@book{E01, Author = {Herbert Edelsbrunner}, Title = {Geometry and Topology for Mesh Generation}, Publisher = {Cambridge University Press}, Pages = {162}, ISBN = {0-521-79309-2}, Year = {2001} } @book{R95, Author = {Paulo Ribenboim}, Title = {The New Book of Prime Number Records, 3rd edition}, Publisher = {Springer-Verlag, New York, NY}, Pages = {xxiv+541}, ISBN = {0-387-94457-5}, Year = {1995} } @book{S98, author = {David Singer}, title = {Geometry: Plane and Fancy}, year = {1998}, isbn = {0387983066}, publisher = {Springer} } @article{B82, author = {James F. Blinn}, title = {A Generalization of Algebraic Surface Drawing}, journal = {ACM Trans. Graph.}, volume = {1}, number = {3}, year = {1982}, issn = {0730-0301}, pages = {235--256}, doi = {http://doi.acm.org/10.1145/357306.357310}, publisher = {ACM}, address = {New York, NY, USA}, } @article{CLLPRW99, author = "H.Y. Chen and I.K. Lee and S. Leopoldseder and H. Pottmann and T. Randrup and J. Wallner", title = "On Surface Approximation Using Developable Surfaces", journal = "Graphical models and image processing: GMIP", volume = "61", number = "2", pages = "110--124", year = "1999", url = "citeseer.ist.psu.edu/article/chen99surface.html" } @book{N71, author = {Nils Nilsson}, title = {Problem-Solving Methods in Artificial Intelligence}, year = {1971}, isbn = {07-046573-8}, publisher = {McGraw-Hill, Inc} } @article{RT75, author = {Robert Read and Robert Tarjan}, title = {Bounds on Backtrack Algorithms for Listing Cycles, Paths and Spanning Trees}, year = {1975}, journal = {Networks}, volume = {5}, pages = {237--252} } @Article{D59, author = {E. W. Dijkstra}, title = {A note on two problems in connexion with graphs}, year ={1959}, journal = {Numerische Mathematik}, volume={1}, pages={269–-271} } @Mastersthesis{S97b, author = {Malcolm Smith}, title ={Generating Spanning Trees}, year = {1997}, school = {University of Victoria} } @Mastersthesis{L06, author = {Brendan Lucier}, title ={Unfolding and Reconstructing Polyhedra}, chapter = {4}, year = {2006}, school = {University of Waterloo} } @article{B58, author = {J. Bertrand}, title = {Note sur la th\'{e}orie des poly\`{e}dres r\'{e}guliers}, journal = {Comptes rendus des s\'{e}ances de l'Acad\'{e}mie des Sciences}, volume= {46}, year={1858}, pages={79--82} } @inproceedings{L06a , title = "Local Overlaps In Special Unfoldings Of Convex Polyhedra" , author = "Brendan Lucier" , booktitle = "Proceedings of the 18th Canadian Conference on Computational Geometry (CCCG 2006)" , site = "Kingston" , year = "2006" , pages = "97--100" } @article{L67, author={Joshua Lederberg}, title={Hamilton Circuits of Convex Trivalent Polyhedra (Up to 18 Vertices)}, journal={The American Mathematical Monthly}, volume={74}, number={5}, month={May}, year={1967}, pages={522--527}, url={http://links.jstor.org/sici?sici=0002-9890\%28196705\%2974\%3A5\%3C522\%3AHCOCTP\%3E2.0.CO\%3B2-1} } @InProceedings{AER05, author = { Lyuba Alboul and Gilberto Echeverria and Marcos Rodrigues }, title = { Discrete Curvatures and Gauss Maps for Polyhedral Surfaces }, booktitle = { Proceedings of the 21st European Workshop on Computational Geometry (EWCG), Eindhoven, Netherlands }, year = { 2005 }, pages = {69--72} } % Commented out Unpublished{PR98, author = "T. Pisanski and M. Randi\'{c}", title = "Bridges between geometry and graph theory", year = "1998", url = "http://citeseer.ist.psu.edu/441832.html", note = "T. Pisanski, M. Randi\'{c}, Bridges between geometry and graph theory, to appear" } @techreport{BO08 , author = "Alex Benton and Joseph O'Rourke" , title = "A Class of Convex Polyhedra with Few Edge Unfoldings" , note = "http://arxiv.org/abs/0801.4019" , number = "089" , institution = "Smith College" , year = "2008" , month = "Jan" } @techreport{O07 , author = "Joseph O'Rourke" , title = "Band Unfoldings and Prismatoids: A Counterexample" , note = "arXiv:0710.0811v2 [cs.CG]" , number = "087" , institution = "Smith College" , year = "2007" , month = "Oct" } @article{S75, author={G.C. Shephard}, title={Convex polytopes with convex nets}, year={1975}, journal={Math. Proc. Camb. Phil. Soc}, pages={389--403} } @article{OS89 , author = "Joseph O'Rourke and Catherine Schevon" , title = "On the development of closed convex curves on 3-polytopes" , journal = "J. Geom." , volume = 13 , year = 1989 , pages = "152--157" } @inproceedings{OS89b, author = {Joseph O'Rourke and Catherine Schevon}, title = {Computing the geodesic diameter of a 3-polytope}, booktitle = {SCG '89: Proceedings of the fifth annual symposium on Computational geometry}, year = {1989}, isbn = {0-89791-318-3}, pages = {370--379}, location = {Saarbruchen, West Germany}, doi = {http://doi.acm.org/10.1145/73833.73874}, publisher = {ACM}, address = {New York, NY, USA}, } @inproceedings{B06, author={Alex Benton}, title={Angular Criteria for Unfoldable Convex Polyhedra}, booktitle={Curve and Surface Design: Avignon 2006}, editor={Patrick Chenin and Tom Lyche and Larry L. Schumaker}, pages={41--47}, year={2006}, } @inproceedings{B07, title = {A Developable Surface of Uniformly Negative Internal Angle Deficit}, author = {Alex Benton}, booktitle = {IMA Conference on the Mathematics of Surfaces}, editor = {Ralph R. Martin and Malcolm A. Sabin and Joab R. Winkler}, pages = {64-77}, publisher = {Springer}, series = {Lecture Notes in Computer Science}, url = {http://dblp.uni-trier.de/db/conf/ima-ms/ima-ms2007.html#Benton07}, volume = {4647}, year = {2007}, description = {dblp}, ee = {http://dx.doi.org/10.1007/978-3-540-73843-5_4}, isbn = {978-3-540-73842-8}, date = {2007-08-30}, keywords = {dblp} } @inproceedings{BO07, author = {Alex Benton and Joseph O'Rourke}, title = {Unfolding Polyhedra via Cut-Tree Truncation}, booktitle = {Proceedings of the 19th Annual Canadian Conference on Computational Geometry ({CCCG} 2007)}, year = {2007}, publisher = {Carleton University, Ottawa, Canada}, month = {August}, pages = {77--80}, } @inproceedings{P07, author = {Val Pinciu}, title = {On the Fewest Nets Problem for Convex Polyhedra}, booktitle = {Proceedings of the 19th Annual Canadian Conference on Computational Geometry ({CCCG} 2007)}, year = {2007}, publisher = {Carleton University, Ottawa, Canada}, month = {August}, pages = {21--24}, } @book{DO07, author = {Erik D. Demaine and Joseph O'Rourke}, title = {Geometric Folding Algorithms: Linkages, Origami, Polyhedra}, year = {2007}, isbn = {0521857570}, publisher = {Cambridge University Press}, address = {New York, NY, USA}, } @book{A61, author={Paul Alexandroff}, title={Elementary Concepts of Topology}, year={1961}, publisher={Dover Publications Inc, New York}, isbn={0-486-60747-X} } @book{L76, author={Imre Lakatos}, title={Proofs and Refutations}, year={1976}, publisher={Cambridge University Press}, isbn={0-521-29038-4} } @inproceedings{NGH04, author = {Xinlai Ni and Michael Garland and John C. Hart}, title = {Fair morse functions for extracting the topological structure of a surface mesh}, booktitle = {SIGGRAPH '04: ACM SIGGRAPH 2004 Papers}, year = {2004}, pages = {613--622}, location = {Los Angeles, California}, doi = {http://doi.acm.org/10.1145/1186562.1015769}, publisher = {ACM}, address = {New York, NY, USA} } @inproceedings{MMSB99, author = {Mathieu Desbrun and Mark Meyer and Peter Schr\"{o}der and Alan H. Barr}, title = {Implicit fairing of irregular meshes using diffusion and curvature flow}, booktitle = {SIGGRAPH '99: Proceedings of the 26th annual conference on Computer graphics and interactive techniques}, year = {1999}, isbn = {0-201-48560-5}, pages = {317--324}, doi = {http://doi.acm.org/10.1145/311535.311576}, publisher = {ACM Press/Addison-Wesley Publishing Co.}, address = {New York, NY, USA}, } @article{BCM03, author = {V. Borrelli and F. Cazals and J.M. Morvan}, title = {On the angular defect of triangulations and the pointwise approximation of curvatures}, journal = {Comput. Aided Geom. Des.}, volume = {20}, number = {6}, year = {2003}, issn = {0167-8396}, pages = {319--341}, doi = {http://dx.doi.org/10.1016/S0167-8396(03)00077-3}, publisher = {Elsevier Science Publishers B. V.}, address = {Amsterdam, The Netherlands, The Netherlands}, } @inproceedings{T95, author = {G. Taubin}, title = {Estimating the tensor of curvature of a surface from a polyhedral approximation}, booktitle = {ICCV '95: Proceedings of the Fifth International Conference on Computer Vision}, year = {1995}, isbn = {0-8186-7042-8}, pages = {902}, publisher = {IEEE Computer Society}, address = {Washington, DC, USA}, } @book{S77, author={Albrecht D{\"u}rer}, title={The Painter's Manual, translated by W.L. Strauss (1977)}, year={1525}, publisher={Abaris Books}, ISBN="0913870528" } @incollection{DO05 , title = "A Survey of Folding and Unfolding in Computational Geometry" , author = "Erik D.~Demaine and Joseph O'Rourke" , publisher = "Cambridge University Press" , year = 2005 , booktitle = "Combinatorial and Computational Geometry" , series = "Mathematics Sciences Research Institute Publications" , volume = 52 , editor = "Jacob E. Goodman and J{\'a}nos Pach and Emo Welzl" , pages = "167--211" } @article{DDLO02 , author = "Erik D.~Demaine and Martin L.~Demaine and Anna Lubiw and Joseph O'Rourke" , title = "Enumerating Foldings and Unfoldings between Polygons and Polytopes" , journal = "Graphs and Combin." , year = 2002 , volume = 18 , number = 1 , pages = "93--104" } @inproceedings{O98 , author = "Joseph O'Rourke" , title = "Folding and unfolding in computational geometry" , booktitle = "Proc. 1998 Japan Conf. Discrete Comput. Geom." , series = "Lecture Notes Comput. Sci." , volume = 1763 , publisher = "Springer-Verlag" , year = 2000 , pages = "258--266" , comment = "Papers from the {\em Japan Conf. Discrete Comput. Geom.}, Tokyo, Dec. 1998" } @inproceedings{DEEHO02 , author = "Erik D.~Demaine and David Eppstein and Jeff Erickson and George W. Hart and Joseph O'Rourke" , title = "Vertex-Unfoldings of Simplicial Manifolds" , booktitle = "18th Annu. ACM Sympos. Comput. Geom." , year = 2002 , pages = "237--243" , location = "Barcelona" , succeeds = "deeho-vusp-01" } @inproceedings{BDEK99, author={Marshall Bern and Erik Demaine and David Eppstein and Eric Kuo}, title={Ununfoldable Polyhedra}, booktitle={Proceedings of the 11th Canadian Conference on Computational Geometry}, pages={13--16}, year={1999}, month={August}, publisher={CCCG'99, Vancouver, British Columbia, Canada}, url={http://citeseer.nj.nec.com/bern99ununfoldable.html} } @article{BDEKMS99, title = {Ununfoldable polyhedra with convex faces}, author = {Marshall Wayne Bern and Erik D. Demaine and David Eppstein and Eric Heng-Shiang Kuo and Andrea Mantler and Jack Snoeyink}, journal = {Computational Geometry Theory {\&} Applications}, volume = {24}, number = {2}, pages = {51--62}, month = {February}, year = {2003}, url = {http://dx.doi.org/10.1016/S0925-7721(02)00091-3}, review = {MR-2003m:52017} } @inproceedings{BDDLOORW98 , author = "Therese Biedl and Erik D.~Demaine and Martin L.~Demaine and Anna Lubiw and Joseph O'Rourke and Mark Overmars and Steve Robbins and Sue Whitesides" , title = "Unfolding Some Classes of Orthogonal Polyhedra" , booktitle = "Proc. 10th Canad. Conf. Comput. Geom." , year = 1998 , pages = "70--71" , url = "http://cgm.cs.mcgill.ca/cccg98/proceedings/cccg98-biedl-unfolding.ps.gz" , update = "00.03 orourke" } @inproceedings{ADLMOST04 , author = "Greg Aloupis and Erik D.~Demaine and Stefan Langermann and Pat Morin and Joseph O'Rourke and Ileana Streinu and Godfried Toussaint" , title = "Unfolding Polyhedral Bands" , booktitle = "Proc. 16th Canad. Conf. Comp. Geom." , year = 2004 , pages = "60--63" } @Article{DDM99, AUTHOR = {Erik D. Demaine and Martin L. Demaine and Joseph S. B. Mitchell}, TITLE = {Folding Flat Silhouettes and Wrapping Polyhedral Packages: New Results in Computational Origami}, JOURNAL = {Computational Geometry: Theory and Applications}, journalurl = {http://www.elsevier.com/locate/issn/09257721}, VOLUME = 16, NUMBER = 1, YEAR = 2000, PAGES = {3--21}, NOTE = {Special issue of selected papers from the 3rd CGC Workshop on Computational Geometry, 1998.}, LENGTH = {23 pages}, PAPERS = {SoCG99; CGC98}, replaces = {SoCG99; CGC98}, WEBPAGES = {wrapping}, COPYRIGHT = {The paper is \copyright Elsevier Science Netherlands.} } @techreport{LO96 , author = "Anna Lubiw and Joseph O'Rourke" , title = "When can a polygon fold to a polytope?" , type = "Technical {Report}" , number = 048 , institution = "Dept. Comput. Sci., Smith College" , month = Jun , year = 1996 , note = "Presented at {\em Amer. Math. Soc.} Conf., 5 Oct. 1996" , keywords = "polytopes" , update = "96.09 orourke" } @article{MMP87, author = {Joseph S. B. Mitchell and David M. Mount and Christos H. Papadimitriou}, title = {The discrete geodesic problem}, journal = {SIAM J. Comput.}, volume = {16}, number = {4}, year = {1987}, issn = {0097-5397}, pages = {647--668}, doi = {http://dx.doi.org/10.1137/0216045}, publisher = {Society for Industrial and Applied Mathematics}, address = {Philadelphia, PA, USA}, } @techreport{AO91 , author = "Boris Aronov and Joseph O'Rourke" , title = "Nonoverlap of the star unfolding" , number = "002" , institution = "Smith College" , address = "Northampton, MA" , month = "Mar" , year = "1991" } @inproceedings{AAOS90 , author = "Pankaj K. Agarwal and Boris Aronov and Joseph O'Rourke and C. Schevon" , title = "Star unfolding of a polytope with applications" , booktitle = "Proc. 2nd Scand. Workshop Algorithm Theory" , series = "Lecture Notes Comput. Sci." , volume = 447 , publisher = "Springer-Verlag" , year = 1990 , pages = "251--263" , keywords = "motion planning, shortest paths, polytopes, diameter, edge sequences, unfolding of polytopes" , precedes = "aaos-supa-93" , update = "98.03 orourke, 96.05 agarwal" } @inproceedings{DO02 , author = "Erik D.~Demaine and Joseph O'Rourke" , title = "Open Problems from {CCCG} 2002 [Problem 43]" , booktitle = "Proc. 15th Canad. Conf. Comput. Geom." , site = "Halifax" , year = 2003 , url = "http://arXiv.org/abs/cs/0212050" , pages = "178--181" , note = "arXiv:cs/0212050" } @inproceedings{BCO04 , author = "Nadia Benbernou and Patricia Cahn and Joseph O'Rourke" , title = "Unfolding Smooth Prismatoids" , year = 2004 , url = "http://arxiv.org/abs/cs.CG/0407063" , pages = "12--13" , booktitle = "Proc. 14th Annu. Fall Workshop Comput. Geom." , month = Nov , note = "arXiv:cs.CG/0407063" } %COMMENTED OUT... Article{MP03, author={Ezra Miller and Igor Pak}, title={Geodesic Flow on Convex Polyhedra and Nonoverlapping Unfolding}, journal={Discrete {\&} Comp. Geometry (Invited 20th Anniversary Issue)}, year={2003} } @article{BLS99, author = {Therese Biedl and Anna Lubiw and Julie Sun}, title = {When can a net fold to a polyhedron?}, journal = {Comput. Geom. Theory Appl.}, volume = {31}, number = {3}, year = {2005}, issn = {0925-7721}, pages = {207--218}, doi = {http://dx.doi.org/10.1016/j.comgeo.2004.12.004}, publisher = {Elsevier Science Publishers B. V.}, address = {Amsterdam, The Netherlands, The Netherlands}, } @inproceedings{BG04 , title = "When can a graph form an orthogonal polyhedron?" , author = "Therese Biedl and Burkay Genc" , booktitle = "Proceedings of the 16th Canadian Conference on Computational Geometry (CCCG 2004)" , site = "Montr\'{e}al" , year = 2004 , pages = "53--56" } %COMMENTED OUT... Article{SS01, author = {A. Sheffer and E. de Sturler}, title = {Parameterization of Faceted Surfaces for Meshing using Angle-Based Flattening}, year = {2001}, journal = {Engineering with Computers}, volume={17}, pages={326--337} } @article{SH02, author = "Alla Sheffer and John Hart", title = "Seamster: Inconspicuous Low-Distortion Texture Seam Layout", journal = "Proc. IEEE Visualization", year = "2002", url = "http://citeseer.ist.psu.edu/sheffer02seamster.html", pages={291--298} } %COMMENTED OUT... Article{S02, author = "Alla Sheffer", title = "Spanning tree seams for reducing parameterization distortion of triangulated surfaces", journal = "Shape Modelling International", year = "2002", url = "citeseer.ist.psu.edu/sheffer02spanning.html", pages={61--66} } @article{SBBC00, author = "Alla Sheffer and Michel Bercovier and Ted D. Blacker and Jan Clements", title = "Virtual Topology Operators for Meshing", journal = "International Journal of Computational Geometry and Applications", volume = "10", number = "3", pages = "309-331", year = "2000", url = "citeseer.ist.psu.edu/sheffer97virtual.html" } @article{H99, author = "J. Hart", title = "Using the CW-complex to represent the topological structure of implicit surfaces and solids", year = "1999", journal = "Proc. Implicit Surfaces '99, Eurographics/SIGGRAPH", pages = "107-112", url = "citeseer.ist.psu.edu/hart99using.html" } @techreport{PW99, author = "H. Pottmann and J. Wallner", title = "Approximation Algorithms for Developable Surfaces - Technical Report No 51", year = "1998", month = "April", institution = "Institut fur Geometrie", url = "citeseer.ist.psu.edu/article/pottmann98approximation.html" } @techreport{DBGPH05, author={Shen Dong and Peer-Timo Bremer and Michael Garland and Valerio Pascucci and John C Hart}, title={Quadrangulating a Mesh using Laplacian Eigenvectors}, year={2005}, month={June}, institution={University of Illinois} } @article{G02, author={Branko Grunbaum}, title={No-Net Polyhedra}, year={2002}, volume={11}, pages={111--114}, journal={Geombinatorics} } @phdthesis{S97, author={Wolfram Schlickenrieder}, title={Nets of Polyhedra}, year={1997}, school={Technische Universitat Berlin}, url={citeseer.ist.psu.edu/schlickenrieder97nets.html} } @misc{P02, author = "Konrad Polthier", title = "Polyhedral surfaces of constant mean curvature (extract: chapters 1,3,4)", journal = "Habilitationsschrift", publisher = "Technische Universitt Berlin", year = "2002", url = "citeseer.ist.psu.edu/polthier02polyhedral.html" } @misc{MDSB02, author = {M. Meyer and M. Desbrun and P. Schr{\"o}der and A. Barr}, title = "Discrete Differential Geometry Operators for Triangulated 2-Manifolds", journal = "VisMath.", year = "2002", url = "citeseer.ist.psu.edu/meyer02discrete.html" } @article{A02, author={Lyuba Alboul}, title={Curvature Criteria in Surface Reconstruction}, year={2002}, journal={Communications on Applied Mathematics}, publisher={Russian Academy of Sciences, Computing Centre, Moscow}, url={http://www.ccas.ru/gridgen/ggta02/papers/Alboul.pdf}, pages={7--25} } @inproceedings{SMSER03, author = {Tatiana Surazhsky and Evgeni Magid and Octavian Soldea and Gershon Elber and Ehud Rivlin}, title = {A comparison of Gaussian and mean curvatures estimation methods on triangular meshes}, booktitle = {Proceedings of the 2003 {IEEE} International Conference on Robotics and Automation, {ICRA} 2003, September 14-19, 2003, Taipei, Taiwan}, publisher = {IEEE}, organization={IEEE}, year = {2003}, pages = {1021--1026}, } @inproceedings{DHKL01, author = {Nira Dyn and Kai Hormann and Sun-Jeong Kim and David Levin}, title = {Optimizing 3D triangulations using discrete curvature analysis}, booktitle = {Mathematical Methods for Curves and Surfaces: Oslo 2000}, year = {2001}, isbn = {0-8265-1378-6}, pages = {135--146}, publisher = {Vanderbilt University}, address = {Nashville, TN, USA}, } @article{MW00, author = {D. S. Meek and D. J. Walton}, title = {On surface normal and Gaussian curvature approximations given data sampled from a smooth surface}, journal = {Comput. Aided Geom. Des.}, volume = {17}, number = {6}, year = {2000}, issn = {0167-8396}, pages = {521--543}, doi = {http://dx.doi.org/10.1016/S0167-8396(00)00006-6}, publisher = {Elsevier Science Publishers B. V.}, address = {Amsterdam, The Netherlands, The Netherlands}, } @inproceedings{HA03, author = {F. H{\'e}troy and D. Attali}, title = {Detection of constrictions on closed polyhedral surfaces}, booktitle = {VISSYM '03: Proceedings of the symposium on Data visualisation 2003}, year = {2003}, isbn = {1-58113-698-6}, pages = {67--74}, location = {Grenoble, France}, publisher = {Eurographics Association}, address = {Aire-la-Ville, Switzerland, Switzerland}, } @techreport{GG04, title = {Improved Curvature Estimation on Triangular Meshes}, author = {Tim Gatzke and Cindy Grimm}, number = {2004-9}, institution = {Washington University in St. Louis}, year = {2004} } @Article{HP04a, title = "Anisotropic filtering of non-linear surface features", author = "Klaus Hildebrandt and Konrad Polthier", journal = "Computer Graphics Forum", editor = "M.-P.~Cani and M.~Slater", volume = "23(3)", pages = "391-400", year = "2004", month = "September", address = "Grenoble, France", note = "Proc. Eurographics 2004", } @article{PP93, author = "Ulrich Pinkall and Konrad Polthier", title = "Computing Discrete Minimal Surfaces and Their Conjugates", journal = "Experimental Mathematics", volume = "2", number = "1", pages = "15--36", year = "1993", url = "citeseer.ist.psu.edu/article/pinkall93computing.html" } @inproceedings{VA97, author = "Kasturi R. Varadarajan and Pankaj K. Agarwal", title = "Approximating Shortest Paths on a Nonconvex Polyhedron", booktitle = "{IEEE} Symposium on Foundations of Computer Science", pages = "182-191", year = "1997", url = "citeseer.ist.psu.edu/varadarajan97approximating.html" } @inproceedings{LMS97, author = "Mark Lanthier and Anil Maheshwari and J{\"o}rg-R{\"u}diger Sack", title = "Approximating Weighted Shortest Paths on Polyhedral Surfaces", booktitle = "6th Annual Video Review of Computational Geometry, Proc. 13th {ACM} Symp. Computational Geometry", month = "4--6", publisher = "ACM Press", pages = "485--486", year = "1997", url = "citeseer.ist.psu.edu/article/lanthier97approximating.html" } @inproceedings{ALMS98, author = "Lyudmil Aleksandrov and Mark Lanthier and Anil Maheshwari and J{\"o}rg-R{\"u}diger Sack", title = "An epsilon-Approximation for Weighted Shortest Paths on Polyhedral Surfaces", booktitle = "Scandinavian Workshop on Algorithm Theory", pages = "11-22", year = "1998", url = "citeseer.ist.psu.edu/aleksandrov98epsilonapproximation.html" } @article{F97b, author = {Robert W. Floyd}, title = {Algorithm 97: Shortest path}, journal = {Commun. ACM}, volume = {5}, number = {6}, year = {1962}, issn = {0001-0782}, pages = {345}, doi = {http://doi.acm.org/10.1145/367766.368168}, publisher = {ACM}, address = {New York, NY, USA}, } @inproceedings{KO00 , author = "Biliana Kaneva and Joseph O'Rourke" , title = "An Implementation of {Chen \& Han's} Shortest Paths Algorithm" , booktitle = "Proc. 12th Canad. Conf. Comput. Geom." , site = "New Brunswick" , month = aug , year = 2000 , pages = "139--146" , url = "http://cs.smith.edu/~orourke/ShortestPaths/" , keywords = "shortest paths" , update = "02.03 icking, 01.11 orourke, 01.04 icking+orourke, 00.11 smid, 00.07 orourke" } @article{O99 , author = "Joseph O'Rourke" , title = "Computational geometry column 35" , journal = "Internat. J. Comput. Geom. Appl." , volume = "4--5" , year = 1999 , pages = "513--515" , note = "Also in {\em SIGACT News}, 30(2):31-32 (1999), Issue 111" , keywords = "shortest paths" , update = "00.03 orourke" , annote = "The subquadratic algorithm of Kapoor for finding shortest paths on a polyhedron is described." } @article{KR00, author = "Sanjiv Kapoor and H. Ramesh", title = "An Algorithm for Enumerating All Spanning Trees of a Directed Graph", journal = "Algorithmica", volume = "27", number = "2", pages = "120--130", year = "2000", url = "citeseer.ist.psu.edu/93995.html" } @inproceedings{HP04b, author = {Michael Hofer and Helmut Pottmann}, title = {Energy-minimizing splines in manifolds}, booktitle = {SIGGRAPH '04: ACM SIGGRAPH 2004 Papers}, year = {2004}, pages = {284--293}, location = {Los Angeles, California}, doi = {http://doi.acm.org/10.1145/1186562.1015716}, publisher = {ACM}, address = {New York, NY, USA}, } @inproceedings{GE04, author = {Chris Gray and William Evans}, title = {Optimistic shortest paths on uncertain terrains}, booktitle = {Proceedings of the 16th Canadian Conference on Computational Geometry, CCCG 2004, Concordia University, Montreal, Quebec, Canada, August 9-11}, year = {2004}, pages = {68-71}, ee = {http://www.cccg.ca/proceedings/2004/48.pdf}, bibsource = {DBLP, http://dblp.uni-trier.de} } @article{AMOT90, author = {Ravindra K. Ahuja and Kurt Mehlhorn and James Orlin and Robert E. Tarjan}, title = {Faster algorithms for the shortest path problem}, journal = {J. ACM}, volume = {37}, number = {2}, year = {1990}, issn = {0004-5411}, pages = {213--223}, doi = {http://doi.acm.org/10.1145/77600.77615}, publisher = {ACM}, address = {New York, NY, USA}, } @inproceedings{CGR94, author = "Boris V. Cherkassky and Andrew V. Goldberg and Tomasz Radzik", title = "Shortest Paths Algorithms: Theory and Experimental Evaluation", booktitle = "{SODA}: {ACM}-{SIAM} Symposium on Discrete Algorithms (A Conference on Theoretical and Experimental Analysis of Discrete Algorithms)", year = "1994", url = "citeseer.ist.psu.edu/cherkassky93shortest.html" } @article{CH96, author = "J. Chen and Y. Han", title = "Shortest paths on a polyhedron; Part I: computing shortest paths", journal = "Int. J. Comput. Geom. and Appl.", volume = "6(2)", pages = "127--144", year = "1996", url = "citeseer.ist.psu.edu/chen92shortest.html" } @article{GMS04, author={R. Graham and H. McCabe and S. Sheridan}, title={Pathfinding in Computer Games}, year={2004}, issue={8}, journal={ITB Journal}, publisher={Institute of Technology Blanchardstown}, url={http://gamesitb.com/pathgraham.pdf}, pages={1--31} } @inproceedings{BM04, author = "Devin J. Balkcom and Matthew T. Mason", title = "Introducing robotic origami folding", booktitle = "{IEEE} International Conference on Robotics and Automation", year = "2004", pages = "3245-3250" } @article{STL06, author = {Idan Shatz and Ayellet Tal and George Leifman}, title = {Paper craft models from meshes}, journal = {Vis. Comput.}, volume = {22}, number = {9}, year = {2006}, issn = {0178-2789}, pages = {825--834}, doi = {http://dx.doi.org/10.1007/s00371-006-0067-6}, publisher = {Springer-Verlag New York, Inc.}, address = {Secaucus, NJ, USA}, } @inproceedings{MS04, author = {Jun Mitani and Hiromasa Suzuki}, title = {Making papercraft toys from meshes using strip-based approximate unfolding}, booktitle = {SIGGRAPH '04: ACM SIGGRAPH 2004 Papers}, year = {2004}, pages = {259--263}, location = {Los Angeles, California}, doi = {http://doi.acm.org/10.1145/1186562.1015711}, publisher = {ACM}, address = {New York, NY, USA}, } @inproceedings{DDL00, author = {Erik D. Demaine and Martin L. Demaine and Anna Lubiw}, title = {Folding and Cutting Paper}, booktitle = {JCDCG '98: Revised Papers from the Japanese Conference on Discrete and Computational Geometry}, year = {2000}, isbn = {3-540-67181-1}, pages = {104--118}, publisher = {Springer-Verlag}, address = {London, UK}, } @article{MHC05, author = {J. McCartney and B. K. Hinds and K. W. Chong}, title = {Pattern flattening for orthotropic materials}, journal = {Computer-Aided Design}, volume = {37}, number = {6}, year = {2005}, pages = {631-644}, ee = {http://dx.doi.org/10.1016/j.cad.2004.09.006}, bibsource = {DBLP, http://dblp.uni-trier.de} } @Article{TLT04, author = "K. Tai and W. Liu and G. Thimm", title = "Unfolding and Flat Layout Design of Non-Manifold 3D Folded Structures", journal = "Computer-Aided Design \& Applications", year = {2004}, volume = {1}, number = "1-4", pages = "439--448", ISSN = "1686-4360" } @article{GBKK98, author = "S.K. Gupta and D.A. Bourne and K. Kim and S.S. Krishnan", title = "Automated Process Planning for Sheet Metal Bending Operations", journal = "Journal of Manufacturing Systems", volume={17(5)}, pages = "338--360", year = "1998" } @article{MM01, author = "P. Morin and J. Morrison", title = "The geometry of carpentry and joinery", journal = "Discrete Applied Mathematics", volume = "144(3)", year = "2004", pages = "374--380", url = "\url{http://citeseer.ist.psu.edu/morin01geometry.html}" } @book{L94, author={B. Van Loon}, title={Geodesic Domes}, year={1994}, month={Feb}, publisher={Tarquin Press}, isbn={0906212928} } @book{G76, author={H.B. Griffiths}, title={Surfaces}, year={1976}, publisher={Cambridge University Press}, isbn={0521206960} } @misc{L06b, author={J. M. Lavric}, title={Litio - 3D}, year={2006}, note={\url{http://www.litio3d.com.ar/}} } @misc{H06, author={A. Van H{\"u}{\"u}ksloot}, title={Papyromania}, year={2006}, note={\url{http://www.papyromania.nl/}} } @misc{C07, author={Matthew Chadwick}, title={Celeriac.net - {Unfolder}}, year={2007}, note={\url{http://celeriac.net/unfolder/}} } @misc{R02, author={{Revcad Software, Inc}}, title={Sheet Lightning}, year={2002}, note={\url{http://www.revcad.com/Sheet5/index.html}} } @misc{Y05, author={{Yamaha, Inc}}, title={Realistic Paper Crafts}, year={2005}, note={\url{http://www.yamaha-motor.co.jp/global/entertainment/papercraft/}} } @misc{T02, author={{Tama Software, Inc}}, title={Pepakura}, year={2002}, note={\url{http://www.tamasoft.co.jp/pepakura-en/}} } @misc{W99, author={Eric Weisstein}, title={MathWorld}, year={1999}, note={\url{http://mathworld.wolfram.com/}} } @misc{P03, author={Konrad Polthier}, title={Imaging maths - Unfolding polyhedra}, year={2003}, note={\url{http://plus.maths.org/issue27/features/mathart/index.html}} } @misc{B07n, year="2007", author="Jonathan F. Bard", title="Cycles in an Undirected Graph", note={\url{https://www.me.utexas.edu/~bard/IP/Handouts/cycles.pdf}} } @misc{F97a, author={Komei Fukuda}, title={Strange Unfoldings of Convex Polytopes}, year={1997}, note={\url{http://www.ifor.math.ethz.ch/~fukuda/unfold_home/unfold_open.html}} } @misc{NF94, author={Makoto Namiki and Komei Fukuda}, title={Unfolding 3-dimensional convex polytopes: A package for mathematica 1.2 or 2.0}, year={1994}, note={\url{ftp://ftp.ifor.math.ethz.ch/pub/fukuda/mathematica/UnfoldPolytope.tar.Z}} } @misc{E05, author={David Epstein}, title={The Geometry Junkyard - Nineteen Proofs of {E}uler's Formula}, year={2005}, note={\url{http://www.ics.uci.edu/~eppstein/junkyard/euler/}} } @misc{B97, author={Paul Bourke}, title={Implicit Surfaces}, year={1997}, note={\url{http://ozviz.wasp.uwa.edu.au/~pbourke/modelling\_rendering/implicitsurf/}} } ---