved Triangular Subdivision Schemes}, booktitle = {CGI '98: Proceedings of the Computer Graphics International 1998}, year = {1998}, pages = {626--632}, address = {Washington, DC, USA}, publisher = {IEEE Computer Society}, } @ARTICLE{Prautzsch:1998:GSA, author = {H.~Prautzsch and G.~Umlauf }, title = {A ${G}^2$ subdivision algorithm.}, year = {1998}, journal = {Computing}, volume = {13}, pages = {217--224}, } @ARTICLE{PrSaSmKa03, author = {P.~Prusinkiewicz and F.~Samavati and C.~Smith and R.~Karwowski }, title = {L-system description of subdivision curves.}, journal = {International Journal of Shape Modeling}, year = {2003}, volume = {9}, pages = {41--59} } @INPROCEEDINGS{Qin:1999:ECN, author = {K.~Qin and H.~Wang }, title = {Eigenanalysis and continuity of non-uniform {D}oo-{S}abin surfaces.}, booktitle = {Proc Pacific Graphics 99}, year = {1999}, pages = {179--186}, } @INPROCEEDINGS{QuGr92, author = {R.~Qu and J.~Gregory }, title = {A subdivision algorithm for non-uniform {B}-splines}, booktitle = {Approximation Theory, Spline Functions and Applications}, editor = {Singh}, year = {1992}, pages = {423--436}, } @INPROCEEDINGS{Reif:1995-6, author = {U.~Reif}, title = {Some new results on subdivision algorithms for meshes of arbitrary topology}, booktitle = {Wavelets and Multilevel Approximation}, year = {1995}, editor = {C.K.~Chui and L.L.~Schumaker}, volume = {2}, series = {Series in Approximations and Decompositions}, pages = {367--374}, publisher = {World Scientific} } @BOOK{Reif:1999:habil, title = {Analyse und {K}onstruktion von {S}ubdivisionsalgorithmen f{\"u}r {F}reiformfl{\"a}chen beliebiger {T}opologie}, publisher = {Shaker Verlag}, year = {1999}, author = {U.~Reif}, note = {Habilitationsschrift} } @ARTICLE{Reif:1998:turbs, author = {U.~Reif}, title = {T{U}{R}{B}{S}---topologically unrestricted rational ${B}$-splines}, journal = {Constructive Approximation}, year = {1998}, volume = {14}, pages = {57--77}, number = {1} } @ARTICLE{Reif:1997:RSS, author = {U.~Reif}, title = {A refinable space of smooth spline surfaces of arbitrary topological genus}, journal = {Journal of Approximation Theory}, year = {1997}, volume = {90}, pages = {174--199}, number = {2} } @ARTICLE{Reif:1996:DES, author = {U.~Reif }, title = {A degree estimate for subdivision surfaces of higher regularity.}, journal = {Proc. AMS}, year = {1996}, volume = {124}, pages = {2167--2174}, number = {7}, } @ARTICLE{Reif:1995:UAS, author = {U.~Reif}, title = {A unified approach to subdivision algorithms near extraordinary vertices}, journal = j-CAGD, year = {1995}, volume = {12}, pages = {153--174}, number = {2}, } @ARTICLE{Reif:1995:DTB, author = {U.~Reif}, title = {A note on degenerate triangular {B}e\'zier patches}, journal = j-CAGD, year = {1995}, volume = {12}, pages = {547--550}, number = {5}, address = {Amsterdam, The Netherlands, The Netherlands}, publisher = {Elsevier Science Publishers B. V.} } @PHDTHESIS{Reif:1993:thesis, author = {U.~Reif}, title = {Neue {A}spekte in der {T}heorie der {F}reiformfl{\"a}chen beliebiger {T}opologie}, school = {Universit{\"a}t Stuttgart}, year = {1993} } @INPROCEEDINGS{Reif:2005, author = {U.~Reif and J.~Peters}, title = {Structural Analysis of Subdivision Surfaces -- A Summary}, booktitle = {Topics in Multivariate Approximation and Interpolation}, year = {2005}, editor = {K.~Jetter et al.}, volume = {12}, pages = {149--190} } @ARTICLE{Reif:2001:CSS, author = { U.~Reif and P.~Schr{\"o}der}, title = {Curvature Smoothness of Subdivision Surfaces}, journal = {Advances in Computational Mathematics}, year = {2001}, volume = {14}, pages = {157--174}, number = {2} } @ARTICLE{Riesenfeld:1975:CA, author = {R.F.~Riesenfeld}, title = {On {C}haikin's algorithm}, journal = {{IEEE} Computer Graphics and Applications}, year = {1975}, volume = {4}, pages = {304--310} } @INPROCEEDINGS{SkAkPa01, author = {S.~Skaria and E.~Akleman and F.~Parke }, title = {Modeling subdivision control meshes for creating cartoon faces.}, booktitle = {Proc Shape Modeling and Applications 2001}, year = {2001}, pages = {216--225}, } @INPROCEEDINGS{Sabin:1986:RD, author = {M.~Sabin}, title = {Recursive Division}, booktitle = {The Mathematics of Surfaces}, year = {1986}, editor = {J.~Gregory}, pages = {269--282}, publisher = {Clarendon Press, Oxford}, isbn = {0 19 853609 7}, } @ARTICLE{Sa04, author = {M.~Sabin }, title = {A circle-preserving interpolatory subdivision scheme.}, journal = {(in preparation)}, year = {2004} } @INPROCEEDINGS{Sa02a, author = {M.~Sabin }, title = {Eigenanalysis and Artifacts of Subdivision Curves and Surfaces.}, booktitle = {Primus Workshop Proceedings}, year = {2002}, pages = {69--92} } @INPROCEEDINGS{Sa02b, author = {M.~Sabin }, title = {Subdivision of Box-Splines.}, booktitle = {Primus Workshop Proceedings}, year = {2002}, pages = {3--23} } @INPROCEEDINGS{Sa02c, author = {M.~Sabin }, title = {Subdivision Surfaces.}, booktitle = {Handbook of Computer Aided Geometric Design}, year = {2002}, pages = {309--326}, publisher = {Elsevier}, editors = {G.~Farin and J.~Hoschek and M.~Kim} } @INPROCEEDINGS{Sa02d, author = {M.~Sabin }, title = {Interrogation of Subdivision Surfaces.}, booktitle = {Handbook of Computer Aided Geometric Design}, year = {2002}, pages = {327--341}, publisher = {Elsevier}, editors = {G.~Farin and J.~Hoschek and M.~Kim} } @INPROCEEDINGS{Sabin:1991:CRD, author = {M.~Sabin }, title = {Cubic recursive division with bounded curvature.}, booktitle = {Curves and Surfaces}, editor = {L.L.~Schumaker and J.~Laurent and A.~LeMehaute}, publisher = { Academic Press}, year = {1991}, pages = {411--414}, } @INPROCEEDINGS{Sa91b, author = {M.~Sabin }, title = {$\omega$-convergence, a criterion for linear approximation.}, booktitle = {Curves and Surfaces}, editor = {L.L.~Schumaker and J.~Laurent and A.~LeMehaute}, publisher = { Academic Press}, year = {1991}, pages = {415--420}, } @INPROCEEDINGS{SaBe03, author = {M.~Sabin and A.~Bejancu }, title = {Boundary conditions for the 3-direction box-spline}, booktitle = {Maths of Surfaces X}, year = {2003}, } @INPROCEEDINGS{Sabin:2002:ATS, author = {M.~Sabin and L.~Barthe}, title = {Analysis and tuning of subdivision algorithms}, booktitle = {Curves and Surfaces}, year = {2002}, publisher = {Vanderbilt Press} } @ARTICLE{SaDoHaIv03, author = {M.~Sabin and N.~Dodgson and M.~Hassan and I.~Ivrissimtzis}, title = {Curvature behaviours at extraordinary points of subdivision surfaces}, journal = {CAD}, year = {2003}, pages = {1047--1051}, vol = {35} } @INPROCEEDINGS{SaBa03, author = {M.~Sabin and L.~Barthe }, title = {Artifacts in recursive subdivision surfaces.}, booktitle = {St Malo 2002}, year = {2003}, pages = {353--362}, } @TECHREPORT{SaBa01, author = {F.~Samavati and R.~Bartels }, title = {Reversing Subdivision using local linear conditions: generating multiresolutions on regular triangular meshes.}, institution = {University of Waterloo}, year = {2001}, number = {http://www.cgl.uwaterloo.ca/~rhbartel/Papers/TriMesh.pdf} } @ARTICLE{SaBa99, author = {F.~Samavati and R.~Bartels }, title = {Multiresolution curve and surface representation: reversing subdivision rules by least-squares data fitting.}, journal = {Computer Graphics Forum}, year = {1999}, volume = {18}, pages = {97--119} } @ARTICLE{Samavati:2002, author = {F.~Samavati and M.-A.~Nezam and R.~Bartels}, title = {Multiresolution Surfaces having Arbitrary Topologies by a Reverse {D}oo Subdivision Method}, journal = {Computer Graphics Forum}, year = {2002}, volume = {21}, pages = {121--134}, number = {2}, doi = {10.1111/1467-8659.00572}, eprint = {http://www.blackwell-synergy.com/doi/pdf/10.1111/1467-8659.00572}, url = {http://www.blackwell-synergy.com/doi/abs/10.1111/1467-8659.00572} } @ARTICLE{Schaefer:CTQ:2005, author = {S.~Schaefer and J.~Warren}, title = {On {C}$^2$ triangle/quad subdivision}, journal = {ACM Transactions on Graphics}, year = {2005}, volume = {24}, pages = {28--36}, number = {1} } @ARTICLE{Sc03, author = {P.~Schr{\"o}der}, title = {Subdivision as a fundamental Building Block of Digital Geometry Processing Algorithms.}, journal = {J. Comput. Appl. Math.}, year = {2002}, volume = {149}, pages = {207--219}, number = {1}, } @BOOK{Sc81, title = {`Spline Functions'}, publisher = {John Wiley}, year = {1981}, author = {L.L.~Schumaker }, address = {New York} } @INPROCEEDINGS{SeSeSa98, author = {T.~Sederberg and D.~Sewell and M.~Sabin }, title = {Non-uniform recursive subdivision surfaces.}, booktitle = {Proceedings of SIGGRAPH 1998}, year = {1998}, pages = {387--394}, } @ARTICLE{sederberg03tsplines, author = {T.W.~Sederberg and J.~Zheng and A.~Bakenov and A.~Nasri}, title = {T-splines and {T}-NURCCs}, journal = {ACM Trans. Graph.}, year = {2003}, volume = {22}, pages = {477--484}, number = {3}, address = {New York, NY, USA}, doi = {http://doi.acm.org/10.1145/882262.882295}, issn = {0730-0301}, publisher = {ACM Press} } @INPROCEEDINGS{Shieu:2005:PCC, author = {L.-J.~Shiue and I.~Jones and J.~Peters}, title = {A Realtime {GPU} Subdivision Kernel}, booktitle = {Siggraph 2005, Computer Graphics Proceedings}, year = {2005}, editor = {Marcus Gross}, series = {Annual Conference Series}, pages = {1010--1015}, publisher = {ACM Press / ACM SIGGRAPH / Addison Wesley Longman} } @INPROCEEDINGS{Shiue:2005:EC, author = {L.-J.~Shiue and J.~Peters}, title = {Mesh Refinement based on {E}uler Encoding}, booktitle = {Proceedings of The International Conference on Shape Modeling and Applications 2005}, year = {2005}, pages = {343--348} } @ARTICLE{Shiue:2003:MMP, author = {L.J.~Shiue and J.~Peters}, title = {Mesh mutation in programmable graphics hardware}, journal = {Eurographics/Siggraph Hardware Workshop}, year = {2003}, pages = {1--10}, } @INPROCEEDINGS{Stam:1998:EEC, author = {J.~Stam}, title = {Exact Evaluation of {C}atmull-{C}lark Subdivision Surfaces at Arbitrary Parameter Values}, booktitle = {SIGGRAPH 98 Proceedings}, year = {1998}, editor = {M.~Cohen}, pages = {395--404}, publisher = {Addison Wesley} } @ARTICLE{St01, author = {J.~Stam}, title = {On subdivision schemes generalizing uniform {B}-spline surfaces of arbitrary degree}, journal = {CAGD}, year = {2001}, volume = {18}, pages = {383--396}, } @Article{Dahmen:1985-1, author = {W.~Dahmen and N.~Dyn and D.~Levin }, title = {On the convergence rates of subdivision algorithms for box splines }, journal = {Constructive Approximation }, year = {1985}, volume = {1}, pages = {305--322 } } @MISC{stam98evaluation, author = {J.~Stam}, title = {Evaluation Of {L}oop Subdivision Surfaces}, year = {1998}, text = {J.~Stam. Evaluation Of Loop Subdivision Surfaces. SIGGRAPH '98 CDROM Proceedings, 1998.}, note = {SIGGRAPH '98 CDROM Proceedings}, } @ARTICLE{Stam:QTS:2003, author = {J.~Stam and C.T.~Loop}, title = {Quad/Triangle Subdivision}, journal = {Computer Graphics Forum}, year = {2003}, volume = {22}, pages = {79--86}, number = {1} } @PHDTHESIS{Storry:1985, author = {D.J.T.~Storry}, title = {B-spline surfaces over an irregular topology by recursive subdivision}, year = {1985}, school = {Leicestershire}, institution = {Loughborough University of Technology} } @INPROCEEDINGS{SuTaKa99, author = {H.~Suzuki and S.~Takeuchi and T.~Kanai }, title = {Subdivision surface fitting to a range of points.}, booktitle = {Proc. Pacific Graphics 99}, year = {1999}, pages = {158--167} } @ARTICLE{Takahashi:1999:MCD, author = {S.~Takahashi}, title = {Multiresolution Constraints for designing subdivision surfaces via local smoothing}, journal = {IEEE}, year = {1999}, pages = {168--178,323}, } @ARTICLE{Ta02, author = {G.~Taubin }, title = {Detecting and Reconstructing subdivision connectivity.}, journal = {The Visual Computer}, year = {2002}, volume = {18}, pages = {357--367}, number = {5-6} } @INPROCEEDINGS{Umlauf:2005:ATS, author = {G.~Umlauf}, title = {Analysis and tuning of subdivision algorithms}, booktitle = {SCCG '05: Proceedings of the 21st spring conference on Computer graphics}, year = {2005}, pages = {33--40}, address = {New York, NY, USA}, publisher = {ACM Press}, } @ARTICLE{Umlauf:1996:ACM, author = {G.~Umlauf}, title = {Analyzing the characteristic map of triangular subdivision schemes}, journal = {Constructive Approximation}, year = {2000}, volume = {16}, pages = {145--155}, number = {1}, } @INPROCEEDINGS{Umlauf:2003:TVS, author = {G.~Umlauf}, title = {A Technique for Verifying the Smoothness of Subdivision Schemes}, booktitle = {Geometric Modeling and Computing: Seattle 2003}, editor = {M.L.~Lucian, M.~Neamtu}, publisher = {Nashboro Press}, year = {2004}, } @PHDTHESIS{Umlauf:1999:thesis, author = {G.~Umlauf}, title = {Glatte Freiformfl{\"a}chen und optimierte Unterteilungsalgorithmen}, year = {1999}, school = { Informatik}, publisher = {Verlag Shaker, Aachen}, institution = { University of Karlsruhe} } @ARTICLE{Velho:2001:USM, author = {L.~Velho}, title = {Using semiregular 4-8 meshes for subdivision surfaces}, journal = {Journal of Graphics Tools}, year = {2001}, volume = {5}, number = {3}, page = {35--47} } @ARTICLE{Velho:2001:Q48, author = {L.~Velho }, title = {Quasi 4-8 subdivision.}, journal = j-CAGD, year = {2001}, volume = {18}, pages = {345--358}, number = {4}, } @ARTICLE{Velho:2001:48S, author = {L.~Velho and D.~Zorin }, title = {4-8 subdivision.}, journal = j-CAGD, year = {2001}, volume = {18}, pages = {397--427}, number = {5}, } @ARTICLE{DaMi86, author = {W.~Dahmen and C.~Micchelli}, title = {On the piecewise structure of discrete box-splines}, journal = j-CAGD, year = {1986}, volume = {3}, pages = {185--191}, } @INPROCEEDINGS{Wa97, author = {J.~Warren }, title = {Sparse filter banks for binary subdivision schemes}, booktitle = {Mathematics of Surfaces VII }, year = {1997}, pages = {427--438} } @INPROCEEDINGS{Wa95, author = {J.~Warren }, title = {Binary subdivision schemes for functions of irregular knot sequences.}, booktitle = {Ulvik 1996}, year = {1995}, pages = {543--562}, } @BOOK{WaWe02, title = {Subdivision Methods for Geometric design.}, publisher = {Morgan Kaufmann}, year = {2002}, author = {J.~Warren and H.~Weimer }, address = {New York} } @ARTICLE{WaSc04, author = {J.~Warren and S.~Schaefer}, title = {A Factored Approach to Subdivision Surfaces}, journal = {Computer graphics and applications, IEEE}, year = {2004}, volume = {24}, pages = {74--81}, issue = {3}, } @INPROCEEDINGS{WeWa99, author = {H.~Weimer and J.~Warren}, title = {Subdivision Schemes for fluid flow.}, booktitle = {Proc ACM SIGGRAPH 99}, year = {1999}, pages = {111--120}, } @ARTICLE{WeWa98, author = {H.~Weimer and J.~Warren}, title = {Subdivision Schemes for Thin Plate Splines}, journal = {Com{\-}pu{\-}ter Graphics Forum}, year = {1998}, volume = {17}, pages = {303--313}, number = {3}, url = {citeseer.ist.psu.edu/weimer97subdivision.html} } @INPROCEEDINGS{Wu:2005:AEM, author = {X.~Wu and J.~Peters}, title = {An Accurate Error Measure for Adaptive Subdivision Surfaces}, booktitle = {Proceedings of The International Conference on Shape Modeling and Applications 2005}, year = {2005}, pages = {51--57} } @ARTICLE{Wu:2004:IDS, author = {X.~Wu and J.~Peters}, title = {Interference Detection for Subdivision Surfaces}, journal = {Computer Graphics Forum, Eurographics 2004}, year = {2004}, volume = {23}, pages = {577--585}, number = {3}, } @ARTICLE{XieYu04, author = {G.~Xie and T.P.~Yu}, title = {Smoothness Analysis of Nonlinear Subdivision Schemes of Homogeneous and Affine Invariant Type}, journal = {Constructive Approximation}, year = {2004}, note = {To appear. Preprint available at http://www.rpi.edu/$\sim$yut/Papers/quasilinear.pdf} } @article{Hoellig:1990:GS, author = {K.~H{\"o}llig and H.~M{\"o}gerle}, title = {G-splines}, volume = {7}, number = {1-4}, journal = j-CAGD, year = {1990}, pages = {197--208}, } @ARTICLE{ZhGu02, author = {H.-X.~Zhang and G.-J.~Wang}, title = {Honeycomb subdivision}, journal = {Journal of Software}, year = {2002}, volume = {13}, pages = {1--9}, number = {4}, } @PHDTHESIS{Zorin:1997:thesis, author = {D.~Zorin}, title = {Subdivision and multiresolution surface representations}, school = {Caltech, Pasadena}, year = {1997} } @ARTICLE{ZoKr02, author = {D.~Zorin and D.~Kristjansson }, title = {Evaluation of piecewise smooth subdivision surfaces.}, journal = {The Visual Computer}, year = {2002}, volume = {18}, pages = {299--315}, number = {5-6}, } @INPROCEEDINGS{Zorin:1996:ISM, author = {D.~Zorin and P.~Schr{\"o}der and W.~Sweldens }, title = {Interpolatory subdivision for meshes with arbitrary topology.}, booktitle = {Proc ACM SIGGRAPH 1996}, year = {1996}, pages = {189--192} } @ARTICLE{Zorin:2001:primdual, author = {D.~Zorin and P.~Schr{\"o}der }, title = {A unified framework for primal/dual quadrilateral subdivision schemes.}, journal = {CAGD}, year = {2001}, volume = {18}, pages = {429--454} } @Article{Zulti06, author = "A.~Zulti and A.~Levin and D.~Levin and M.~Teicher", title = "${C}^2$ subdivision over triangulations with one extraordinary point", journal = j-CAGD, year = "2006", number = "2", volume = "23", pages = "157--178", address = {Amsterdam, The Netherlands, The Netherlands}, issn = {0167-8396}, publisher = {Elsevier Science Publishers B. V.}, URL = "http://dx.doi.org/10.1016/j.cagd.2005.06.001", } @PROCEEDINGS{CoMeSc03, title = {Curve and Surface Fitting}, year = {2003}, editor = {A.~Cohen and J.-L.~Merrian and L.L.~Schumaker}, address = {Brentwood TN}, publisher = {Nashboro Press, ISBN 0-9728482-1-5} } @PROCEEDINGS{DoFlSa04, title = {Advances in Multiresolution for Geometric Modelling}, year = {2005}, editor = {N.~Dodgson and M.~Floater and M.~Sabin }, publisher = {Springer}, } @PROCEEDINGS{Ru96, title = {SIGGRAPH proceedings 1996}, year = {1996}, editor = {H.~Rushmeier}, publisher = {Addison Wesley} } @PROCEEDINGS{GoMa97, title = {Mathematics of Surfaces VII}, year = {1997}, editor = {T.~Goodman and R.~Martin}, address = {Winchester, UK}, publisher = {Information Geometers Ltd., ISBN 1-874728-12-7} } @INPROCEEDINGS{ScWa03, author = {S.~Schaefer and J.~Warren }, title = {A factored interpolatory subdivision scheme for quadrilateral surfaces}, booktitle = {St Malo 2002}, year = {2003}, pages = {373--382}, } @ARTICLE{Zwart:1973:MSN, author = {P.B.~Zwart}, title = {Multivariate Splines with Nondegenerate Partitions}, journal = {SIAM Journal on Numerical Analysis}, year = {1973}, volume = {10}, pages = {665--673}, number = {4}, } @Article{Dahmen:1984:SAG, author = "W.~Dahmen and C.~Micchelli", title = "Subdivision algorithms for the generation of box spline surfaces", journal = j-CAGD, year = "1984", volume = "1", number = "2", pages = "115--129", } @Article{journals/tog/PrautzschU06, title = "Parametrizations for triangular ${G}^k$ spline surfaces of low degree", author = "H.~Prautzsch and G.~Umlauf", journal = "ACM Trans. Graph", year = "2006", number = "4", volume = "25", pages = "1281--1293", } @article{Zorin:2000:SSS, AUTHOR = {D.~Zorin}, TITLE = {Smoothness of stationary subdivision on irregular meshes}, JOURNAL = {Constructive Approximation}, VOLUME = {16}, YEAR = {2000}, NUMBER = {3}, PAGES = {359--397}, } @article{Zorin:2000:MAC, AUTHOR = {D.~Zorin}, TITLE = {A method for analysis of {$C\sp 1$}-continuity of subdivision surfaces}, JOURNAL = {SIAM J. Numer. Anal.}, VOLUME = {37}, YEAR = {2000}, NUMBER = {5}, PAGES = {1677--1708}, } @article{Shenkman:1999:NBS, AUTHOR = {P.~Shenkman and N.~Dyn and D.~Levin}, TITLE = {Normals of the butterfly subdivision scheme surfaces and their applications}, NOTE = {Special issue: computational methods in computer graphics}, JOURNAL = {J. Comput. Appl. Math.}, FJOURNAL = {Journal of Computational and Applied Mathematics}, VOLUME = {102}, YEAR = {1999}, NUMBER = {1}, PAGES = {157--180}, } @phdthesis{Grinspun:thesis, title = "The Basis Refinement Method", author = "E.~Grinspun", school = "California Institute of Technology", year = "2003", note = "page 39" } @InProceedings{Grinspun:2002, author = "E.~Grinspun and P.~Krysl and P.~Schr{\"o}der", title = "{CHARMS}: {A} Simple Framework for Adaptive Simulation", editor = "J.~Hughes", series = "Annual Conference Series", booktitle = "SIGGRAPH 2002 Conference Proceedings", publisher = "ACM Press/ACM SIGGRAPH", year = "2002", pages = "281--290", } @Article{Lounsbery:1997:MAS, author = "M.~Lounsbery and T.D.~De{R}ose and J.~Warren", title = "Multiresolution Analysis for Surfaces of Arbitrary Topological Type", journal = "ACM Transactions on Graphics", year = "1997", volume = "16", number = "1", pages = "34--73", } @article{Nasri:1987:subd, author = {A.H.~Nasri}, title = {Polyhedral subdivision methods on free-form surfaces}, journal = "ACM Transactions on Graphics", year = {1987}, volume = {6}, number = {1}, pages = {29--73}, } @Misc{Stam:1998:ELS, title = "Evaluation of {L}oop Subdivision Surfaces", author = "J.~Stam", year = "1998", booktitle = "SIGGRAPH 98 Proceedings notes", } @InProceedings{Kobbelt:1998:PAC, author = "L.~Kobbelt", title = "Tight Bounding Volumes for Subdivision Surfaces", pages = "17--26", editor = "Bob Werner", booktitle = "Pacific-Graphics'98", publisher = "IEEE", year = "1998", } @Article{Lutterkort:2001:TLB, author = "D.~Lutterkort and J.~Peters", title = {Tight Linear bounds on the distance between a spline and its {B}-spline control polygon}, journal = "Numerische Mathematik", volume = "89", year = "2001", pages= "735--748", } @Article{Nairn:1999:SQB, author = "D.~Nairn and J.~Peters and D.~Lutterkort", title = "Sharp, quantitative bounds on the distance between a polynomial piece and its {B{\'e}zier} control polygon", journal = j-CAGD, volume = "16", number = "7", year = "1999", ISSN = "0167-8396", pages= "613--633", } @article{prautzsch:kobbelt:94, author = {H.~Prautzsch and L.~Kobbelt}, title = {Convergence of subdivision and degree elevation}, journal ={Advances in Computational Mathematics}, volume = {2}, year = {1994}, pages = {143--154}, } @article{reif:2000, author = {U.~Reif}, title = {Best bounds on the approximation of polynomials and splines by their control structure}, journal = j-CAGD, pages = {579--589}, year = {2000}, volume = {17}, number = {6}, } @Article{Filip86, author = "D.~Filip and R.~Magedson and R.~Markot", title = "Surface algorithms using bounds on derivatives", journal = j-CAGD, year = "1986", volume = "3", number = "4", pages = "295--311", keywords = "surface mesh", } @book{Jury:1964:TAz, author = {E.I.~Jury}, title = {Theory and Applications of the $z$-Transform Method}, publisher = {Wiley, New York}, year = {1964} } @article{deRham:1956:SCP, AUTHOR = {G.~de Rham}, TITLE = {Sur une courbe plane}, JOURNAL = {J. Math. Pures Appl. (9)}, FJOURNAL = {Journal de Math\'ematiques Pures et Appliqu\'ees. Neuvi\`eme S\'erie}, VOLUME = {35}, YEAR = {1956}, PAGES = {25--42}, } @article{deRham:1947:UPD, AUTHOR = {G.~de Rham}, TITLE = {Un peu de math\'ematiques \`a propos d'une courbe plane}, JOURNAL = {Elemente der Math.}, VOLUME = {2}, YEAR = {1947}, PAGES = {73--76, 89--97}, } @Article{Cohen:1984:DBS, author = "E.~Cohen and T.~Lyche and R.F.~Riesenfeld", title = "Discrete box splines and refinement algorithms", journal = j-CAGD, year = "1984", volume = "1", number = "2", pages = "131--148", } @InProceedings{Litke:2001:FSS, author = "N.~Litke and A.~Levin and P.~Schr{\"o}der", title = "Fitting subdivision surfaces", pages = "319--324", booktitle = "Proceedings of the Conference on Visualization 2001 ({VIS}-01)", editor = "T.~Ertl and K.~Joy and A.~Varshney", publisher = "IEEE Computer Society", year = "2001", } @incollection{Cohen:1996:SIM, AUTHOR = {A.~Cohen and N.~Dyn and D.~Levin}, TITLE = {Stability and inter-dependence of matrix subdivision schemes}, BOOKTITLE = {Advanced topics in multivariate approximation (Montecatini Terme, 1995)}, SERIES = {Ser. Approx. Decompos.}, VOLUME = {8}, PAGES = {33--45}, PUBLISHER = {World Sci. Publ., River Edge, NJ}, YEAR = {1996}, } @article{Xue:2006:JSS, AUTHOR = {Y.~Xue and T.~Yu and T.~Duchamp}, TITLE = {Jet subdivision schemes on the {$k$}-regular complex}, journal = j-CAGD, VOLUME = {23}, YEAR = {2006}, NUMBER = {4}, PAGES = {361--396}, } @Article{Peters:1997:CVS, author = "J.~Peters and A.~Nasri", title = "Computing Volumes of Solids Enclosed by Recursive Subdivision Surfaces", journal = j-CGF, volume = "16", number = "3", year = "1997", pages= "C89--C94", } @article{Labsik:2000:IsS, author = {U.~Labsik and G.~Greiner}, title = {Interpolatory $\sqrt{3}$-subdivision}, journal = {Computer Graphics Forum (EUROGRAPHICS 2000)}, volume = {19}, number = {3}, pages = {131--138}, year = {2000}, } @InProceedings{Zorin:2006:CCC, author = "D.~Zorin", title = "Constructing Curvature-continuous Surfaces by Blending", booktitle = "Eurographics Symposium on Geometry Processing", editor = "A.~Sheffer and K.~Polthier", year = "2006", publisher = "Eurographics Association", pages = "31--40", } @book{Prautzsch:2002:BBT, AUTHOR = {H.~Prautzsch and W.~Boehm and M.~Paluszny}, TITLE = {B\'ezier and {B}-spline techniques}, SERIES = {Mathematics and Visualization}, PUBLISHER = {Springer-Verlag}, ADDRESS = {Berlin}, YEAR = {2002}, PAGES = {xiv+304}, } @article{Rioul:1992:SRC, author = {O.~Rioul}, title = {Simple Regularity Criteria for Subdivision Schemes}, journal = {SIAM Journal on Mathematical Analysis}, volume = {23}, number ={6}, pages = {1544--1576}, year = {1992} } @article{Dyn:1990:UPI, author = {N.~Dyn and D.~Levin and C.A.~Micchelli}, title = {Using parameters to increase smoothness of curves and surfaces generated by subdivision}, journal = j-CAGD, volume = {7}, year = {1990}, pages = {129--140} } @Article{Wang:1999, title = "Fast Implementation of Scale-Space by Interpolatory Subdivision Scheme", author = "Y.-P.~Wang and R.~Qu", journal = "IEEE Trans. Pattern Anal. Mach. Intell", year = "1999", number = "9", volume = "21", pages = "933--939", } @article{Gregory:1996:NCC, author = {J.A.~Gregory and R.~Qu}, title = {Nonuniform corner cutting}, journal = j-CAGD, volume = {13}, number = {8}, year = {1996}, pages = {763--772}, publisher = {Elsevier Science Publishers B. V.}, address = {Amsterdam, The Netherlands, The Netherlands}, } @Article{BaKo04, author = "L.~Barthe and L.~Kobbelt", title = "Subdivision scheme tuning around extraordinary vertices", journal = j-CAGD, year = "2004", volume = "21", number = "6", pages = "561--583", } @InProceedings{Ginkel:2006:CST, editor = "A.~Cohen, J.L.~Merrien, L.L.~Schumaker", booktitle = "Curve and Surface Fitting", year = "2006", publisher = "Nashboro Press", author = "I.~Ginkel and G.~Umlauf", title = "Controlling a subdivision tuning method", pages = "170--179", } @InProceedings{Ginkel:2007:TSA, author = "I.~Ginkel and G.~Umlauf", title = "Tuning subdivision algorithms using constrained energy minimization", editor = "J.~Winkler", booktitle = "Mathematics of Surfaces XII", year = "2007", publisher = "Springer-Verlag", pages = "166--176", } @INPROCEEDINGS{BaMoDoSa02, Author = "L.~Barthe and B.~Mora and N.~Dodgson and M.~Sabin ", Title = "Triquadratic reconstruction for interactive modelling of potential fields.", Year = "2002", Booktitle = "Proceeding: Shape Modeling and Applications 2002", Pages = "145--153", } @phdthesis{Prautzsch:1984:thesis, author = {H.~Prautzsch}, title = {Unterteilungsalgorithmen f\"ur multivariate Splines, Ein geometrischer Zugang}, institution = {Universit\"at Braunschweig}, school = {Dissertation}, year = {1984} } @Article{journals/tog/KobbeltS98, title = "A Multiresolution Framework for Variational Subdivision", author = "L.~Kobbelt and P.~Schr{\"o}der", journal = "ACM Trans. Graph", year = "1998", number = "4", volume = "17", pages = "209--237", } @PHDTHESIS{Schweitzer:1996:thesis, author = {J.~Schweitzer}, title = {Analysis and Applications of Subdivision Surfaces}, institution = {University of Washington}, school = {Dept Computer Science and Engineering}, year = {1996}, } @BOOK{Fulton:1995:AT, title = {Algebraic Topology}, publisher = {Springer-Verlag}, year = {1995}, author = {W.~Fulton}, series = {Graduate Texts in Mathematics}, address = {New York} } @Article{Goodman:1996:IBM, title = "Injective bivariate maps", author = " T.N.T.~Goodman and K.~Unsworth", journal = "Annals of Numerical Mathematics", year = "1996", volume = "3", pages = "91--104", } @article{Daubechies:1988:OBC, author = "I.~Daubechies", title = "Orthonormal bases of compactly supported wavelets", journal = "Comm. Pure. Appl. Math.", year = "1988", volume = "41", pages = "909--996" } @book{Daubechies:1992:TLW, author = "I.~Daubechies", title = "Ten Lectures on Wavelets", publisher = "SIAM, Philadelphia", year = 1992 } @article{Daubechies:1992:TSD, author = "I.~Daubechies and J.C.~Lagarias", title = "Two-scale difference equations. {I}. Existence and global regularity of solutions", journal = "SIAM J. Math. Anal.", year = "1992", volume = "22", pages = "1388--1410" } @article{Daubechies:1992:TSD2, author = "I.~Daubechies and J.C.~Lagarias", title = "Two-scale difference equations. {II}. Local regularity, infinite products of matrices and fractals", journal = "SIAM J. Math. Anal.", year = "1992", volume = "23", pages = "1031--1079" } @mastersthesis{Hed, author = "S.~Hed", title ="Analysis of Subdivision Schemes for surfaces", school = "Tel-Aviv university", year = "1990" } @inproceedings{Marinov:2005:GC4, author = "M.~Marinov and N.~Dyn and D.~Levin", title = "Geometrically Controlled 4-Point Interpolatory Schemes", booktitle ="Advances in Multiresolution for Geometric Modelling", editor = "N.A.~Dodgson, M.S.~Floater, M.A.~Sabin", publisher = "Springer-Verlag", year = "2005", pages = "301--318", } @article{Donoho:2000:NPT, author = "D.~Donoho and T.~Yu", title = "Nonlinear pyramidal transforms based on median-interpolation", journal = "SIAM J. Math. Anal.", year = "2000", volume = "31", pages = "1030--1061" } @article{Kuijt:1998:CPI, author = "F.~Kuijt and R.~van Damme", title = "Convexity preserving interpolatory subdivision schemes", journal = "Constr. Approx.", year = "1998" , volume = "14(14)", pages = "609--630" } @phdthesis{Strela:1996:MW, author = "V.~Strela", title = "Multiwavelets:Theory and Applications", school ={.}, institution = "MIT", year = "1996" } @article{Plonka:1997:AOP, author = "G.~Plonka", title = "Approximation order provided by refinable function vectors", journal = "Constr. Approx.", year = "1997", volume = "13", pages = "221--244" } @article{Moeller:2004:MRF, author = "H.~M{\"o}ller and T.~Sauer", title = "Multivariate refinable functions of high approximation order via quotient ideals of {L}aurent polynomials", journal = "Advances Comput. Math.", year = "2004", volume = "20", pages = "205--228" } @article{Charina:2005:RMV, author = "M.~Charina and C.~Conti and T.~Sauer", title = "Regularity of multivariate vector subdivision schemes", journal = "Numer. Algo.", year = "2005", volume = "39", pages = "97--113" } @InProceedings{Myles:2007:ECC, author = "A.~Myles and K.~Kar{\v c}iauskas and J.~Peters", title = "Extending {C}atmull-{C}lark Subdivision and {PCCM} with Polar Structures", booktitle = "Proceedings of Pacific Graphics, Hawaii", publisher = "ACM Press", editor = "M.~Alexa and S.~Gortler and T.~Ju", pages = "313--320", year = "2007" } @article{RDSDS, author = "I.~Rahman and I.~Drori and V.~Stodden and D.~Donoho and P.~Schr{\"o}der", title = "Multiscale representations for manifold valued data", journal = "SIAM J. on Multiscale Modeling and Simulations", year = "2005", pages = "1201--1232", } @book{doCarmo, AUTHOR = {M.P.~do Carmo}, TITLE = {Differential geometry of curves and surfaces}, NOTE = {Translated from the Portuguese}, PUBLISHER = {Prentice-Hall Inc.}, ADDRESS = {Englewood Cliffs, N.J.}, YEAR = {1976}, PAGES = {viii+503}, } @proceedings{Zorin-2000-course, editor = {D.~Zorin and P.~Schr{\"o}der}, title = "Subdivision for Modeling and Animation", series = "Course Notes", year = 2000, publisher = "ACM SIGGRAPH", } @article{sig-lec37-1999, author = {D.~Zorin}, title = {Implementing subdivision and Multiresolution Meshes}, journal = {Chapter 6 of Course notes 37 of SIGGRAPH 99}, year = {1999} } @article{Micchelli:URC:1989, AUTHOR = {C.A.~Micchelli and H.~Prautzsch}, TITLE = {Uniform refinement of curves}, JOURNAL = {Linear Algebra Appl.}, VOLUME = {114/115}, YEAR = {1989}, PAGES = {841--870}, } @InProceedings{Schaefer:2007:exact, author = "S.~Schaefer and J.~Warren", title = "Exact Evaluation of Non-Polynomial Subdivision Schemes at Rational Parameter Values", booktitle = "Proceedings of Pacific Graphics 2007", year = "2007", } @article{Shi:2004:bi5, author = {X.~Shi and T.~Wanga and P.~Yu}, title = {A practical construction of ${G}^1$ smooth biquintic {B}-spline surfaces over arbitrary topology}, journal = {Computer Aided Design}, volume = {36}, number = {5}, year = {2004}, issn = {0167-8396}, pages = {413--424}, doi = {http://dx.doi.org/10.1016/S0010-4485(03)00111-8}, publisher = {Elsevier Science Publishers B. V.}, address = {Amsterdam, The Netherlands, The Netherlands}, } @InProceedings{BS07c, author = "T.~Boubekeur and C.~Schlick", title = "{QAS}: {R}eal-time Quadratic Approximation of Subdivision Surfaces", booktitle = "Proceedings of Pacific Graphics 2007", year = "2007", keywords = "subdivision rendering, geometry synthesis", url = "http://iparla.labri.fr/publications/2007/BS07c" } @inproceedings{Boo:2001:adaptive, author = {M.~B\'{o}o and M.~Amor and M.~Doggett and J.~Hirche and W.~Strasser}, title = {Hardware support for adaptive subdivision surface rendering}, booktitle = {HWWS '01: Proceedings of the ACM SIGGRAPH/EUROGRAPHICS workshop on Graphics hardware}, year = {2001}, isbn = {1-58113-407-X}, pages = {33--40}, doi = {http://doi.acm.org/10.1145/383507.383522}, publisher = {ACM Press}, address = {New York, NY, USA}, } @inproceedings{Bischoff:2000:loop, author = {S.~Bischoff and L.~Kobbelt and H.-P.~Seidel}, title = {Towards hardware implementation of loop subdivision}, booktitle = {HWWS '00: Proceedings of the ACM SIGGRAPH/EUROGRAPHICS workshop on Graphics hardware}, year = {2000}, isbn = {1-58113-257-3}, pages = {41--50}, doi = {http://doi.acm.org/10.1145/346876.346886}, publisher = {ACM Press}, address = {New York, NY, USA}, } @inbook{Bunnell:2005:disp_subdiv, author = {Michael Bunnell}, title = {{GPU} Gems 2: {P}rogramming Techniques for High-Performance Graphics and General-Purpose Computation}, chapter = {Adaptive Tessellation of Subdivision Surfaces with Displacement Mapping}, year = {2005}, publisher = {Ad{\-d}i{\-s}on-Wes{\-l}ey}, address = {Reading, MA}, } @article{Shiue:2005:gpu_subdiv, author = {L.-J.~Shiue and I.~Jones and J.~Peters}, title = {A realtime {GPU} subdivision kernel}, journal = {ACM Trans. Graph.}, volume = {24}, number = {3}, year = {2005}, issn = {0730-0301}, pages = {1010--1015}, doi = {http://doi.acm.org/10.1145/1073204.1073304}, publisher = {ACM Press}, address = {New York, NY, USA}, } @inproceedings{Bolz:2002:CC, author = {J.~Bolz and P.~Schr\"{o}der}, title = {Rapid evaluation of {C}atmull-{C}lark subdivision surfaces}, booktitle = {Web3D '02: Proceeding of the seventh international conference on 3D Web technology}, year = {2002}, isbn = {1-58113-468-1}, pages = {11--17}, doi = {http://doi.acm.org/10.1145/504502.504505}, publisher = {ACM Press}, address = {New York, NY, USA}, } @misc{Bolz:2004:eval, author = "J.~Bolz and P.~Schr{\"o}der", title = "Evaluation of Subdivision Surfaces on Programmable Graphics Hardware", note = "http://www.multires.caltech.edu/pubs/GPUSubD.pdf", } @TECHREPORT{Loop:2007:bi3, author = "C.~Loop and S.~Schaefer", title = "Approximating {C}atmull-{C}lark Subdivision Surfaces with Bicubic Patches", institution = "Microsoft Research, MSR-TR-2007-44", year = "2007", } @Article{Ying:2004:SMB, author = "L.~Ying and D.~Zorin", title = "A simple manifold-based construction of surfaces of arbitrary smoothness", journal = "ACM Transactions on Graphics", volume = "23", number = "3", pages = "271--275", year = "2004", } @article{Mustafa:EEB:2005, author = "G.~Mustafa and C.~Falai and J.~Deng", title = "Estimating error bounds for binary subdivision curves/surfaces", journal = "J. Comp. Appl. Math.", year = "2005" } @article{Zeng:CFD:2005, author = "X.-M.~Zeng and X.J.~Chen", title = "Computational formula of depth for {C}atmull-{C}lark subdivion surfaces", journal = "J. Comp. Appl. Math.", volume = "195", number = "1", pages = "252--262", year = "2006" } @InProceedings{Cheng06a, author = "G.~Chen and F.~Cheng", title = "Matrix based subdivision depth computation for extra-ordinary {C}atmull-{C}lark subdivision surface patches", booktitle = "Proceedings of GMP 2006 (LNCS 4077)", pages = "545--552", year = "2006", } @article{Cheng06b, author = "F.~Cheng and J.~Yong", title = "Subdivision depth computation for {C}atmull-{C}lark subdivision surfaces", journal = "Computer Aided Design \& Applications", pages = "485--494", volume = "3", year = "2006", } @InProceedings{Cheng06c, author = "F.~Cheng and G.~Chen and J.~Yong", title = "Subdivision depth computation for extra-ordinary {C}atmull-{C}lark subdivision surface patches", booktitle = "Proceedings of GMP 2006 (LNCS 4077)", pages = "545--552", year = "2006", } @InProceedings{Huang07a, author = "Z.~Huang and G.~Wang", title = "Improved error estimate for extraordinary {C}atmull-{C}lark subdivision surface patches", booktitle = "Proceedings of CGI 2007", year = "2007", } @InProceedings{Huang07b, author = "Z.~Huang and G.~Wang", title = "Distance between a {C}atmull-{C}lark subdivision surface and its limit mesh", booktitle = "Proceedings of the 2007 ACM symposium on Solid and physical modeling", pages = "233--240", year = "2007", } @InProceedings{Reif:Sheffield, author = {U.~Reif}, title = {An Appropriate Geometric Invariant for the ${C}^2$-Analysis of Subdivision Surfaces}, booktitle = {Mathematics of Surfaces XII}, editor = {R.~Martin and M.~Sabin and J.~Winkler}, publisher = {Springer}, year = {2007}, pages = {364--377} } @Article{Reif:1996-4, author = {U.~Reif}, title = {On Constructing Topologically Unrestricted {B}-Splines}, year = {1996}, journal = {{Z}eitschrift f\"ur {A}ngewandte {M}athematik und {M}echanik}, volume = {76}, note = {Suppl.\ 1}, pages = {73--74} } @MASTERSTHESIS{Hartmann:2005, author = {R.~Hartmann}, title = {Formeigenschaften von {S}ubdivisionsalgorithmen}, school = {Technische Universit{\"a}t Darmstadt}, year = {2005} } @phdthesis{Sabin:phdthesis, author = {M.A.~Sabin}, title = "The use of piecewise forms for the numerical representation of shape", school = "MTA Budapest", year = "1977", } @Article{journals/cagd/WallnerD05, author = "J.~Wallner and N.~Dyn", title = "Convergence and {C} $^1$ analysis of subdivision schemes on manifolds by proximity", journal = j-CAGD, year = "2005", number = "7", volume = "22", pages = "593--622", } @Article{journals/tog/WallnerP06, author = "J.~Wallner and H.~Pottmann", title = "Intrinsic subdivision with smooth limits for graphics and animation", journal = "ACM Trans. Graph", year = "2006", number = "2", volume = "25", pages = "356--374", } @inproceedings{Shiue-2004-CGAL, author = {L.-J.~Shiue and P.~Alliez and R.~Ursu and L.~Kettner}, title = {A Tutorial on {CGAL} Polyhedron for Subdivision Algorithms}, year = {2004}, booktitle = {2nd CGAL User Workshop}, note = {http://www.cgal.org/Tutorials/Polyhedron/} } @InProceedings{Schaefer:SST:2004, author = "S.~Schaefer and J.~Hakenberg and J.~Warren", title = "Smooth Subdivision of Tetrahedral Meshes", pages = "151--158", editor = "D.~Fellner and S.~Spencer", booktitle = "Proceedings of the 2004 Eurographics/{ACM} {SIGGRAPH} Symposium on Geometry Processing ({SGP}-04)", publisher = "Eurographics Association", address = "Aire-la-Ville, Switzerland", year = "2004", } @Article{Chui:MVS:2006, author = "C.K.~Chui and Q.~Jiang", title = "Matrix-valued subdivision schemes for generating surfaces with extraordinary vertices", journal = j-CAGD, year = "2006", number = "5", volume = "23", pages = "419--438", } @InProceedings{Green:SBM:2002, author = "S. Green and G. Turkiyyah and D. Storti", title = "Subdivision-Based Multilevel Methods for Large Scale Engineering Simulation of Thin Shells", pages = "265--272", editor = "K.~Lee and N.M.~Patrikalakis", booktitle = "Proceedings of the seventh {ACM} Symposium on Modeling and Application ({SM}-02)", publisher = "ACM Press", address = "New York", year = "2002", } @Article{Goldman, author = "R.~Goldman and J.~Warren", title = "An Extension of {C}haikin's Algorithm to {B}-Spline Curves with Knots in Geometric Progression", journal = "CVGIP: Graphical Model and Image Processing", year = "1993", number = "1", volume = "55", pages = "58--62", } @phdthesis{Grohs:thesis, author = "P.~Grohs", title = "Smoothness Analysis of nonlinear Subdivision Schemes on regular grids", school = "TU-Wien", year = "2007", } @TECHREPORT{Myles:2007:bi5, author = "A.~Myles and Y.~Yeo and J.~Peters", title = "Bi-quintic {$C^1$} surfaces via perturbation", institution = "University of Florida, Dept CISE, TR-2007-423", year = "2007", } #title = "{GPU} Conversion of Quad Meshes to Smooth Surfaces", @TECHREPORT{Ni:2007:cpatch, author = "T.~L.~Ni and Y.~Yeo and A.~Myles and V.~Goel and J.~Peters", title = "Smooth Surfaces from 4-sided Facets", institution = "University of Florida, Dept CISE, TR-2007-427", year = "2007", } @article{Chalmoviansky:NCS:200x, author = "P.~Chalmoviansky and B.~Juetler", title = "A non-linear circle-preserving subdivision scheme", journal = "Advances in Computational Mathematics", year = "to appear", } @inproceedings{Nasri:FCC:2006, author = "A.~Nasri and M.~Sabin and R.~Abu Zaki and N.~Nassiri and R.~Santina", title = "Feature Curves with Cross Curvature Control on {C}atmull-{C}lark Subdivision Surfaces", booktitle = "Proc. of the Computer Graphics International 2006, Springer Lecture Notes in Computer Science 4035", editor = "H.P.~Seidel and T.~Nishita and Q.~Peng", pages = "761--768", year = "2006" } @inproceedings{Nasri:AER:2006, author = "A.~Abbas and A.~Nasri and W.~Ma", title = "An Approach for Embedding Regular Analytic Shapes within Subdivision Surfaces", booktitle = "Proc. of the Computer Graphics International 2006, Springer Lecture Notes in Computer Science 4035", editor = "H.P.~Seidel and T.~Nishita and Q.~Peng", pages = "417--429", year = "2006" } @TECHREPORT{Karciauskas:2007:ASS, author = "K.~Kar{\v c}iauskas and J.~Peters", title= "Adjustable Speed Subdivision Surfaces", institution = "University of Florida, Dept CISE, TR-2007-430", year = "2007", }