%% This BibTeX bibliography file was created using BibDesk. %% http://bibdesk.sourceforge.net/ %% Created for Ken Arroyo Ohori at 2016-03-13 17:57:55 +0100 %% Saved with string encoding Unicode (UTF-8) @article{Patterson02, Author = {Tom Patterson}, Journal = {Cartographic Perspectives}, Month = {Fall}, Title = {Getting Real: Reflecting on the New Look of National Park Service Maps}, Volume = {43}, Year = {2002}} @incollection{Liu13, Author = {Liu Liu and Sisi Zlatanova}, Booktitle = {ISPRS Acquisition and Modelling of Indoor and Enclosed Environments 2013}, Publisher = {ISPRS}, Title = {Generating navigation models from existing building data}, Volume = {XL--4/W4}, Year = {2013}} @phdthesis{Garland99, Author = {Michael Garland}, School = {Carnegie Mellon University}, Title = {Quadric-Based Polygonal Surface Simplification}, Year = {1999}} @article{Decoret03, Author = {Xavier D\'ecoret and Fr\'edo Durand and Fran\c{c}ois X. Sillion and Julie Dorsey}, Journal = {ACM Transactions on Graphics}, Number = {3}, Pages = {689--696}, Title = {Billboard Clouds for Extreme Model Simplification}, Volume = {22}, Year = {2003}} @article{Biljecki15a, Author = {Filip Biljecki and Jantien Stoter and Hugo Ledoux and Sisi Zlatanova and Arzu \c{C}\"oltekin}, Journal = {ISPRS International Journal of Geo-Information}, Month = {December}, Number = {4}, Pages = {2842--2889}, Title = {Applications of {3D} City Models: State of the Art Review}, Volume = {4}, Year = {2015}} @inproceedings{Bellet12, Author = {Thomas Bellet and Agn\'es Arnould and Pascale {Le Gall}}, Booktitle = {Approches Formelles dans l'Assistance au D\'eveloppement de Logiciels (AFDL), Jan 2012, Grenoble, France}, Month = {jan}, Title = {{JERBOA}: un modeleur g\'eom\'etrique \`a base de r\`egles}, Year = {2012}} @inproceedings{Horna06, Author = {S\'ebastien Horna and Guillaume Damiand and Daniel Meneveaux and Yves Bertrand}, Booktitle = {Journ\'ees de l'Association Francophone d'Informatique Graphique, Bordeaux, 2006}, Title = {Reconstruction topologique {3D} de b\^atiments}, Year = {2006}} @incollection{Chu09, Author = {Alan Chu and Chi-Wing Fu and Andrew J. Hanson and Pheng-Ann Heng}, Booktitle = {IEEE Transactions on Visualization and Computer Graphics}, Number = {6}, Pages = {1587--1594}, Publisher = {IEEE}, Title = {{GL4D}: A {GPU}-based Architecture for Interactive {4D} Visualization}, Volume = {15}, Year = {2009}} @incollection{Bajaj98, Author = {C. L. Bajaj and V. Pascucci and G. Rabbiolo}, Booktitle = {IEEE Symposium on Volume Visualization}, Publisher = {IEEE}, Title = {Hypervolume Visualization: A Challenge in Simplicity}, Year = {1998}} @incollection{Feiner90, Author = {Steven Feiner and Clifford Beshers}, Booktitle = {Proceedings of the 1990 symposium on Interactive 3D graphics}, Pages = {37--38}, Publisher = {ACM}, Title = {Visualizing $n$-Dimensional Virtual Worlds with $n$-Vision}, Year = {1990}} @unpublished{Leys08, Author = {Jos Leys and \'Etienne Ghys and Aureli\'en Alvarez}, Note = {Available at \url{http://www.dimensions-math.org/Dim_E.htm}}, Title = {Dimensions: une promenade math\'ematique}, Year = {2008}} @unpublished{Chisholm00, Author = {Matt Chisholm}, Month = may, Note = {Available at \url{https://theory.org/geotopo/3-sphere/3-sphere.ps}}, Title = {The Sphere in Three Dimensions and Higher: Generalizations and Special Cases}, Year = {2000}} @book{Steeb11, Author = {Willi-Hans Steeb}, Edition = {5th}, Publisher = {World Scientific Publishing}, Title = {The Nonlinear Workbook}, Year = {2011}} @inproceedings{vanElfrinkhof97, Address = {Delft}, Author = {L. {van Elfrinkhof}}, Booktitle = {Handelingen van het 6e Nederlandsch Natuurkundig en Geneeskundig Congres}, Pages = {237--240}, Title = {Eene eigenschap van de orthogonale substitutie van de vierde orde}, Year = {1897}} @article{Cole90, Author = {F. N. Cole}, Journal = {American Journal of Mathematics}, Month = jan, Number = {2}, Pages = {191--210}, Title = {On Rotations in Space of Four Dimensions}, Volume = {12}, Year = {1890}} @article{Massey83, Author = {W. S. Massey}, Journal = {The American Mathematical Monthly}, Month = dec, Number = {10}, Pages = {697--701}, Title = {Cross Products of Vectors in Higher Dimensional {E}uclidean Spaces}, Volume = {90}, Year = {1983}} @unpublished{Elduque04, Author = {Alberto Elduque}, Month = apr, Note = {Talk presented at the Seminario Rubio de Francia of the Universidad de Zaragoza on April 1, 2004}, Title = {Vector Cross Products}, Year = {2004}} @book{Shreiner13, Author = {Dave Shreiner and Graham Sellers and John Kessenich and Bill Licea-Kane and {Khronos ARB Working Group}}, Edition = {8th}, Publisher = {Addison-Wesley}, Title = {{OpenGL} Programming Guide: The Official Guide to Learning {OpenGL}, Version 4.3}, Year = {2013}} @book{Marden96, Author = {John I. Marden}, Month = {August}, Publisher = {Chapman \& Hall}, Series = {CRC Monographs on Statistics \& Applied Probability}, Title = {Analyzing and Modeling Rank Data}, Volume = {64}, Year = {1996}} @techreport{EFI15, Author = {{EFI}}, Institution = {{Expertenkommission Forschung und Innovation}}, Title = {{G}utachten 2015: zu {F}orschung, {I}nnovation und technologischer {L}eistungsf\"ahigkeit {D}eutschlands}, Year = {2015}} @unpublished{Hargreaves11, Author = {Ian Hargreaves}, Month = may, Note = {Independent report commissioned by United Kingdom Prime Minister David Cameron}, Title = {Digital Opportunity: A Review of Intellectural Property and Growth}, Year = {2011}} @techreport{Reda14, Author = {Julia Reda}, Institution = {European Parliament Commitee on Legal Affairs}, Title = {Draft report on the implementation of {D}irective 2001/29/{EC} of the {E}uropean {P}arliament and of the {C}ouncil of 22 {M}ay 2001 on the harmonisation of certain aspects of copyright and related rights in the information society}, Year = {2014}} @book{Hughes14, Author = {John F. Hughes and Andries {van Dam} and Morgan McGuire and David F. Sklar and James D. Foley and Steven K. Feiner and Kurt Akeley}, Edition = {3rd}, Publisher = {Addison-Wesley}, Title = {Computer Graphics: Principles and Practice}, Year = {2014}} @incollection{Foley92, Author = {Thomas A. Foley and Gregory M. Nielson}, Booktitle = {The System Engineer's Handbook: A guide to building {VMEbus} and {VXIbus} systems}, Chapter = {19}, Editor = {John Black}, Pages = {223--237}, Publisher = {Academic Press}, Title = {Practical Techniques for Producing {3D} Graphical Images}, Year = {1992}} @phdthesis{Brisson90, Author = {Erik Brisson}, School = {University of Washington}, Title = {Representation of $d$-dimensional geometric objects}, Year = {1990}} @book{Salomon08, Author = {David Salomon}, Publisher = {Springer London}, Series = {Undergraduate Topics in Computer Science}, Title = {A Concise Introduction to Data Compression}, Year = {2008}} @book{Salomon06, Author = {David Salomon}, Publisher = {Springer New York}, Title = {Curves and Surfaces for Computer Graphics}, Year = {2006}} @book{Salomon11, Author = {David Salomon}, Editor = {David Gries and Fred. B. Schneider}, Publisher = {Springer London}, Series = {Texts in Computer Science}, Title = {The Computer Graphics Manual}, Volume = {2}, Year = {2011}} @unpublished{Hanson01, Author = {Andrew J. Hanson and Daniel Weiskopf}, Note = {Siggraph 2001 Tutorial}, Title = {Visualizing Relativity}, Year = {2001}} @incollection{Hanson94, Author = {Andrew J. Hanson}, Booktitle = {Graphics Gems IV}, Chapter = {II.6}, Editor = {Paul S. Heckbert}, Pages = {149--170}, Publisher = {Academic Press Professional}, Title = {Geometry for $N$-Dimensional Graphics}, Year = {1994}} @book{Comninos06, Author = {Peter Comninos}, Edition = {1}, Publisher = {Springer-Verlag London}, Title = {Mathematical and Computer Programming Techniques for Computer Graphics}, Year = {2006}} @article{Egenhofer95, Author = {Max J. Egenhofer}, Journal = {International Journal of Geographical Information Systems}, Number = {5}, Pages = {555--565}, Title = {Modeling Conceptual Neighborhoods of Topological Line-Region Relations}, Volume = {9}, Year = {1995}} @incollection{Egenhofer91b, Author = {Max J. Egenhofer}, Booktitle = {Advances in Spatial Databases}, Editor = {Oliver G\"unther and Hans-J\"org Schek}, Publisher = {Springer Berlin Heidelberg}, Series = {Lecture Notes in Computer Science}, Title = {Reasoning about binary topological relations}, Volume = {525}, Year = {1991}} @article{Lage15, Author = {Marcos Lage and Luiz Fernando Martha and J. P. Moitinho {de Almeida} and H\`elio Lopes}, Journal = {Engineering with Computers}, Title = {{IBHM}: index‐based data structures for {2D} and {3D} hybrid meshes}, Year = {2015}} @article{Akleman15, Author = {Ergun Akleman and Jianer Chen and Jonathan L. Gross}, Journal = {Computers \& Graphics}, Pages = {306--326}, Title = {Block meshes: Topologically robust shape modeling with graphs embedded on 3-manifolds}, Volume = {46}, Year = {2015}} @unpublished{Kraft14, Author = {Bernold Kraft and Wolfgang Huhnt}, Note = {Available at \url{http://www.academia.edu/12434817/Geometrically_Complete_Building_Models}}, Title = {Geometrically Complete Building Models}, Year = {2014}} @incollection{Dube12, Author = {Matthew P. Dube and Max J. Egenhofer}, Booktitle = {Geographic Information Science}, Editor = {Ningchuan Xiao and Mei-Po Kwan and Michael F. Goodchild and Shashi Shekhar}, Pages = {72--86}, Publisher = {Springer Berlin Heidelberg}, Series = {Lecture Notes in Computer Science}, Title = {An Ordering of Convex Topological Relations}, Volume = {7478}, Year = {2012}} @article{Joppa13, Author = {Lucas N. Joppa and Greg McInerny and Richard Harper and Lara Salido and Kenji Takeda and Kenton O'Hara and David Gavaghan and Stephen Emmott}, Journal = {Science}, Month = may, Pages = {814--815}, Title = {Troubling Trends in Scientific Software Use}, Volume = {340}, Year = {2013}} @book{Dieudonne09, Author = {Jean Dieudonn\'e}, Publisher = {Birkh\"auser Boston}, Series = {Modern Birkh\"auser Classics}, Title = {A History of Algebraic and Differential Topology, 1900 - 1960}, Year = {2009}} @incollection{Bradley15, Author = {Patrick E. Bradley}, Booktitle = {Statistical Learning and Data Sciences}, Editor = {Alexander Gammerman and Vladimir Vovk and Harris Papadopoulos}, Month = apr, Pages = {406--413}, Publisher = {Springer International Publishing}, Series = {Lecture Notes in Computer Science}, Title = {Supporting Data Analytics for Smart Cities: An Overview of Data Models and Topology}, Volume = {9047}, Year = {2015}} @book{Hinton88, Author = {Charles Howard Hinton}, Publisher = {Swan Sonnenschein \& Co. Ltd.}, Title = {A New Era of Thought}, Year = {1888}} @article{Pellerin14, Author = {Jeanne Pellerin and Bruno L\'evy and Guillaume Caumon and Arnaud Botella}, Journal = {Computers \& Geosciences}, Pages = {103--116}, Title = {Automatic surface remeshing of {3D} structural models at specified resolution: A method based on {V}oronoi diagrams}, Volume = {62}, Year = {2014}} @incollection{Balsys07, Author = {Ron J. Balsys and Kevin G. Suffern}, Booktitle = {Computer Graphics, Imaging and Visualisation}, Publisher = {IEEE}, Title = {Point Based Rendering of Implicit 4-Dimensional Surfaces}, Year = {2007}} @article{Zhang07, Author = {Hui Zhang and Andrew J. Hanson}, Journal = {IEEE Transactions on Visualization and Computer Graphics}, Month = {November/December}, Number = {6}, Pages = {1688--1695}, Title = {Shadow-Driven {4D} Haptic Visualization}, Volume = {13}, Year = {2007}} @article{Elberink13, Author = {Sander Oude Elberink and Jantien Stoter and Hugo Ledoux and Tom Commandeur}, Journal = {Photogrammetric Engineering \& Remote Sensing}, Month = feb, Number = {2}, Pages = {147--158}, Title = {Generation and Dissemination of a National Virtual {3D} City and Landscape Model for the Netherlands}, Volume = {79}, Year = {2013}} @article{Ince12, Author = {Darrel C. Ince and Leslie Hatton and John Graham-Cumming}, Journal = {Nature}, Month = feb, Pages = {487--488}, Title = {The case for open computer programs}, Volume = {482}, Year = {2012}} @article{Morin12, Author = {A. Morin and J. Urban and I. Foster and A. Sali and D. Baker and P. Sliz}, Journal = {Science}, Month = apr, Pages = {159--160}, Title = {Shining Light into Black Boxes}, Volume = {336}, Year = {2012}} @article{delaLosa99, Author = {Arnaud {de la Losa} and Bernard Cervelle}, Journal = {Computers \& Graphics}, Month = aug, Number = {4}, Pages = {469--468}, Title = {{3D} Topological modeling and visualisation for {3D} {GIS}}, Volume = {23}, Year = {1999}} @manual{ISO19123:2007, Author = {{ISO}}, Organization = {{International Organization for Standardization}}, Title = {Geographic information --- Schema for coverage geometry and functions}, Year = {2007}} @article{Hetroy11, Author = {Franck H{\'{e}}troy and St{\'{e}}phanie Rey and Carlos And{\'{u}}jar and Pere Brunet and {\`{A}}lvar Vinacua}, Journal = {Computer-Aided Design}, Number = {1}, Pages = {101--113}, Title = {Mesh repair with user-friendly topology control}, Volume = {43}, Year = {2011}} @article{Bischoff05, Author = {Stephan Bischoff and Darko Pavic and Leif Kobbelt}, Journal = {ACM Transactions on Graphics}, Number = {4}, Pages = {1332--1352}, Title = {Automatic restoration of polygon models}, Volume = {24}, Year = {2005}} @article{Nooruddin03, Author = {Nooruddin, F.S. and Turk, G.}, Journal = {IEEE Transactions on Visualization and Computer Graphics}, Number = {2}, Pages = {191--205}, Title = {Simplification and repair of polygonal models using volumetric techniques}, Volume = {9}, Year = {2003}} @inproceedings{Alam13, Address = {Istanbul, Turkey}, Author = {N. Alam and D. Wagner and M. Wewetzer and M. Pries and V. Coors}, Booktitle = {ISPRS Annals of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Proceedings of the ISPRS 8th 3DGeoInfo Conference {\&} WG II/2 Workshop}, Editor = {Isikdag, Umit}, Pages = {1--6}, Title = {Towards automatic validation and healing of {CityGML} models for geometric and semantic consistency}, Year = {2013}} @inproceedings{Bogdahn10, Author = {Bogdahn, J. and Coors, V.}, Booktitle = {Proceedings International Conference on 3D Geoinformation}, Editor = {Kolbe, T. H. and K\"oning, G. and Nagel, C.}, Pages = {13--17}, Title = {Towards an automated healing of {3D} urban models}, Volume = {XXXVIII--4/W15}, Year = {2010}} @inproceedings{Podolak05, Author = {Podolak, Joshua and Rusinkiewicz, Szymon}, Booktitle = {Eurographics Symposium on Geometry Processing (2005)}, Editor = {M. Desbrunn and H. Pottmann}, Pages = {33--42}, Title = {Atomic volumes for mesh completion}, Year = {2005}} @article{Lancaster81, Author = {P. Lancaster and K. Salkauskas}, Journal = {Mathematics of Computation}, Month = jul, Number = {155}, Pages = {141--158}, Title = {Surfaces Generated by Moving Least Squares Methods}, Volume = {37}, Year = {1981}} @article{Wang07, Author = {Jianning Wang and Manuel M. Oliveira}, Journal = {Image and Vision Computing}, Number = {1}, Pages = {103--113}, Title = {Filling holes on locally smooth surfaces reconstructed from point clouds}, Volume = {25}, Year = {2007}} @article{Levy03, Author = {Bruno L\'evy}, Journal = {ACM Transactions on Graphics}, Month = jul, Number = {3}, Pages = {364--369}, Title = {Dual Domain Extrapolation}, Volume = {22}, Year = {2003}} @incollection{Bohn92, Author = {Jan Helge B{\o}hn and Michael J. Wozny}, Booktitle = {Selected and Expanded Papers from the IFIP TC5/WG5.2 Working Conference on Geometric Modeling for Product Realization}, Pages = {297--319}, Publisher = {North-Holland Publishing Co}, Title = {A topology-based approach for shell-closure}, Year = {1992}} @article{Ju09, Author = {Tao Ju}, Journal = {Journal of Computer Science and Technology}, Month = jan, Number = {1}, Pages = {19--29}, Title = {Fixing Geometric Errors on Polygonal Models: A Survey}, Volume = {24}, Year = {2009}} @incollection{Barequet97a, Author = {Gill Barequet and Subodh Kumar}, Booktitle = {Proceedings of VisuaIization '97}, Publisher = {IEEE}, Title = {Repairing {CAD} Models}, Year = {1997}} @incollection{Turk94, Address = {New York, NY, USA}, Author = {Greg Turk and Marc Levoy}, Booktitle = {SIGGRAPH '94 Proceedings of the 21st annual conference on Computer graphics and interactive techniques}, Pages = {311--318}, Publisher = {ACM}, Title = {Zippered Polygon Meshes from Range Images}, Year = {1994}} @article{Barequet95, Author = {Gill Barequet and Micha Sharir}, Journal = {Computer Aided Geometric Design}, Month = mar, Number = {2}, Pages = {207--229}, Title = {Filling gaps in the boundary of a polyhedron}, Volume = {12}, Year = {1995}} @article{Sheng95, Author = {Xuejun Sheng and Ingo R. Meier}, Journal = {IEEE Computer Graphics and Applications}, Month = nov, Title = {Generating Topological Structures for Surface Models}, Year = {1995}} @inproceedings{Rock92, Author = {Stephen J. Rock and Michael J. Wozny}, Booktitle = {Solid Freeform Fabrication Symposium Proceedings}, Pages = {251--259}, Title = {Generating Topological Information from a ``Bucket of Facets''}, Year = {1992}} @article{Attene09, Author = {Marco Attene and Daniela Giorgi and Massimo Ferri and Bianca Falcidieno}, Journal = {Computer Aided Geometric Design}, Month = nov, Number = {8}, Pages = {850--864}, Title = {On converting sets of tetrahedra to combinatorial and {PL} manifolds}, Volume = {26}, Year = {2009}} @article{Gueziec01, Author = {Andr\'e Gu\'eziec and Francis Lazarus}, Journal = {IEEE Transactions on Visualization and Computer Graphics}, Month = {April--June}, Number = {2}, Pages = {136--151}, Title = {Cutting and Stitching: Converting Sets of Polygons to Manifold Surfaces}, Volume = {7}, Year = {2001}} @techreport{Rossignac99a, Author = {Jarek Rossignac and David Cardoze}, Institution = {Georgia Institute of Technology}, Number = {SM99--020}, Title = {Matchmaker: Manifold {BReps} for non-manifold r-sets}, Year = {1999}} @incollection{Muller06, Author = {Pascal M\"uller and Peter Wonka and Simon Haegler and Andreas Ulmer and Luc {van Gool}}, Booktitle = {SIGGRAPH '06}, Publisher = {ACM}, Title = {Procedural Modeling of Buildings}, Year = {2006}} @inproceedings{Badawy99, Author = {Wael M. Badawy and Walid G. Aref}, Booktitle = {Proceedings of the 7th ACM International Symposium on Advances in Geographic Information Systems}, Pages = {97--102}, Publisher = {ACM}, Title = {On Local Heuristics to Speed Up Polygon-Polygon Intersection Tests}, Year = {1999}} @book{Panigrahi14, Author = {Narayan Panigrahi}, Publisher = {CRC Press}, Title = {Computing in Geographic Information Systems}, Year = {2014}} @article{Hahmanna13, Author = {Stefan Hahmanna and Dirk Burghardt}, Journal = {International Journal of Geographical Information Science}, Number = {6}, Pages = {1171--1189}, Title = {How much information is geospatially referenced? Networks and cognition}, Volume = {27}, Year = {2013}} @techreport{ODAS11, Author = {ODAS}, Institution = {Ohio Department of Administrative Services}, Month = sep, Title = {Ohio's Location Based Response System: How one set of highly accurate, shared mapping data is saving time, money and lives across the Buckeye State}, Type = {White Paper}, Year = {2011}} @article{Franklin92, Author = {Carl Franklin}, Journal = {Database}, Month = {abr}, Number = {2}, Pages = {17--22}, Title = {An introduction to geographic information systems: linking maps to databases}, Volume = {15}, Year = {1992}} @book{Biggs92, Author = {G. David Garson and Robert S. Biggs}, Publisher = {SAGE Publications}, Series = {Quantitative Applications in the Social Sciences}, Title = {Analytic Mapping and Geographic Databases}, Volume = {87}, Year = {1992}} @techreport{McKenney98, Author = {Dan McKenney}, Institution = {International TechneGroup Incorporated}, Title = {Model quality: The key to {CAD}/{CAM}/{CAE} interoperability}, Year = {1998}} @article{Untereiner15, Author = {L. Untereiner and P. Kraemer and D. Cazier and D. Bechmann}, Journal = {Computer Graphics Forum}, Title = {{CPH}: A Compact Representation for Hierarchical Meshes Generated by Primal Refinement}, Year = {2015}} @techreport{Meseure14, Author = {Philippe Meseure and Emmanuelle Darles and Xavier Skapin and Yazid Touileb}, Institution = {XLIM}, Title = {Adaptive Resolution for Topology Modifications in Physically-based Animation}, Year = {2014}} @article{Dalstein15, Author = {Boris Dalstein and R\'emi Ronfard and Michiel van de Panne}, Journal = {ACM Transactions of Graphics}, Number = {4}, Title = {Vector Graphics Animation with Time-Varying Topology}, Volume = {34}, Year = {2015}} @article{Mucke99, Author = {M\"{u}cke, Ernst P. and Saias, Isaac and Zhu, Binhai}, Journal = {Computational Geometry---Theory and Applications}, Pages = {63--83}, Title = {Fast randomized point location without preprocessing in two- and three-dimensional {D}elaunay triangulations}, Volume = {12}, Year = {1999}} @manual{ISO/IEC25436:2007, Author = {{ISO/IEC}}, Organization = {{International Organization for Standardization} and {International Electrotechnical Commission}}, Title = {Information technology --- Eiffel: Analysis, Design and Programming Language}, Year = {2007}} @techreport{Meyer86, Author = {Bertrand Meyer}, Institution = {Interactive Software Engineering}, Number = {TR-EI-12/CO}, Title = {Design by Contract}, Year = {1986}} @techreport{Hoffmann88, Author = {Christoph M. Hoffmann}, Institution = {Purdue University}, Number = {88--771}, Title = {The problems of accuracy and robustness in geometric computation}, Type = {Computer Science Technical Reports}, Year = {1988}} @article{Hoffmann89, Author = {Hoffmann, C. M.}, Journal = {Computer---IEEE Computer Society Press}, Pages = {31--42}, Title = {{T}he problems of accuracy and robustness in geometric computation}, Volume = {22}, Year = {1989}} @book{Lewis98, Address = {Upper Saddle River, New Jersey 07458}, Author = {Harry R. Lewis and Christos H. Papadimitriou}, Publisher = {Prentice-Hall}, Title = {Elements of the theory of computations}, Year = {1998}} @unpublished{Veldhuizen03, Author = {Todd L. Veldhuizen}, Note = {Available at \url{http://ubietylab.net/ubigraph/content/Papers/pdf/CppTuring.pdf}}, Title = {C++ Templates are Turing Complete}, Year = {2003}} @book{Ratschek88, Author = {Helmut Ratschek and Jon Rokne}, Publisher = {Ellis Horwood}, Title = {New computer methods for global optimization}, Year = {1988}} @manual{IEEE754-2008, Address = {3 Park Avenue, New York, NY 10016-5997, USA}, Author = {IEEE}, Month = jun, Organization = {{The Institute of Electrical and Electronics Engineers}}, Title = {IEEE Standard for Floating-Point Arithmetic}, Year = {2008}} @book{Abbott84, Author = {Edwin A. Abbott}, Publisher = {Seely \& Co.}, Title = {Flatland: A Romance of Many Dimensions}, Year = {1884}} @unpublished{Black10, Author = {Don V. Black}, Note = {Available at \url{http://arxiv.org/abs/1201.5788}}, Title = {A toolkit to describe and interactively display three-manifolds embedded in four-space}, Year = {2010}} @techreport{Hoffmann90, Author = {Christoph M. Hoffmann and Jianhua Zhou}, Institution = {Purdue University}, Month = may, Number = {CSD TR--960}, Title = {Visualization of Surfaces in Four-Dimensional Space}, Type = {Computer Science Technical Reports}, Year = {1990}} @mastersthesis{Hollasch91, Author = {Steven Richard Hollasch}, School = {Arizona State University}, Title = {Four-Space Visualization of {4D} Objects}, Year = {1991}} @book{Newton87, Address = {Londoni}, Author = {Isaac Newton}, Publisher = {Josephi Streater}, Title = {Philosophi\ae Naturalis Principia Mathematica}, Year = {1687}} @phdthesis{Wang15, Author = {Zhiyong Wang}, School = {Delft University of Technology}, Title = {Path planning for first responders in the presence of moving obstacles}, Year = {2015}} @book{Nef78, Address = {Bern}, Author = {Walter Nef}, Publisher = {Herbert Lang}, Title = {Beitr\"age zur Theorie der Polyeder: mit Anwendungen in der Computergraphik}, Year = {1978}} @article{Ledoux08, Author = {Ledoux, Hugo and Gold, Christopher M.}, Journal = {International Journal of Geographical Information Science}, Number = {5}, Pages = {547--574}, Title = {Modelling three-dimensional geoscientific fields with the {V}oronoi diagram and its dual}, Volume = {22}, Year = {2008}} @article{Lee02, Author = {Lee, Ickjai and Gahegan, Mark}, Journal = {Transactions in GIS}, Number = {2}, Pages = {89--114}, Title = {{I}nteractive analysis using {V}oronoi diagrams: {A}lgorithms to support dynamic update from a generic triangle-based data structure}, Volume = {6}, Year = {2002}} @article{Dakowicz03, Author = {Dakowicz, Maciej and Gold, Christopher M.}, Journal = {International Journal of Computational Geometry and Applications}, Number = {4}, Pages = {339--357}, Title = {Extracting meaningful slopes from terrain contours}, Volume = {13}, Year = {2003}} @article{Boguslawski11a, Author = {Pawel Boguslawski and Christopher M. Gold and Hugo Ledoux}, Journal = {ISPRS Journal of Photogrammetry \& Remote Sensing}, Pages = {188--197}, Title = {Modelling and analysing {3D} buildings with a primal/dual data structure}, Volume = {66}, Year = {2011}} @incollection{Lee08, Author = {Lee, J. and Zlatanova, Sisi}, Booktitle = {Geospatial Information Technology for Emergency Response}, Editor = {Zlatanova, S. and Li, Jonathan}, Pages = {143--168}, Publisher = {Taylor \& Francis}, Title = {A {3D} data model and topological analyses for emergency response in urban areas}, Year = {2008}} @article{Lee08a, Author = {Lee, J. and Kwan, M.-P.}, Journal = {International Journal of Geographical Information Science}, Number = {10}, Pages = {1039--1056}, Title = {A combinatorial data model for representing topological relations among {3D} geographical features in micro-spatial environments}, Volume = {19}, Year = {2005}} @article{Gold91, Author = {Gold, Christopher M.}, Journal = {CISM Journal}, Number = {1}, Pages = {65--80}, Title = {{P}roblems with handling spatial data---the {V}oronoi approach}, Volume = {45}, Year = {1991}} @inproceedings{Weber98, Author = {Robert Weber and Hans-J. Schek and Stephen Blott}, Booktitle = {Proceedings of the 24th VLDB Conference}, Pages = {194--205}, Publisher = {ACM}, Title = {A Quantitative Analysis and Performance Study for Similarity-Search Methods in High-Dimensional Spaces}, Year = {1998}} @inproceedings{Sellis87, Author = {Timos Sellis and Nick Roussopoulos and Christos Faloutsos}, Booktitle = {Proceedings of 13th International Conference on Very Large Data Bases}, Title = {The {R}+-Tree: A dynamic index for multi-dimensional objects}, Year = {1987}} @incollection{Meng07, Author = {Liqiu Meng and Andrea Forberg}, Booktitle = {Generalisation of Geographic Information: Cartographic Modelling and Applications}, Editor = {W.A. Mackaness and A. Ruas and L.T. Sarajkoski}, Pages = {211--232}, Publisher = {Elsevier}, Title = {{3D} Building Generalisation}, Year = {2007}} @incollection{Geiger15, Author = {Andreas Geiger and Joachim Benner and Karl Heinz Haefele}, Booktitle = {3D Geoinformation Science}, Editor = {Martin Breunig and Mulhim Al-Doori and Edgar Butwilowski and Paul V. Kuper and Joachim Benner and Karl Heinz Haefele}, Pages = {19--35}, Publisher = {Springer International Publishing Switzerland}, Series = {Lecture Notes in Geoinformation and Cartography}, Title = {Generalization of {3D} {IFC} Building Models}, Year = {2015}} @article{Blaschke10, Author = {T. Blaschke}, Journal = {ISPRS Journal of Photogrammetry and Remote Sensing}, Month = jan, Number = {1}, Pages = {2--16}, Title = {Object based image analysis for remote sensing}, Volume = {65}, Year = {2010}} @article{Biljecki14a, Author = {Filip Biljecki and Hugo Ledoux and Jantien Stoter}, Journal = {GIM International}, Month = nov, Number = {11}, Pages = {21--23}, Title = {Redefining the Level of Detail for {3D} models}, Volume = {28}, Year = {2014}} @manual{ISO14882:2015, Author = {ISO}, Organization = {{International Organization for Standardization}}, Title = {Information technology --- Programming languages --- C++}, Year = {2015}} @article{Alexander24, Author = {J. W. Alexander}, Journal = {Proceedings of the National Academy of Sciences of the United States of America}, Number = {1}, Pages = {8--10}, Title = {An Example of a Simply Connected Surface Bounding a Region which is not Simply Connected}, Volume = {10}, Year = {1924}} @article{ArroyoOhori15b, Author = {Ken {Arroyo Ohori} and Hugo Ledoux and Filip Biljecki and Jantien Stoter}, Journal = {ISPRS International Journal of Geo-Information}, Month = jul, Number = {3}, Pages = {1055--1075}, Title = {Modelling a {3D} city model and its levels of detail as a true {4D} model}, Year = {2015}} @phdthesis{Nagel14, Author = {Claus Nagel}, Month = mar, School = {Technische Universit\"at Berlin}, Title = {Spatio-Semantic Modelling of Indoor Environments for Indoor Navigation}, Year = {2014}} @article{Meister71, Author = {Albrecht Ludwig Friedrich Meister}, Journal = {Novi Commentarii Societatis Reglae Scientiarum Gottingensis}, Pages = {144--180}, Title = {Generalia de genesi figurarum planarum et inde pendentibus earum affectionibus}, Volume = {1}, Year = {1771}} @book{Cromley92, Author = {Robert G. Cromley}, Publisher = {Prentice Hall}, Title = {Digital Cartography}, Year = {1992}} @manual{ISO19136:2007, Author = {{ISO}}, Organization = {{International Organization for Standardization}}, Title = {Geographic information --- Geography Markup Language (GML)}, Year = {2007}} @article{Poincare93, Author = {Henri Poincar\'e}, Journal = {Comptes rendus hebdomadaires de l'Acad\'emie des sciences de Paris}, Pages = {144--145}, Title = {Sur la g\'en\'eralisation d'un th\'eor\`eme d'{E}uler relatif aux poly\`edres}, Volume = {117}, Year = {1893}} @book{Cheng12, Author = {Siu-Wing Cheng and Tamal Krishna Dey and Jonathan Richard Shewchuk}, Publisher = {CRC Press}, Title = {Delaunay Mesh Generation}, Year = {2012}} @incollection{Dollner05, Author = {J\"urgen D\"ollner and Henrik Buchholz}, Booktitle = {GIS'05}, Pages = {173--181}, Publisher = {ACM}, Title = {Continuous Level-of-Detail Modeling of Buildings in {3D} City Models}, Year = {2005}} @incollection{Kolbe05, Author = {Thomas H. Kolbe and Gerhard Gr\"oger and Lutz Pl\"umer}, Booktitle = {Geo-information for Disaster Management}, Editor = {Peter {van Oosterom} and Siyka Zlatanova and Elfriede M. Fendel}, Pages = {883--899}, Publisher = {Springer Berlin Heidelberg}, Title = {{CityGML}: Interoperable Access to {3D} City Models}, Year = {2005}} @article{Groger11a, Author = {Gerhard Gr\"oger and Lutz Pl\"umer}, Journal = {Geoinformatica}, Pages = {137--165}, Title = {How to achieve consistency for {3D} city models}, Volume = {15}, Year = {2011}} @inproceedings{Zlatanova04, Author = {Siyka Zlatanova and Daniel Holweg}, Booktitle = {Proceedings of the 4th International Symposium on Mobile Mapping Technology}, Title = {{3D} Geo-information in Emergency Response: A Framework}, Year = {2004}} @inproceedings{Dollner06, Author = {J\"urgen D\"ollner and Thomas H. Kolbe and Falko Liecke and Takis Sgouros and Karin Teichmann}, Booktitle = {UDMS 2006}, Title = {The Virtual {3D} City Model of {B}erlin --- Managing, Integrating and Communicating Complex Urban Information}, Year = {2006}} @misc{Ramsey10, Author = {Paul Ramsey}, Howpublished = {Presentation at FOSS4G 2010. Available at \url{http://2010.foss4g.org/presentations/3369.pdf}}, Title = {{P}ost{GIS}: Tips for Power Users}, Year = {2010}} @article{Zhang14, Author = {Zhang, Xiang and Ai, Tinghua and Stoter, Jantien and Zhao, Xi}, Journal = {ISPRS Journal of Photogrammetry and Remote Sensing}, Month = jun, Pages = {147--163}, Title = {Data matching of building polygons at multiple map scales improved by contextual information and relaxation}, Volume = {92}, Year = {2014}} @inproceedings{Hampe03, Author = {Mark Hampe and Karl-Heinrich Anders and Monica Sester}, Booktitle = {Proceedings of the 21st International Cartographic Conference}, Pages = {192--202}, Title = {{MRDB} applications for data revision and real-time generalisation}, Year = {2003}} @inproceedings{Devogele96, Address = {Delft, Netherlands}, Author = {T. Devogele and J. Trevisan and L. Raynal}, Booktitle = {Proceedings of the 7th International Symposium on Spatial Data Handling}, Pages = {337-351}, Title = {Building a Multi-scale Database with Scale-transition Relationships}, Year = {1996}} @incollection{Veltkamp01, Author = {Remco C. Veltkamp and Michiel Hagedoorn}, Booktitle = {Principles of Visual Information Retrieval}, Pages = {87--119}, Publisher = {Springer London}, Series = {Advances in Pattern Recognition}, Title = {State of the Art in Shape Matching}, Year = {2001}} @incollection{Nagel09, Author = {Claus Nagel and Alexandra Stadler and Thomas H. Kolbe}, Booktitle = {GeoWeb 2009 Academic Track - Cityscapes}, Editor = {Thomas H. Kolbe and Hao Zhang and Sisi Zlatanova}, Month = jul, Pages = {46--53}, Publisher = {ISPRS Archives}, Title = {Conceptual requirements for the automatic reconstruction of building information models from uninterpreted 3D models}, Volume = {XXXVIII-3-4/C3}, Year = {2009}} @article{Attene13, Author = {Marco Attene and Marcel Campen and Leif Kobbelt}, Journal = {ACM Computing Surveys}, Number = {2}, Title = {Polygon mesh repairing: An application perspectice}, Volume = {45}, Year = {2013}} @article{Earman77, Author = {John Earman}, Journal = {No\^us}, Number = {3}, Pages = {211--226}, Title = {How to Talk about the Topology of Time}, Volume = {11}, Year = {1977}} @manual{ISO19125-1:2006, Author = {ISO}, Month = mar, Organization = {{International Organization for Standardization}}, Title = {Geographic information --- Simple feature access --- Part 1: Common architecture}, Year = {2006}} @manual{ISO19108:2002, Author = {{ISO}}, Month = feb, Organization = {{International Organization for Standardization}}, Title = {Geographic information --- Temporal schema}, Year = {2005}} @manual{ISO19108:2002/Cor1:2006, Author = {ISO}, Month = jul, Organization = {{International Organization for Standardization}}, Title = {Geographic information --- Temporal schema}, Year = {2008}} @manual{ISO19107:2005, Author = {{ISO}}, Month = feb, Organization = {{International Organization for Standardization}}, Title = {Geographic Information --- Spatial Schema}, Year = {2005}} @manual{ISO10303:2014, Author = {ISO}, Month = aug, Organization = {{International Organization for Standardization}}, Title = {Industrial automation systems and integration - Product data representation and exchange}, Year = {2014}} @manual{ISO16739:2013, Author = {ISO}, Month = mar, Organization = {{International Organization for Standardization}}, Title = {Industry Foundation Classes (IFC) for data sharing in the construction and facility management industries}, Year = {2013}} @manual{ISO19125-2:2006, Author = {ISO}, Month = mar, Organization = {{International Organization for Standardization}}, Title = {Geoinformation --- Simple feature access --- Part 2: SQL option}, Year = {2006}} @manual{ISO19137:2008, Author = {ISO}, Month = may, Organization = {{International Organization for Standardization}}, Title = {Geographic information --- Core profile of the spatial schema}, Year = {2008}} @book{Artin11, Author = {Emil Artin}, Publisher = {Nabu Press}, Title = {Geometric Algebra}, Year = {2011}} @article{Stevens46, Author = {S. S. Stevens}, Journal = {Science}, Number = {2684}, Pages = {677--680}, Title = {On the Theory of Scales of Measurement}, Volume = {103}, Year = {1946}} @article{Hagerstrand70, Author = {Torsten H\"agerstrand}, Journal = {Papers of the Regional Science Association}, Number = {1}, Pages = {6--21}, Title = {What about people in Regional Science?}, Volume = {24}, Year = {1970}} @inproceedings{Kraak03, Author = {Menno-Jan Kraak}, Booktitle = {Proceedings of the 21st International Cartographic Conference}, Pages = {1988-1996}, Title = {The space-time cube revisited from a geovisualization perspective}, Year = {2003}} @inproceedings{Basri05, Author = {Moshe Blank and Lena Gorelick and Eli Shechtman and Michal Irani and Ronen Basri}, Booktitle = {Proceedings of the 10th IEEE International Conference on Computer Vision}, Title = {Actions as Space-Time Shapes}, Year = {2005}} @article{ArroyoOhori15a, Author = {Ken {Arroyo Ohori} and Hugo Ledoux and Jantien Stoter}, Journal = {International Journal of Geographical Information Science}, Title = {A dimension-independent extrusion algorithm using generalised maps}, Year = {2015}} @article{ArroyoOhori15, Author = {Ken {Arroyo Ohori} and Hugo Ledoux and Jantien Stoter}, Journal = {International Journal of Geographical Information Science}, Month = feb, Number = {5}, Pages = {825--849}, Title = {An evaluation and classification of {nD} topological data structures for the representation of objects in a higher-dimensional {GIS}}, Volume = {29}, Year = {2015}} @article{Goodchild01, Author = {Michael F. Goodchild}, Journal = {International Journal of Applied Earth Observation and Geoinformation}, Number = {2}, Pages = {114--120}, Title = {Metrics of scale in remote sensing and {GIS}}, Volume = {3}, Year = {2001}} @article{Zhao12, Author = {Junqiao Zhao and Qing Zhu and Zhiqiang Du and Tiantian Feng and Yeting Zhang}, Journal = {ISPRS Journal of Photogrammetry and Remote Sensing}, Month = mar, Pages = {95--111}, Title = {Mathematical morphology-based generalization of complex {3D} building models incorporating semantic relationships}, Volume = {68}, Year = {2012}} @incollection{Kazhdan06, Author = {Michael Kazhdan and Matthew Bolitho1 and Hugues Hoppe2}, Booktitle = {Eurographics Symposium on Geometry Processing}, Editor = {Konrad Polthier and Alla Sheffer}, Publisher = {The Eurographics Association}, Title = {Poisson Surface Reconstruction}, Year = {2006}} @incollection{Amenta98, Author = {Nina Amenta and Marshall Bern}, Booktitle = {SCG '98 Proceedings of the 14th annual symposium on Computational geometry}, Pages = {39--48}, Publisher = {ACM}, Title = {Surface reconstruction by {V}oronoi filtering}, Year = {1998}} @incollection{Lindstrom98, Author = {Peter Lindstrom and Greg Turk}, Booktitle = {VIS '98 Proceedings of the conference on Visualization '98}, Pages = {279--286}, Publisher = {IEEE Computer Society Press}, Title = {Fast and memory efficient polygonal simplification}, Year = {1998}} @incollection{Garland97, Author = {Michael Garland and Paul S. Heckbert}, Booktitle = {SIGGRAPH '97 Proceedings of the 24th annual conference on Computer graphics and interactive techniques}, Pages = {209--216}, Publisher = {ACM Press/Addison-Wesley Publishing}, Title = {Surface simplification using quadric error metrics}, Year = {1997}} @incollection{Rigaux95, Author = {Philippe Rigaux and Michel Scholl}, Booktitle = {Advances in Spatial Databases}, Editor = {Max J. Egenhofer and John R. Herring}, Pages = {170--183}, Publisher = {Springer Berlin Heidelberg}, Series = {Lecture Notes in Computer Science}, Title = {Multi-Scale Partitions: Application to Spatial and Statistical Databases}, Volume = {951}, Year = {1995}} @techreport{Filho95, Author = {Waldemar Celes Filho and Luiz Henrique {de Figueiredo} and Marcelo Gattass and Paulo Cezar Carvalho}, Institution = {Department of Computer Science, University of Waterloo}, Number = {CS-95-53}, Title = {A topological data structure for hierarchical planar subdivisions}, Year = {1995}} @article{Tofper66, Author = {F. T\"ofper and W. Pillerwizer}, Journal = {The Cartographic Journal}, Month = may, Number = {1}, Pages = {10--16}, Title = {The Principles of Selection}, Volume = {3}, Year = {1966}} @incollection{Gunther88, Author = {Oliver G\"unther}, Booktitle = {Efficient structures for geometric data management}, Chapter = {6}, Pages = {85--121}, Publisher = {Springer Berlin Heidelberg}, Series = {Lecture Notes in Computer Science}, Title = {The arc tree: An approximation scheme to represent arbitrary curved shapes}, Volume = {337}, Year = {1988}} @inproceedings{Jones86, Author = {Jones, C.B. and Abraham, I.M.}, Booktitle = {Proceedings of the 2nd International Symposium on Spatial Data Handling}, Editor = {Marble, D.}, Pages = {384--398}, Title = {Design considerations for a scale-independent cartographic database}, Year = {1986}} @article{Ballard81, Author = {Dana H. Ballard}, Journal = {Communications of the ACM}, Month = may, Number = {5}, Pages = {310--321}, Title = {Strip Trees: A Hierarchical Representation for Curves}, Volume = {24}, Year = {1981}} @techreport{Buttenfield89, Author = {Barbara P. Buttenfield and Joseph S. DeLotto}, Institution = {National Center for Geographic Information and Analysis}, Number = {89--3}, Title = {Multiple Representations: Scientific Report for the Specialist Meeting}, Year = {1989}} @techreport{CEC95, Author = {CEC}, Institution = {Commission of the European Communities}, Title = {CORINE Land Cover}, Year = {1995}} @manual{SGK75, Author = {SGK}, Organization = {Der Schweizerischen Gesellschaft f\"ur Kartographie}, Title = {Kartographische Generalisierung}, Year = {1975}} @book{Robinson95, Author = {Arthur Howard Robinson}, Publisher = {Wiley}, Title = {Elements of cartography}, Year = {1995}} @techreport{Shead10, Author = {Timothy M. Shead}, Institution = {The K-3D Project}, Title = {Universal Relational Storage for Geometric Primitives}, Year = {2010}} @phdthesis{Strasser74, Author = {Wolfgang Stra{\ss}er}, School = {Technische Universit\"at Berlin}, Title = {Schnelle Kurven- und Fl\"achendarstellung auf graphischen Sichtger\"aten}, Year = {1974}} @article{Kuhn05, Author = {Werner Kuhn}, Journal = {Journal on Data Semantics}, Title = {Geospatial Semantics: Why, of What, and How?}, Year = {2005}} @incollection{Biljecki15, Author = {Biljecki, Filip and Ledoux, Hugo and Stoter, Jantien}, Booktitle = {3D Geoinformation Science. The Selected Papers of the 3D GeoInfo 2014}, Editor = {Breunig, Martin and Mulhim, Al-Doori and Butwilowski, Edgar and Kuper, Paul Vincent and Benner, Joachim and H{\"a}fele, Karl-Heinz}, Pages = {1--17}, Publisher = {Springer International Publishing}, Title = {Improving the Consistency of Multi-{LOD} {CityGML} Datasets by Removing Redundancy}, Year = {2015}} @phdthesis{Versprille75, Author = {Kenneth James Versprille}, School = {Syracuse University}, Title = {Computer-aided design applications of the rational b-spline approximation form}, Year = {1975}} @phdthesis{Bezier77, Author = {Pierre B\'ezier}, School = {Universit\'e Pierre et Marie Curie}, Title = {Essai de d\'efinition num\'erique des courbes et des surfaces experimentales: Contribution \`a l'\'etude des propri\'et\'es des courbes et des surfaces param\'etriques polynomiales \`a coefficients vectoriels}, Year = {1977}} @techreport{Cori75, Author = {Robert Cori}, Institution = {Soci\'et\'e math\'ematique de France}, Title = {Un code pour les graphes planaires et ses applications}, Year = {1975}} @incollection{Hanrahan82, Author = {Patrick M. Hanrahan}, Booktitle = {SIGGRAPH '82 Proceedings of the 9th annual conference on Computer graphics and interactive techniques}, Pages = {77-84}, Publisher = {ACM}, Title = {Creating volume models from edge-vertex graphs}, Year = {1982}} @incollection{Brewer86, Author = {John A. {Brewer III} and S. Mark Courter}, Booktitle = {SIGGRAPH '86 Proceedings of the 13th annual conference on Computer graphics and interactive techniques}, Number = {4}, Publisher = {ACM}, Title = {Automated conversion of curvilinear wire-frame models to surface boundary models; a topological approach}, Volume = {20}, Year = {1986}} @article{Brouwer11, Author = {L.E.J. Brouwer}, Journal = {Mathematische Annalen}, Pages = {314--319}, Title = {Beweis des {J}ordanschen {S}atzes f\"ur den $n$-dimensionalen {R}aum}, Volume = {71}, Year = {1911}} @book{van-Dalen13, Author = {Dirk {van Dalen}}, Publisher = {Springer Science+Business Media}, Title = {L.E.J. Brouwer --- Topologist, Intuitionist, Philosopher}, Year = {2013}} @article{Lebesgue11, Author = {M. Lebesgue}, Journal = {Comptes rendus de l'Acad\'emie des Sciences}, Pages = {841--844}, Title = {Sur l'invariance du nombre de dimensions d'un espace et sur le theor\`eme de {M}. {J}ordan relatif aux variet\'e ferm\'ees}, Volume = {152}, Year = {1911}} @book{Sagan94, Author = {Hans Sagan}, Publisher = {Springer Science+Business Media}, Title = {Space-Filling Curves}, Year = {1994}} @techreport{Requicha78, Author = {Aristides A. G. Requicha and Robert B. Tilove}, Institution = {University of Rochester}, Number = {27}, Title = {Mathematical Foundations of Constructive Solid Geometry: General Topology of Closed Regular Sets}, Type = {Production Automation Project Technical Memorandum}, Year = {1978}} @article{Blackmore94, Author = {Denis Blackmore and Ming C. Leu and Frank Shih}, Journal = {Computer-Aided Design}, Month = apr, Number = {4}, Pages = {315--326}, Title = {Analysis and modelling of deformed swept volumes}, Volume = {26}, Year = {1994}} @article{Weld90, Author = {John D. Weld and Ming C. Leu}, Journal = {The International Journal of Robotics Research}, Number = {5}, Pages = {105--117}, Title = {Geometric Representation of Swept Volumes with Application to Polyhedral Objects}, Volume = {9}, Year = {1990}} @article{Lee82, Author = {Yong Tsui Lee and Aristides A. G. Requicha}, Journal = {Communications of the ACM}, Number = {9}, Pages = {635--641}, Title = {Algorithms for Computing the Volume and Other Integral Properties of Solids. {I}. {K}nown Methods and Open Issues}, Volume = {25}, Year = {1982}} @incollection{Kada07, Author = {Martin Kada}, Booktitle = {COSIT 2007}, Pages = {222--237}, Publisher = {Springer-Verlag Berlin Heidelberg}, Series = {Lecture Notes in Computer Science}, Title = {Scale-Dependent Simplification of {3D} Building Models Based on Cell Decomposition and Primitive Instancing}, Volume = {4736}, Year = {2007}} @book{Devlin93, Author = {Keith Devlin}, Publisher = {Springer-Verlag}, Title = {The Joy of Sets: Fundamentals of Contemporary Set Theory}, Year = {1993}} @article{Cantor74, Author = {Georg Cantor}, Journal = {Journal f{\"u}r die reine und angewandte Mathematik}, Pages = {258--262}, Title = {Ueber eine {E}igenschaft des Inbegriffs aller reellen algebraischen {Z}ahlen}, Volume = {77}, Year = {1874}} @techreport{Meagher80, Author = {Donald Meagher}, Institution = {Rensselaer Polytechnic Institute}, Title = {Octree Encoding: a New Technique for the Representation, Manipulation and Display of Arbitrary 3-D Objects by Computer}, Year = {1980}} @article{Keil02, Author = {Mark Keil and Jack Snoeyink}, Journal = {International Journal of Computational Geometry and Applications}, Number = {181}, Title = {On the time bound for convex decomposition of simple polygons}, Volume = {12}, Year = {2002}} @article{Rvachev63, Author = {V. L. Rvachev}, Journal = {Doklady Akademii Nauk SSSR}, Number = {4}, Pages = {765--767}, Title = {On the analytical description of certain geometrical objects}, Volume = {153}, Year = {1963}} @article{Preparata79, Author = {F.P. Preparata and D.E. Muller}, Journal = {Theoretical Computer Science}, Number = {1}, Pages = {45--55}, Title = {Finding the intersection of $n$ half-spaces in time $O(n \log n)$}, Volume = {8}, Year = {1979}} @article{Freundschuh97, Author = {Scott M. Freundschuh and Max J. Egenhofer}, Journal = {Transactions in GIS}, Number = {4}, Pages = {361--375}, Title = {Human Conceptions of Spaces: Implications for Geographic Information Systems}, Volume = {2}, Year = {1997}} @book{Hoffmann92, Author = {Christoph M. Hoffmann}, Publisher = {Morgan Kaufmann Publishers}, Title = {Geometric and solid modeling}, Year = {1992}} @techreport{Requicha77, Author = {A. A. G. Requicha and H. B. Voelcker}, Institution = {College of Engineering \& Applied Science, The University of Rochester}, Month = nov, Number = {25}, Title = {Constructive Solid Geometry}, Type = {Technical Memorandum}, Year = {1977}} @book{Foley95, Author = {James D. Foley and Andries {van Dam} and Steven K. Feiner and John F. Hughes}, Publisher = {Addison-Wesley Professional}, Title = {Computer Graphics: Principles and Practice in C}, Year = {1995}} @article{Euler41, Author = {Leonhard Euler}, Journal = {Commentarii academiae scientiarum Petropolitanae}, Pages = {128--140}, Title = {Solutio problematis ad geometriam situs pertinentis}, Volume = {8}, Year = {1741}} @book{Henle94, Author = {Michael Henle}, Publisher = {Dover Publications}, Title = {A Combinatorial Introduction to Topology}, Year = {1994}} @book{Hausdorff14, Address = {Leipzig}, Author = {Felix Hausdorff}, Publisher = {Verlag von Veit \& Comp.}, Title = {Grundz\"uge der Mengenlehre}, Year = {1914}} @book{Bolyai32, Author = {J\'anos Bolyai}, Publisher = {Maros-V\'as\'arhelyini}, Title = {Appendix Scientiam Spatii Absolute Veram Exhibens}, Year = {1832}} @book{Lobachevsky40, Address = {Berlin}, Author = {Nikolai Lobachevsky}, Publisher = {Funcke}, Title = {Geometrische Untersuchungen zur Theorie der Parallellinien}, Year = {1840}} @article{de-Fermat79, Author = {Pierre {de Fermat}}, Journal = {Varia opera mathematica}, Pages = {1--8}, Title = {Ad Locos Planos et Solidos Isagoge}, Year = {1679}} @book{Fitzpatrick08, Author = {Richard Fitzpatrick}, Publisher = {Richard Fitzpatrick}, Title = {Euclid's Elements of Geometry}, Year = {2008}} @book{Burrough86, Author = {P.A. Burrough}, Publisher = {Taylor \& Francis}, Title = {Principles of geographical information systems for land resources assessment}, Year = {1986}} @book{Bailey95, Author = {Trevor C. Bailey and Anthony C. Gatrell}, Publisher = {Longman}, Title = {Interactive spatial data analysis}, Year = {1995}} @article{Stoter14, Author = {Stoter, J.E. and M. Post and V. van Altena and R. Nijhuis and B. Bruns}, Journal = {Cartography and Geographic Information Science}, Month = jan, Number = {1}, Pages = {1-13}, Title = {Fully automated generalisation of a 1:50k map from 1:10k data}, Volume = {41}, Year = {2014}} @inproceedings{Vandysheva12, Author = {Natalia Vandysheva and Sergey Sapelnikov and Peter {van Oosterom} and Marian {de Vries} and Boudewijn Spiering and Rik Wouters and Andreas Hoogeveen and Veliko Penkov}, Booktitle = {FIG Working Week 2012}, Month = {May}, Title = {The {3D} Cadastre Prototype and Pilot in the {R}ussian {F}ederation}, Year = {2012}} @manual{GML3.2.1, Author = {{OGC}}, Month = {August}, Organization = {{Open Geospatial Consortium}}, Title = {{OpenGIS} Geography Markup Language (GML) Encoding Standard. Version 3.2.1}, Year = {2007}} @manual{GML3.3, Author = {{OGC}}, Month = {December}, Organization = {{Open Geospatial Consortium}}, Title = {{OGC} {G}eography {M}arkup {L}anguage --- Extended schemas and encoding rules. Version 3.3.0}, Year = {2012}} @book{Damiand14, Author = {Guillaume Damiand and Pascal Lienhardt}, Publisher = {CRC Press}, Title = {Combinatorial Maps: Efficient Data Structures for Computer Graphics and Image Processing}, Year = {2014}} @inproceedings{Aguila03, Author = {Ricardo P\'erez Aguila and Antonio Aguilera Ram\'irez}, Booktitle = {WSCG'2003}, Month = feb, Publisher = {UNION Agency - Science Press}, Title = {Classifying Edges and Faces as Manifold or Non-Manifold Elements in {4D} Orthogonal Pseudo-Polytopes}, Year = {2003}} @mastersthesis{Donkers13, Author = {Sjors Donkers}, Month = {December}, School = {Delft University of Technology}, Title = {Automatic generation of {CityGML} {LoD3} building models from {IFC} models}, Year = {2013}} @inproceedings{Xiong10, Author = {Xuehan Xiong and Daniel Huber}, Booktitle = {Proceedings of the British Machine Vision Conference (BMVC)}, Title = {Using Context to Create Semantic {3D} Models of Indoor Environments}, Year = {2010}} @article{Sternberg13, Author = {Harald Sternberg and Friedrich Keller and Thomas Willemsen}, Journal = {Journal of Applied Geodesy}, Pages = {231--246}, Title = {Precise indoor mapping as a basis for coarse indoor navigation}, Volume = {7}, Year = {2013}} @incollection{Jamali14, Author = {Ali Jamali and Pawel Boguslawski and Christopher M. Gold and Alias Abdul Rahman}, Booktitle = {Innovations in 3D Geo-Information Sciences}, Pages = {1--11}, Publisher = {Springer International Publishing}, Series = {Lecture Notes in Geoinformation and Cartography}, Title = {Rapid Indoor Data Acquisition Technique for Indoor Building Surveying for Cadastre Application}, Year = {2014}} @mastersthesis{Martin05, Author = {Jess Martin}, School = {Trinity University}, Title = {Algorithmic Beauty of Buildings Methods for Procedural Building Generation}, Year = {2005}} @inproceedings{Johnston08, Author = {Matthew Johnston and Avideh Zakhor}, Booktitle = {Proceedings of Three-Dimensional Image Capture and Applications}, Title = {Estimating building floor-plans from exterior using laser scanners}, Year = {2008}} @incollection{Budroni09, Author = {Angela Budroni and Jan B\"ohm}, Booktitle = {3D Virtual Reconstruction and Visualization of Complex Architectures}, Publisher = {ISPRS}, Series = {ISPRS Archives}, Title = {Toward automatic reconstruction of interiors from laser data}, Volume = {XXXVIII-5/W1}, Year = {2009}} @inproceedings{Okorn10, Author = {Brian Okorn and Xuehan Xiong and Burcu Akinci and Daniel Huber}, Booktitle = {Proceedings of the Symposium on 3D Data Processing, Visualization and Transmission}, Title = {Toward Automated Modeling of Floor Plans}, Year = {2010}} @inproceedings{Goetz11, Author = {M. Goetz and A. Zipf}, Booktitle = {Proceedings of the UDMS: Urban and Regional Data Management: 2011}, Title = {Extending {OpenStreetMap} to Indoor Environments: Bringing Volunteered Geographic Information to the Next Level}, Year = {2011}} @manual{NEN2580, Author = {{NEN}}, Month = {May}, Title = {NEN 2580:2007 nl: Areas and volumes of buildings - Terms, definitions and methods of determination}, Year = {2007}} @book{Homotopy13, Author = {{The Univalent Foundations Program Institute for Advanced Study}}, Publisher = {Institute for Advanced Study}, Title = {Homotopy Type Theory: Univalent Foundations of Mathematics}} @incollection{Wagner13, Author = {Detlev Wagner and Mark Wewetzer and J\"urgen Bogdahn and Nazmul Alam and Margitta Pries and Volker Coors}, Booktitle = {Progress and New Trends in 3D Geoinformation Sciences}, Editor = {J. Pouliot and S. Daniel and F. Hubert and A. Zamyadi}, Publisher = {Springer Berlin Heidelberg}, Series = {Lecture Notes in Geoinformation and Cartography}, Title = {Geometric-semantical consistency validation of {CityGML} models}, Year = {2013}} @incollection{Hagedorn09, Author = {Benjamin Hagedorn and Matthias Trapp and Tassilo Glander and J\"urgen D\"ollner}, Booktitle = {2009 Tenth International Conference on Mobile Data Management: Systems, Services and Middleware}, Publisher = {IEEE Computer Society}, Title = {Towards an Indoor Level-of-Detail Model for Route Visualization}, Year = {2009}} @inproceedings{Guercke09, Author = {Richard Guercke and Claus Brenner}, Booktitle = {Proceedings of the 12th AGILE International Conference on Geographic Information Science 2009}, Title = {A Framework for the Generalization of {3D} City Models}, Year = {2009}} @incollection{Emgard08, Author = {L. Emg{\aa}rd and S. Zlatanova}, Booktitle = {Urban and Regional Data Management --- UDMS Annual 2007}, Editor = {V. Coors and M. Rumor and E.M. Fendel and S. Zlatanova}, Publisher = {Taylor \& Francis}, Title = {Design of an integrated {3D} information model}, Year = {2008}} @inproceedings{Dominguez11, Author = {B. Dom\'inguez and \'A.L. Garc\'ia and F.R. Feito}, Booktitle = {Proceedings of the Joint ISPRS Workshop on 3D City Modelling \& Applications and the 6th 3D GeoInfo Conference}, Pages = {209--222}, Title = {Semantic and topological representation of building indoors: an overview}, Volume = {66}, Year = {2011}} @article{Guercke11, Author = {R. Guercke and T. G\"otzelmann and C. Brenner and M. Sester}, Journal = {ISPRS Journal of Photogrammetry and Remote Sensing}, Pages = {209--222}, Title = {Aggregation of LoD 1 building models as an optimization problem}, Volume = {66}, Year = {2011}} @incollection{Vosselman01, Author = {George Vosselman and Sander Dijkman}, Booktitle = {International Archives of Photogrammetry and Remote Sensing}, Publisher = {International Society for Photogrammetry and Remote Sensing}, Title = {{3D} building model reconstruction from point clouds and ground plans}, Volume = {XXXIV-3/W4}, Year = {2001}} @article{Dilo09, Author = {Arta Dilo and Peter {van Oosterom} and Arjen Hofman}, Pages = {388--402}, Title = {Constrained {tGAP} for generalization between scales: The case of {D}utch topographic data}, Volume = {33}, Year = {2009}} @article{Biljecki14, Author = {Filip Biljecki and Hugo Ledoux and Jantien Stoter and Junqiao Zhao}, Journal = {Computers, Environment and Urban Systems}, Pages = {1--15}, Title = {Formalisation of the level of detail in {3D} city modelling}, Volume = {48}, Year = {2014}} @inproceedings{Bedard02, Author = {Bernier B\'edard}, Booktitle = {Joint Workshop on Multi-Scale Representations of Spatial Data}, Title = {Supporting Multiple Representations with Spatial View Management and the Concept of ``VUEL''}, Year = {2002}} @book{Salomon07, Author = {David Salomon}, Edition = {Fourth Edition}, Publisher = {Springer}, Title = {Data Compression: The Complete Reference}, Year = {2007}} @book{Borg05, Author = {Ingwer Borg and Patrick J.F. Groenen}, Edition = {2nd Edition}, Publisher = {Springer}, Series = {Springer Series in Statistics}, Title = {Modern Multidimensional Scaling: Theory and Applications}, Year = {2005}} @incollection{David93, Author = {Benoit David and Laurent Raynal and Guylaine Schorter and V\'eronique Mansart}, Booktitle = {Database and Expert Systems Applications}, Editor = {Vladim\'ir Ma\v{r}\'ik and Ji\v{r}\'i La\v{z}ansk\'y and Roland R. Wagner}, Pages = {377--383}, Publisher = {Springer Berlin Heidelberg}, Series = {Lecture Notes in Computer Science}, Title = {GeO2: Object-oriented contribution for a geographical DBMS?}, Volume = {720}, Year = {1993}} @article{Bryant85, Author = {Robin P. Bryant and David Singerman}, Journal = {Quarterly Journal of Mathematics}, Number = {2}, Pages = {17--41}, Title = {Foundations of the theory of maps on surfaces with boundary}, Volume = {36}, Year = {1985}} @book{Edelsbrunner14, Author = {Herbert Edelsbrunner}, Publisher = {Springer}, Series = {Springer Briefs in Applied Sciences and Technology}, Title = {A Short Course in Computational Geometry and Topology}, Year = {2014}} @article{Fisher97, Author = {P. Fisher}, Journal = {International Journal of Remote Sensing}, Number = {3}, Pages = {679--685}, Title = {The pixel: a snare and a delusion}, Volume = {18}, Year = {1997}} @incollection{Hazelton98, Author = {N.W.J. Hazelton}, Booktitle = {Spatial and Temporal Reasoning in Geographic Information Systems}, Editor = {Egenhofer, M.J. and Golledge, R.G.}, Pages = {63--73}, Publisher = {Oxford University Press}, Title = {Some Operations Requirements for a Multi-Temporal {4-D} {GIS}}, Year = {1998}} @article{Molenaar92, Author = {Martien Molenaar}, Journal = {ITC Journal}, Pages = {25--33}, Title = {A topology for {3D} vector maps}, Volume = {1}, Year = {1992}} @book{Raper89, Editor = {Jonathan Raper}, Publisher = {Taylor \& Francis}, Title = {Three Dimensional Applications in Geographic Information Systems}, Year = {1989}} @book{Worboys04, Author = {Michael Worboys and Matt Duckham}, Edition = {2nd}, Publisher = {CRC Press}, Title = {{GIS}: A Computational Perspective}, Year = {2004}} @manual{ESRITopology, Author = {{ESRI}}, Month = {July}, Organization = {{ESRI}}, Title = {{GIS} Topology}, Year = {2005}} @inproceedings{Dominguez12, Author = {B. Dom\'inguez and \'A.L. Garc\'ia and F.R. Feito}, Booktitle = {GRAPP/IVAPP}, Title = {Semantic and topological representation of building indoors: an overview}, Year = {2012}} @inproceedings{Diakite14, Author = {A. A. Diakit\'e and Guillaume Damiand and D. {van Maercke}}, Booktitle = {Proceedings of the 2nd Eurographics Workshop on Urban Data Modelling and Visualisation}, Title = {Topological Reconstruction of Complex 3D Buildings and Automatic Extraction of Levels of Detail}, Year = {2014}} @unpublished{Prieto10, Author = {Carlos Prieto}, Title = {Elements of Point-Set Topology}, Year = {2010}} @unpublished{Bell92, Author = {Sarah B.M. Bell and Fred C. Holroyd}, Title = {Optimal Hierarchies for Spatial Data Processing}, Year = {1992}} @techreport{McKenzie01, Author = {John W. McKenzie and Ian P. Williamson and N.W.J. Hazelton}, Institution = {Department of Geomatics, The University of Melbourne}, Title = {{4-D} Adaptive {GIS}: Justification and Methodologies}, Year = {2001}} @article{Hamre97, Author = {Torill Hamre and Khalid Azim Mughal and Anita Jacob}, Journal = {Marine Geodesy}, Number = {2--3}, Pages = {121--136}, Title = {A {4D} marine data model: Design and application in ice monitoring}, Volume = {20}, Year = {1997}} @article{Bernard00, Author = {Lard Bernard and Thomas Kr\"uger}, Journal = {Transactions in GIS}, Month = {June}, Number = {3}, Pages = {197--215}, Title = {Integration of GIS and Spatio-temporal Simulation Models: Interoperable Components for Different Simulation Strategies}, Volume = {4}, Year = {2000}} @inproceedings{Bernard98, Author = {Lars Bernard and Benno Schmidt and Ulrich Streit}, Booktitle = {Proceedings of the 8th International Symposium on Spatial Data Handling}, Editor = {T.K. Poiker and N. Chrisman}, Title = {{AtmoGIS} --- Integration of atmospheric models and {GIS}}, Year = {1998}} @article{Liu08, Author = {Yuanxin Liu and Jack Snoeyink}, Journal = {International Journal of Computational Geometry and Applications}, Number = {4}, Pages = {343--355}, Title = {Faraway Point: A Sentinel Point for {D}elaunay Computation}, Volume = {18}, Year = {2008}} @article{Onosato14, Author = {Masahiko Onosato and Yosuke Saito and Fumiki Tanaka and Ryoji Kawagishi}, Journal = {Computer-Aided Civil}, Number = {6}, Pages = {649--658}, Title = {Weaving a Four-dimensional Mesh Model from a Series of Three-dimensional Voxel Models}, Volume = {11}, Year = {2014}} @article{Bucksch14, Author = {Alexander Bucksch and Greg Turk and Joshua Weitz}, Journal = {PLOS ONE}, Number = {1}, Pages = {1--11}, Title = {The Fiber Walk: A Model of Tip-Driven Growth with Lateral Expansion}, Volume = {9}, Year = {2014}} @article{Borradaile14, Author = {Glencora Borradaile and Erin Wolf Chambers}, Journal = {Discrete \& Computational Geometry}, Title = {Covering nearly surface-embedded graphs with a fixed number of balls}, Year = {2014}} @incollection{Tran14, Author = {Phuoc Vinh Tran and Hong Thu Nguyen and Trung Vinh Tran}, Booktitle = {IMCOM (ICUIMC)'14}, Publisher = {ACM}, Title = {Approaching Multi-dimensional Cube for Visualization-based Epidemic Warning System - Dengue Fever}, Year = {2014}} @article{Lopes03, Author = {H. Lopes and S. Pesco and G. Tavares and M. Maia and A. Xavier}, Journal = {International Journal of Shape Modeling}, Number = {1}, Pages = {61--77}, Title = {Handlebody Representation for Surfaces and its Applications to Terrain Modeling}, Volume = {9}, Year = {2003}} @inproceedings{Gomes04, Author = {Abel J. P. Gomes}, Booktitle = {ACM Symposium on Solid Modeling and Applications}, Editor = {P. Brunet and N. Patrikalakis}, Title = {Euler Operators for Stratified Objects with Incomplete Boundaries}, Year = {2004}} @incollection{Suba14, Author = {Radan \v{S}uba and Martijn Meijers and Lina Huang and Peter {van Oosterom}}, Booktitle = {Connecting a Digital Europe Through Location and Place}, Editor = {Joaqu\'in Huerta and Sven Schade and Carlos Granell}, Pages = {275--293}, Publisher = {Springer International Publishing Switzerland}, Title = {An Area Merge Operation for Smooth Zooming}, Year = {2014}} @article{Ferrucci91, Author = {Vincenzo Ferrucci and Alberto Paoluzzi}, Journal = {Computer-Aided Civil}, Number = {1}, Pages = {40--50}, Title = {Extrusion and boundary evaluation for multidimensionaI poIyhedra}, Volume = {23}, Year = {1991}} @article{Pascucci94, Author = {V. Pascucci and V. Ferrucci and A. Paoluzzi}, Journal = {International Journal of Shape Modeling}, Title = {Dimension-Independent Convex-Cell Based HPC Skeletons and Product}, Year = {1994}} @inproceedings{deFloriani10, Author = {Leila {de Floriani} and Annie Hui and Daniele Panozzo and David Canino}, Booktitle = {Proceedings of the 19th International Meshing Roundtable}, Editor = {Suzanne Shontz}, Pages = {403--420}, Title = {A Dimension-Independent Data Structure for Simplicial Complexes}, Year = {2010}} @incollection{Pascucci95, Author = {Valerio Pascucci and Vincenzo Ferrucci and Alberto Paoluzzi}, Booktitle = {Solid Modeling '95}, Pages = {163--174}, Publisher = {ACM}, Title = {Dimension-Independent Convex-Cell Based HPC: Representation Scheme and Implementation Issues}, Year = {1995}} @article{Paoluzzi92, Author = {A. Paoluzzi and C. Sansoni}, Journal = {Computer-Aided Civil}, Number = {7}, Pages = {349--366}, Title = {Programming language for solid variational geometry}, Volume = {24}, Year = {1992}} @incollection{Juan-Arinyo95, Author = {Robert Juan-Arinyo}, Booktitle = {Computer Graphics Forum}, Pages = {281--293}, Publisher = {The Eurographics Association}, Title = {Domain Extension of Isothetic Polyhedra with Minimal CSG Representation}, Volume = {5}, Year = {1995}} @inproceedings{Canino14, Author = {David Canino and Leila {de Floriani}}, Booktitle = {Proceedings of the 22nd International Meshing Roundtable}, Editor = {Josep Sarrate and Matthew Staten}, Pages = {465--483}, Title = {Representing Simplicial Complexes with Mangroves}, Year = {2014}} @article{Peuquet84, Author = {Donna J. Peuquet}, Journal = {Cartographica}, Number = {4}, Pages = {66--113}, Title = {A Conceptual Framework and Comparison of Spatial Data Models}, Volume = {21}, Year = {1984}} @incollection{Couclelis92, Author = {Helen Couclelis}, Booktitle = {Theories and Methods of Spatio-Temporal Reasoning in Geographic Space}, Editor = {A. U. Frank and I. Campari and U. Formentini}, Pages = {65--77}, Publisher = {Springer Berlin Heidelberg}, Series = {Lecture Notes in Computer Science}, Title = {People Manipulate Objects (but Cultivate Fields): Beyond the Raster-Vector Debate in {GIS}}, Volume = {639}, Year = {1992}} @article{Galton01, Author = {Antony Galton}, Journal = {Topoi}, Pages = {173--187}, Title = {Space, Time, and the Representation of Geographical Reality}, Volume = {20}, Year = {2001}} @incollection{Ferrucci93, Author = {Vincenzo Ferrucci}, Booktitle = {2nd ACM Solid Modelling '93}, Pages = {35--42}, Publisher = {ACM}, Title = {Generalised Extrusion of Polyhedra}, Year = {1993}} @incollection{Velho03, Author = {Luiz Velho}, Booktitle = {Eurographics Symposium on Geometry Processing}, Editor = {L. Kobbelt and P. Schr\"oder and H. Hoppe}, Publisher = {The Eurographics Association}, Title = {Stellar Subdivision Grammars}, Year = {2003}} @book{Conway92, Author = {J.H. Conway and N.J.A. Sloane}, Publisher = {Springer-Verlag}, Title = {Sphere Packings, Lattices and Groups}, Year = {1992}} @article{Rossignac91, Author = {Jarek R. Rossignac and Aristides A. G. Requicha}, Journal = {Computer-Aided Design}, Number = {1}, Pages = {21--32}, Title = {Constructive Non-Regularized Geometry}, Volume = {23}, Year = {1991}} @article{Clifford97, Author = {James Clifford and Curtis Dyreson and Tom\'as Isakowitz and Christian S. Jensen and Richard T. Snodgrass}, Journal = {ACM Transactions on Database Systems}, Month = {June}, Number = {2}, Pages = {171--214}, Title = {On the Semantics of ``Now'' in Databases}, Volume = {22}, Year = {1997}} @article{Pasko95, Author = {A. Pasko and V. Adzhiev and A. Sourin and V. Savchenko}, Journal = {The Visual Computer}, Pages = {429--446}, Title = {Function representation in geometric modeling: concepts, implementation and applications}, Volume = {11}, Year = {1995}} @article{Barnes14a, Author = {Richard Barnes and Clarence Lehman and David Mulla}, Journal = {Computers \& Geosciences}, Pages = {117--127}, Title = {Priority-flood: An optimal depression-filling and watershed-labeling algorithm for digital elevation models}, Volume = {62}, Year = {2014}} @article{Barnes14, Author = {Richard Barnes and Clarence Lehman and David Mulla}, Journal = {Computers \& Geosciences}, Month = {January}, Pages = {128--135}, Title = {An efficient assignment of drainage direction over flat surfaces in raster digital elevation models}, Volume = {62}, Year = {2014}} @article{Le13a, Author = {Hai Ha Le and Paul Gabriel and Jan Gietzel and Helmut Schaeben}, Journal = {Computers \& Geosciences}, Pages = {104--115}, Title = {An object-relational spatio-temporal geoscience data model}, Volume = {57}, Year = {2013}} @mastersthesis{Boeters13, Author = {Roeland Boeters}, Month = jun, School = {Delft University of Technology}, Title = {Automatic enhancement of {CityGML} {LoD2} models with interiors and its usability for net internal area determination}, Year = {2013}} @mastersthesis{ArroyoOhori10, Author = {Ken {Arroyo Ohori}}, Month = aug, School = {Delft University of Technology}, Title = {Validation and automatic repair of planar partitions using a constrained triangulation}, Year = {2010}} @techreport{ArroyoOhori11, Author = {Ken {Arroyo Ohori}}, Institution = {OTB Research Institute for the Built Environment, Delft University of Technology}, Month = dec, Number = {57}, Title = {Realising the Foundations of a Higher Dimensional {GIS}: A Study of Higher Dimensional Spatial Data Models, Data Structures and Operations}, Type = {PhD Proposal}, Year = {2011}} @inproceedings{Stoter12a, Address = {Amsterdam, The Netherlands}, Author = {Stoter, Jantien and Ledoux, Hugo and Meijers, Martijn and Arroyo Ohori, Ken and Peter {van Oosterom}}, Booktitle = {Geospatial World Forum 2012}, Month = apr, Title = {{5D} Modeling - applications and advantages}, Year = {2012}} @article{ArroyoOhori12c, Author = {Arroyo Ohori, Ken and Ledoux, Hugo and Meijers, Martijn and Stoter, Jantien}, Journal = {Geo-Info}, Month = oct, Number = {8}, Pages = {4--8}, Title = {Een landsdekkende {BGT}, zonder gaten en overlap}, Volume = {9}, Year = {2012}} @inproceedings{ArroyoOhori12b, Address = {Apeldoorn, The Netherlands}, Author = {Ken {Arroyo Ohori}}, Booktitle = {GIN Symposium}, Month = nov, Title = {Developing {5D} spatial models for {GIS}}, Year = {2012}} @inproceedings{Ledoux11, Address = {Ostrava, Czech Republic}, Author = {Ledoux, Hugo and Arroyo Ohori, Ken}, Booktitle = {Proceedings of GIS Ostrava 2011}, Month = jan, Pages = {377--390}, Title = {Edge-matching polygons with a constrained triangulation}, Year = {2011}} @inproceedings{Ledoux12, Address = {Avignon, France}, Author = {Hugo Ledoux and Ken {Arroyo Ohori} and Martijn Meijers}, Booktitle = {Multidisciplinary Research on Geographical Information in Europe and Beyond. Proceedings of the 15th AGILE International Conference on Geographic Information Science}, Editor = {J\'er\^ome Gensel and Didier Josselin and Danny Vandenbroucke}, Month = apr, Pages = {13--18}, Title = {Automatically repairing invalid polygons with a constrained triangulation}, Year = {2012}} @inproceedings{Stoter12, Address = {Qu\'ebec City, Canada}, Author = {Jantien Stoter and Hugo Ledoux and Martijn Meijers and Ken {Arroyo Ohori}}, Booktitle = {Proceedings of the 7th International 3D GeoInfo Conference}, Editor = {Jacynthe Pouliot and Sylvie Daniel and Fr{\'e}d{\'e}ric Hubert and Alborz Zamyadi}, Month = may, Pages = {7--10}, Publisher = {ISPRS}, Series = {International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences}, Title = {Integrating Scale and Space in {3D} City Models}, Volume = {XXXVIII-4/C26}, Year = {2012}} @inproceedings{ArroyoOhori12a, Address = {Nottingham, United Kingdom}, Author = {Ken {Arroyo Ohori} and Hugo Ledoux and Martijn Meijers}, Booktitle = {Proceedings of the 4th Open Source GIS UK Conference}, Month = sep, Title = {Automatically repairing polygons and planar partitions with prepair and pprepair}, Year = {2012}} @article{ArroyoOhori12, Author = {Ken {Arroyo Ohori} and Hugo Ledoux and Martijn Meijers}, Journal = {Photogrammetrie, Fernerkundung, Geoinformation}, Month = oct, Pages = {613--630}, Title = {Validation and Automatic Repair of Planar Partitions Using a Constrained Triangulation}, Volume = {5}, Year = {2012}} @inproceedings{ArroyoOhori13c, Address = {Leuven, Belgium}, Author = {Ken {Arroyo Ohori} and Filip Biljecki and Jantien Stoter and Hugo Ledoux}, Booktitle = {Geographic Information Science at the Heart of Europe. Proceedings of the 16th AGILE International Conference on Geographic Information Science}, Month = may, Title = {Manipulating higher dimensional spatial information}, Year = {2013}} @incollection{ArroyoOhori13b, Address = {Johor Bahru, Malaysia}, Author = {Ken {Arroyo Ohori} and Pawel Boguslawski and Hugo Ledoux}, Booktitle = {Developments in Multidimensional Spatial Data Models}, Editor = {Abdul Rahman, A. and Boguslawski, P. and Gold, C. and Said, M.N.}, Month = may, Pages = {17--31}, Publisher = {Springer Berlin Heidelberg}, Series = {Lecture Notes in Geoinformation and Cartography}, Title = {Representing the dual of objects in a four-dimensional {GIS}}, Year = {2013}} @incollection{ArroyoOhori13a, Address = {Ho Chi Minh City, Vietnam}, Author = {Ken {Arroyo Ohori} and Hugo Ledoux and Jantien Stoter}, Booktitle = {Computational Science and Its Applications --- ICCSA 2013. 13th International Conference, Ho Chi Minh City, Vietnam, June 24--27, 2013, Proceedings, Part I}, Editor = {B. Murgante and S. Misra and M. Carlini and C. Torre and H.Q. Nguyen and D. Taniar and B. Apduhan and O. Gervasi}, Month = jun, Pages = {526--539}, Publisher = {Springer Berlin Heidelberg}, Series = {Lecture Notes in Computer Science}, Title = {Modelling Higher Dimensional Data for {GIS} Using Generalised Maps}, Volume = {7971}, Year = {2013}} @incollection{ArroyoOhori13, Address = {Orlando, United States}, Author = {Ken {Arroyo Ohori} and Hugo Ledoux}, Booktitle = {SIGSPATIAL'13: Proceedings of the 21st ACM SIGSPATIAL International Conference on Advances in Geographic Information Systems}, Editor = {Craig Knoblock and Peer Kr\"oger and John Krumm and Markus Schneider and Peter Widmayer}, Month = nov, Pages = {398--401}, Publisher = {ACM}, Title = {Using extrusion to generate higher-dimensional {GIS} datasets}, Year = {2013}} @incollection{ArroyoOhori14, Address = {Kolkata, India}, Author = {Ken {Arroyo Ohori} and Guillaume Damiand and Hugo Ledoux}, Booktitle = {Applied Algorithms. First International Conference, ICAA 2014, Kolkata, India, January 13-15, 2014. Proceedings}, Editor = {Prosenjit Gupta and Christos Zaroliagis}, Month = jan, Pages = {37--48}, Publisher = {Springer International Publishing Switzerland}, Series = {Lecture Notes in Computer Science}, Title = {Constructing an n-dimensional cell complex from a soup of (n-1)-dimensional faces}, Volume = {8321}, Year = {2014}} @article{Ledoux14, Author = {Hugo Ledoux and Ken {Arroyo Ohori} and Martijn Meijers}, Journal = {Computers \& Geosciences}, Month = may, Pages = {121--131}, Title = {A triangulation-based approach to automatically repair {GIS} polygons}, Volume = {66}, Year = {2014}} @article{Guting00, Author = {Ralf Hartmut G\"uting and Michael H. B\"ohlen and Martin Erwig and Christian S. Jensen and Nikos A. Lorentzos and Markus Schneider and Michalis Vazirgiannis}, Journal = {ACM Transactions on Database Systems}, Month = {March}, Number = {1}, Pages = {1--42}, Title = {A Foundation for Representing and Querying Moving Objects}, Volume = {25}, Year = {2000}} @incollection{deFloriani93, Author = {Leila {de Floriani} and Paola Marzano}, Booktitle = {Spatial Information Theory A Theoretical Basis for GIS}, Editor = {Andrew U. Frank and Irene Campari}, Publisher = {Springer Berlin Heidelberg}, Title = {Spatial queries and data models}, Year = {1993}} @article{Worboys92a, Author = {Michael F. Worboys}, Journal = {International Journal of Geographical Information Systems}, Number = {5}, Pages = {353--372}, Title = {A generic model for planar geographical objects}, Volume = {6}, Year = {1992}} @article{Clarke81, Author = {Bowman L. Clarke}, Journal = {Notre Dame Journal of Formal Logic}, Number = {3}, Title = {A Calculus of Individuals Based on `Connection'}, Volume = {22}, Year = {1981}} @article{Dehlinger14, Author = {Christophe Dehlinger and Jean-Fran\c{c}ois Dufourd}, Journal = {Computational Geometry: Theory \& Applications}, Title = {Formal specification and proofs for the topology and classification of combinatorial surfaces}, Year = {2014}} @article{Shaffer93, Author = {Clifford A. Shaffer and Ramana Juvvadi and Lenwood S. Heath}, Journal = {Image and Vision Computing}, Month = {September}, Number = {7}, Pages = {402--412}, Title = {Generalized comparison of quadtree and bintree storage requirements}, Volume = {11}, Year = {1993}} @incollection{Boots99, Author = {B. Boots}, Booktitle = {Geographical Information Systems}, Chapter = {36}, Editor = {Longley, Paul A. and Goodchild, Michael F. and Maguire, David J. and Rhind, David W.}, Publisher = {John Wiley \& Sons}, Title = {Spatial tessellations}, Year = {1999}} @article{Lee00, Author = {Y.C. Lee and Z.L. Li and Y.L. Li}, Journal = {ISPRS Journal of Photogrammetry \& Remote Sensing}, Pages = {139--149}, Title = {Taxonomy of space tessellation}, Volume = {55}, Year = {2000}} @article{Jackins83, Author = {Chris L. Jackins and Steven L. Tanimoto}, Journal = {IEEE Transactions on Pattern Analysis and Machine Intelligence}, Month = {September}, Number = {5}, Pages = {533--539}, Title = {Quad-Trees, Oct-Trees, and K-Trees: A Generalized Approach to Recursive Decomposition of Euclidean Space}, Volume = {5}, Year = {1983}} @article{Raper95, Author = {Jonathan Raper and David Livingstone}, Journal = {International Journal of Geographical Information Systems}, Number = {4}, Pages = {359--383}, Title = {Development of a geomorphological spatial model using object-oriented design}, Volume = {9}, Year = {1995}} @incollection{Varma00, Author = {Herman Varma}, Booktitle = {Marine and Coastal Geographical Information Systems}, Chapter = {6}, Editor = {Dawn Wright and Darius Bartlett}, Publisher = {Taylor \& Francis}, Title = {Applying Spatio-Temporal Concepts to Correlative Data Analysis}, Year = {2000}} @inproceedings{Puech85, Author = {Claude Puech and Hussein Yahia}, Booktitle = {Proceedings of the 1st ACM Symposium on Computational Geometry}, Pages = {272--280}, Title = {Quadtrees, octrees, hyperoctrees: a unified analytical approach to tree data structures used in graphics, geometric modeling and image processing}, Year = {1985}} @article{Yau83, Author = {Mann-May Yau and Sargur N. Srihari}, Journal = {Communications of the ACM}, Number = {7}, Pages = {504--515}, Title = {A Hierarchical Data Structure for Multidimensional Digital Images}, Volume = {26}, Year = {1983}} @incollection{Miller97, Author = {Eric J. Miller}, Booktitle = {Innovations in {GIS}}, Chapter = {13}, Editor = {Zarine Kemp}, Pages = {181--197}, Publisher = {Taylor \& Francis}, Title = {Towards a {4D} {GIS}: Four-dimensional interpolation utilizing {K}riging}, Year = {1997}} @article{Rossignac99, Author = {Jarek Rossignac and Andrzej Szymczak}, Journal = {Computational Geometry: Theory \& Applications}, Title = {{W}rap\&{Z}ip decompression of the connectivity of triangle meshes compressed with {E}dgebreaker}, Volume = {14}, Year = {1999}} @inproceedings{Rossignac01, Author = {Jarek Rossignac and Alla Safonova and Andrzej Szymczak}, Booktitle = {Proceedings of the Shape Modeling International Conference}, Title = {3D Compression Made Simple: Edgebreaker on a Corner-Table}, Year = {2001}} @incollection{deFloriani05a, Author = {Leila {de Floriani} and Leif Kobbelt and Enrico Puppo}, Booktitle = {Advances in Multiresolution for Geometric Modelling. Part II}, Editor = {Neil A. Dodgson and Michael S. Floater and Malcolm A. Sabin}, Pages = {49--74}, Publisher = {Springer Berlin Heidelberg}, Series = {Mathematics and Visualization}, Title = {A Survey on Data Structures for Level-of-Detail Models}, Year = {2005}} @incollection{deFloriani05, Author = {Leila {de Floriani} and Annie Hui}, Booktitle = {Eurographics Symposium on Geometry Processing}, Editor = {M. Desbrunn and H. Pottmann}, Publisher = {The Eurographics Association}, Title = {Data structures for simplicial complexes: an analysis and a comparison}, Year = {2005}} @incollection{Lopes97, Author = {H\'elio Lopes and Geovan Tavares}, Booktitle = {SMA '97, Proceedings of the Fourth Symposium on Solid Modeling and Applications}, Editor = {Christoph Hoffmann and Wim Bronsvoort and George Allen and Mike Pratt and David Rosen}, Pages = {10--18}, Publisher = {ACM}, Title = {Structural Operators for Modeling 3-Manifolds}, Year = {1997}} @incollection{Hansen93, Author = {Henning {\O}sterg{\aa}rd Hansen and Niels J{\o}rgen Christensen}, Booktitle = {Proceedings of the 2nd ACM Symposium on Solid Modelling and Applications}, Publisher = {ACM}, Title = {A Model for $n$-Dimensional Boundary Topology}, Year = {1993}} @phdthesis{Choi89, Author = {Y. Choi}, Month = {August}, School = {Carnegie Mellon University}, Title = {Vertex-based Boundary Representation of Non- manifold Geometric Models}, Year = {1989}} @book{Milnor63, Author = {J. Milnor}, Publisher = {Princeton University Press}, Title = {Morse Theory}, Year = {1963}} @article{Pesco04, Author = {Sin\'esio Pesco and Geovan Tavares and H\'elio Lopes}, Journal = {Computers \& Graphics}, Pages = {235--247}, Title = {A stratification approach for modeling two-dimensional cell complexes}, Volume = {28}, Year = {2004}} @incollection{McMains01, Author = {Sara McMains and Joseph M. Hellerstein and Carlo H. S\'equin}, Booktitle = {SMA '01 Proceedings of the sixth ACM symposium on Solid modeling and applications}, Pages = {171--182}, Publisher = {ACM}, Title = {Out-of-Core Build of a Topological Data Structure from Polygon Soup}, Year = {2001}} @incollection{Lee01, Author = {Sang Hun Lee and Kunwoo Lee}, Booktitle = {SMA '01 Proceedings of the 6th ACM Symposium on Solid modeling and Applications}, Editor = {David C. Anderson and Kunwoo Lee}, Pages = {159--170}, Publisher = {ACM}, Title = {Partial Entity Structure: A Compact Non-Manifold Boundary Representation Based on Partial Topological Entities}, Year = {2001}} @incollection{Joy03, Author = {Kenneth I. Joy and Justin Legakis and Ron MacCracken}, Booktitle = {Hierarchical and Geometrical Methods in Scientific Visualization}, Editor = {Gerard Farin and Bernd Hamann and Hans Hagen}, Publisher = {Springer}, Series = {Mathematics and Visualization}, Title = {Data Structures for Multiresolution Representation of Unstructured Meshes}, Year = {2003}} @article{Kallmann01, Author = {Marcelo Kallmann and Daniel Thalmann}, Journal = {Journal of Graphics Tools}, Number = {1}, Pages = {7--18}, Title = {Star-Vertices: A Compact Representation for Planar Meshes with Adjacency Information}, Volume = {6}, Year = {2001}} @article{Gursoz90, Author = {E.L. Gursoz and Y. Choi and F.B. Prinz}, Journal = {Geometric Modeling for Product Engineering}, Title = {Vertex-based representation of non-manifold boundaries}, Year = {1990}} @article{Naylor90, Author = {B. Naylor}, Journal = {Computer-Aided Design}, Number = {4}, Title = {Binary space partitioning trees as an alternative representation of polytopes}, Volume = {22}, Year = {1990}} @incollection{Paoluzzi04, Author = {A. Paoluzzi and V. Pascucci and G. Scorzelli}, Booktitle = {ACM Symposium on Solid Modeling and Applications}, Editor = {G. Elber and N. Patrikalakis and P. Brunet}, Publisher = {ACM}, Title = {Progressive Dimension-Independent {B}oolean Operations}, Year = {2004}} @incollection{Popovic97, Author = {Jovan Popovi\'c and Hughes Hoppe}, Booktitle = {SIGGRAPH '97 Proceedings of the 24th annual conference on Computer graphics and interactive techniques}, Editor = {G. Scott Owen and Turner Whitted and Barbara Mones-Hattal}, Pages = {217--224}, Publisher = {ACM/Addison-Wesley Publishing}, Title = {Progressive Simplicial Complexes}, Year = {1997}} @article{Pasko01, Author = {Alexander Pasko and Valery Adzhiev}, Journal = {Graphical Models}, Pages = {413--442}, Title = {Constructive Hypervolume Modeling}, Volume = {63}, Year = {2001}} @incollection{Samet85, Author = {Hanan Samet and Markku Tamminen}, Booktitle = {SIGGRAPH '85}, Editor = {Pat Cole and Robert Heilman and Brian A. Barsky}, Number = {3}, Pages = {121--130}, Publisher = {ACM}, Title = {Bintrees, {CSG} trees, and time}, Volume = {19}, Year = {1985}} @incollection{Comic12a, Author = {Lidija {\v C}omi\'c and Leila {de Floriani}}, Booktitle = {CTIC 2012}, Publisher = {Springer-Verlag Berlin Heidelberg}, Series = {Lecture Notes in Computer Science}, Title = {Topological Operators on Cell Complexes in Arbitrary Dimensions}, Volume = {7309}, Year = {2012}} @article{Forman98, Author = {Robin Forman}, Journal = {Advances in Mathematics}, Pages = {90--145}, Title = {Morse Theory for Cell Complexes}, Volume = {134}, Year = {1998}} @incollection{Damiand12, Author = {Guillaume Damiand and Rocio Gonzalez-Diaz and Samuel Peltier}, Booktitle = {CTIC 2012}, Publisher = {Springer-Verlag Berlin Heidelberg}, Series = {Lecture Notes in Computer Science}, Title = {Removal Operations in nD Generalized Maps for Efficient Homology Computation}, Volume = {7309}, Year = {2012}} @incollection{Baba-ali08, Author = {Mehdi Baba-ali and Guillaume Damiand and Xavier Skapin and David Marcheix}, Booktitle = {DGCI 2008}, Pages = {141--152}, Publisher = {Springer-Verlag Berlin Heidelberg}, Series = {Lecture Notes in Computer Science}, Title = {Insertion and Expansion Operations for n-Dimensional Generalized Maps}, Volume = {4992}, Year = {2008}} @incollection{Brun01, Author = {Luc Brun and Walter Kropatsch}, Booktitle = {Digital and Image Geometry}, Editor = {Gilles Bertrand and Atsushi Imiya and Reinhard Klette}, Pages = {108--128}, Publisher = {Springer-Verlag Berlin Heidelberg}, Series = {Lecture Notes in Computer Science}, Title = {Introduction to Combinatorial Pyramids}, Volume = {2243}, Year = {2001}} @article{Comic14, Author = {Lidija {\v C}omi\'c and Leila {de Floriani} and Federico Iuricich and Ulderico Fugacci}, Journal = {Computer Vision and Image Understanding}, Pages = {2--12}, Title = {Topological modifications and hierarchical representation of cell complexes in arbitrary dimensions}, Volume = {121}, Year = {2014}} @inproceedings{Maria14, Author = {Mazime Maria and S\'ebastien Horna and Lilian Aveneau}, Booktitle = {Proceedings of the 9th International Joint Conference on Computer Graphics Theory and Applications}, Pages = {225--235}, Title = {Topological Space Partition for Fast Ray Tracing in Architectural Models}, Year = {2014}} @inproceedings{Bezin14, Author = {R. Bezin and B. Crespin and X. Skapin and P. Meseure and O. Terraz}, Booktitle = {EUROGRAPHICS 2014}, Editor = {J.-J. Bourdin and J. Jorge and E. Anderson}, Title = {Programming Topological Operations for Visual Illustrations in an Introductory Geomorphology Course}, Year = {2014}} @phdthesis{Riemann68, Author = {B. Riemann}, School = {Abhandlungen der K\"oniglichen Gesellschaft der Wissenschaften zu G\"ottingen}, Title = {Ueber die Hypothesen, welche der Geometrie zu Grunde liegen}, Year = {1868}} @book{Smith54, Author = {David Eugene Smith and Marcia L. Latham}, Publisher = {Dover Publications}, Title = {The geometry of {R}en\'e {D}escartes}, Year = {1954}} @book{Descartes37, Address = {Leyde}, Author = {Ren\'e Descartes}, Publisher = {Jan Maire}, Title = {Discours de la m\'ethode}, Year = {1637}} @book{Stillwell10, Author = {John Stillwell}, Month = {September}, Publisher = {American Mathematical Society}, Series = {History of Mathematics}, Title = {Papers on Topology: Analysis Situs and Its Five Supplements}, Year = {2010}} @article{Betti71, Author = {Enrico Betti}, Journal = {Annali di Matematica pura ed applicata}, Pages = {140--158}, Title = {Sopra gli spazi di un numero qualunque di dimensioni}, Volume = {4}, Year = {1871}} @incollection{Mobius85, Address = {Leipzig}, Author = {M\"obius, August F}, Booktitle = {Werke 2}, Pages = {433--471}, Publisher = {Hirzel}, Title = {Theorie der elementaren Verwandtschaft}, Year = {1885--1887}} @article{Euler58, Author = {Leonhard Euler}, Journal = {Novi Commentarii academiae scientiarum Petropolitanae}, Pages = {109--140}, Title = {Elementa doctrinae solidorum}, Volume = {4}, Year = {1758}} @article{Penninga08a, Author = {F. Penninga and P. J. M. {van Oosterom}}, Journal = {International Journal of Geographical Information Science}, Month = {July}, Number = {7}, Pages = {751--779}, Title = {A simplicial complex-based {DBMS} approach to {3D} topographic data modelling}, Volume = {22}, Year = {2008}} @article{Poincare04, Author = {M.H. Poincar\'e}, Journal = {Rendiconti del Circolo Matematico di Palermo}, Pages = {45--110}, Title = {Cinqui\`eme compl'ement \`a l'analysis situs}, Volume = {18}, Year = {1904}} @article{Poincare02a, Author = {M.H. Poincar\'e}, Journal = {Journal de math\'ematiques pures et appliqu\'ees}, Number = {8}, Pages = {169--214}, Title = {Sur les cycles des surfaces alg\'ebriques; quatri\`eme compl\'ement \`a l'Analysis Sit\^us}, Volume = {5}, Year = {1902}} @article{Poincare02, Author = {M.H. Poincar\'e}, Journal = {Bulletin de la Soci\'et\'e Math\'ematique de France}, Pages = {49--70}, Title = {Sur certaines surfaces alg\'ebriques. Troisi\`eme compl\'ement \`a l'``Analysis sit\^us''}, Volume = {30}, Year = {1902}} @article{Poincare00, Author = {H. Poincar\'e}, Journal = {Proceedings of the London Mathematical Society}, Pages = {277--308}, Title = {Second compl\'ement \`a l'Analysis Situs}, Volume = {32}, Year = {1900}} @article{Poincare99, Author = {H. Poincar\'e}, Journal = {Rendiconti del Circolo Matematico di Palermo}, Pages = {285--343}, Title = {Compl\'ement \`a l'Analysis Situs}, Volume = {13}, Year = {1899}} @article{Poincare95, Author = {M.H. Poincar\'e}, Journal = {Journal de l'\'Ecole polytechnique}, Number = {1}, Pages = {1--123}, Title = {Analysis Situs}, Volume = {2}, Year = {1895}} @article{Minkowski08, Author = {Hermann Minkowski}, Journal = {Nachrichten von der Gesellschaft der Wissenschaften zu G\"ottingen, Mathematisch-Physikalische Klasse}, Pages = {53--111}, Title = {Die {G}rundgleichungen f\"ur die elektromagnetischen {V}org\"ange in bewegten {K}\"orpern}, Year = {1908}} @inproceedings{Pigot92, Author = {Pigot, Simon and Hazelton, N. W. J.}, Booktitle = {Proceedings of the 5th International Symposium on Spatial Data Handling}, Pages = {580--591}, Title = {The fundamentals of a topological model for a four-dimensional {GIS}}, Year = {1992}} @inproceedings{Worboys92, Author = {Worboys, M.F.}, Booktitle = {Proceedings of the 5th International Symposium on Spatial Data Handling}, Pages = {602--611}, Title = {A Model for Spatio-Temporal Information}, Year = {1992}} @inproceedings{Armstrong88, Author = {Marc P. Armstrong}, Booktitle = {GIS/LIS '88 : proceedings : accessing the world : third annual International Conference, Exhibits, and Workshops}, Pages = {880--889}, Publisher = {American Society for Photogrammetry and Remote Sensing}, Title = {Temporality in Spatial Databases}, Year = {1988}} @article{Vuillemin78, Author = {Jean Vuillemin}, Journal = {Communications of the ACM}, Month = {April}, Number = {4}, Pages = {309--315}, Title = {A Data Structure for Manipulating Priority Queues}, Volume = {21}, Year = {1978}} @phdthesis{Bucksch11, Author = {Alexander Klaus Bucksch}, Month = {April}, School = {Delft University of Technology}, Title = {Revealing the skeleton from imperfect point clouds}, Year = {2011}} @incollection{Couclelis99, Author = {H. Couclelis}, Booktitle = {Geographical Information Systems}, Chapter = {2}, Editor = {Longley, Paul A. and Goodchild, Michael F. and Maguire, David J. and Rhind, David W.}, Pages = {29--38}, Publisher = {John Wiley \& Sons}, Title = {Space, time, geography}, Year = {1999}} @article{Qi13, Author = {Meng Qi and Thanh-Tung Cao and Tiow-Seng Tan}, Journal = {IEEE Transactions on Visualization and Computer Graphics}, Month = {May}, Number = {5}, Pages = {736--748}, Title = {Computing {2D} Constrained {D}elaunay {T}riangulation Using the {GPU}}, Volume = {19}, Year = {2013}} @incollection{Becker14, Author = {Susanne Becker and Volker Walter and Dieter Fritsch}, Booktitle = {Information Fusion and Geographic Information 91 Systems (IF\&GIS 2013)}, Editor = {Vasily Popovich and Christophe Claramunt and Manfred Schrenk and Kyrill Korolenko}, Pages = {91--106}, Publisher = {Springer Berlin Heidelberg}, Series = {Lecture Notes in Geoinformation and Cartography}, Title = {Modeling Concepts for Consistency Analysis of Multiple Representations and Heterogeneous {3D} Geodata}, Year = {2014}} @article{Huisman13, Author = {Otto Huisman and Irvin Feliciano Santiago and Menno-Jan Kraak and Bas Retsios}, Journal = {Cartography and Geographic Information Science}, Number = {3}, Pages = {225--236}, Title = {Developing a Geovisual Analytics Environment for Investigating Archaeological Events: Extending the Space-Time Cube}, Volume = {36}, Year = {2013}} @inproceedings{Jin05, Author = {Peiquan Jin and Lihua Yue and Yuchang Gong}, Booktitle = {Proceedings of the 2005 International Symposium on Spatial-temporal Modeling, Spatial Reasoning, Analysis, Data Mining and Data Fusion}, Title = {Research on a Unified Spatiotemporal Data Model}, Year = {2005}} @incollection{deRoo13, Author = {B. {de Roo} and N. {van de Weghe} and J. Bourgeois and Ph. de Maeyer}, Booktitle = {Proceedings of the 8th 3DGeoInfo Conference \& WG II/2 Workshop, 27 -- 29 November 2013, Istanbul, Turkey}, Month = {November}, Publisher = {ISPRS}, Series = {ISPRS Annals of the Photogrammetry, Remote Sensing and Spatial Information Sciences}, Title = {The temporal dimension in a {4D} archaeological data model: applicability of the geoinformation standard}, Volume = {II-2/W1}, Year = {2013}} @article{Raper01, Author = {Jonathan Raper and David Livingstone}, Journal = {Transactions of the Institute of British Geographers}, Pages = {237--242}, Title = {Let's get real: spatio-temporal identity and geographic entities}, Volume = {26}, Year = {2001}} @article{vanOosterom14, Author = {Peter van Oosterom and Meijers, Martijn}, Journal = {International Journal of Geographical Information Science}, Pages = {455--478}, Title = {Vario-scale data structures supporting smooth zoom and progressive transfer of {2D} and {3D} data}, Volume = {28}, Year = {2014}} @inproceedings{Rubner98, Author = {Yossi Rubner and Carlo Tomasi and Leonidas J. Guibas}, Booktitle = {Proceedings of the 6th International Conference on Computer Vision}, Pages = {59--66}, Title = {A Metric for Distributions with Applications to Image Databases}, Year = {1998}} @article{Eppstein99, Author = {David Eppstein}, Journal = {Journal of Graph Algorithms and Applications}, Number = {3}, Pages = {1--27}, Title = {Subgraph Isomorphism in Planar Graphs and Related Problems}, Volume = {3}, Year = {1999}} @inproceedings{Tossebro12, Author = {Erlend T{\o}ssebro}, Booktitle = {Proceedings of the 8th International Conference on Signal Image Technology and Internet Based Systems}, Pages = {496--502}, Title = {Interpolating Probability Values or Fuzzy Set Values for Uncertain Spatiotemporal Objects}, Year = {2012}} @incollection{Boissonnat12, Author = {Jean-Daniel Boissonnat and Cl\'ement Maria}, Booktitle = {Algorithms --- ESA 2012}, Pages = {731--742}, Publisher = {Springer Berlin Heidelberg}, Series = {Lecture Notes in Computer Science}, Title = {The Simplex Tree: An Efficient Data Structure for General Simplicial Complexes}, Volume = {7501}, Year = {2012}} @article{Boissonnat84, Author = {Jean-Daniel Boissonnat}, Journal = {ACM Transactions on Graphics}, Month = {October}, Number = {4}, Pages = {266--286}, Title = {Geometric Structures for Three-Dimensional Shape Representation}, Volume = {3}, Year = {1984}} @article{Brisson93, Author = {Erik Brisson}, Journal = {Discrete \& Computational Geometry}, Pages = {387--426}, Title = {Representing geometric structures in d dimensions: topology and order}, Volume = {9}, Year = {1993}} @inproceedings{Mobasheri13, Author = {Amin Mobasheri and Mohamed Bakillah and Alexander Zipf and Steve H.L. Liang}, Booktitle = {Proceedings of the 3rd International Conference on Innovative Computing Technology}, Pages = {7--11}, Title = {QualEvS4Geo: A peer-to-peer system architecture for semi-automated quality evaluation of geo-data in SDI}, Year = {2013}} @article{Goshtasby85, Author = {Ardeshir Goshtasby and George C. Stockman}, Journal = {IEEE Transactions on Systems, Man and Cybernetics}, Month = {September/October}, Number = {5}, Pages = {631--638}, Title = {Point Pattern Matching Using Convex Hull Edges}, Volume = {SCM-15}, Year = {1985}} @inproceedings{Yirci13, Author = {Murat Yirci and Mathieu Br\'edif and Julien Perret and Nicolas Paparoditis}, Booktitle = {IWCTS'13}, Title = {2D Arrangement-based Hierarchical Spatial Partitioning: An Application to Pedestrian Network Generation}, Year = {2013}} @inproceedings{Armiti13, Author = {Ayser Armiti and Michael Gertz}, Booktitle = {SIGSPATIAL'13}, Pages = {234--243}, Title = {Efficient Geometric Graph Matching Using Vertex Embedding}, Year = {2013}} @inproceedings{Magillo13, Author = {Paola Magillo and Leila {de Floriani} and Federico Iuricich}, Booktitle = {SIGSPATIAL'13}, Pages = {254--263}, Title = {Morphologically-Aware Elimination of Flat Edges from a TIN}, Year = {2013}} @inproceedings{Gudmundsson13, Author = {Joachim Gudmundsson and Marc {van Kreveld} and Frank Staals}, Booktitle = {SIGSPATIAL'13}, Pages = {144--153}, Title = {Algorithms for Hotspot Computation on Trajectory Data}, Year = {2013}} @inproceedings{Arge13, Author = {Lars Arge and Mark {de Berg} and Constantinos Tsirogiannis}, Booktitle = {SIGSPATIAL'13}, Pages = {264--273}, Title = {Algorithms for Computing Prominence on Grid Terrains}, Year = {2013}} @inproceedings{Park13, Author = {Eunhui Park and David M. Mount}, Booktitle = {SIGSPATIAL'13}, Pages = {364--373}, Title = {Output-Sensitive Well-Separated Pair Decompositions for Dynamic Point Sets}, Year = {2013}} @inproceedings{Mata13, Author = {Felix Mata and Christophe Claramunt}, Booktitle = {SIGSPATIAL'13}, Pages = {534--537}, Title = {Augmented Navigation in Outdoor Environments}, Year = {2013}} @inproceedings{Mahdiraji13a, Author = {Alireza Rezaei Mahdiraji and Peter Baumann and Guntram Berti}, Booktitle = {CIKM'13}, Month = {October}, Pages = {1619--1624}, Publisher = {ACM}, Title = {ImG-Complex: Graph Data Model for Topology of Unstructured Meshes}, Year = {2013}} @incollection{Zhao13, Author = {Junqiao Zhao and Hugo Ledoux and Jantien Stoter}, Booktitle = {ISPRS 8th 3DGeoInfo Conference \& WG II/2 Workshop}, Month = {November}, Pages = {309--317}, Publisher = {ISPRS Archives}, Title = {Automatic Repair of {CityGML} {LoD2} Buildings using Shrink-wrapping}, Volume = {II-2/W1}, Year = {2013}} @book{Huisman09, Address = {Enschede, The Netherlands}, Edition = {4th}, Editor = {Otto Huisman and Rolf A. {de By}}, Publisher = {The International Institute for Geo-Information Science and Earth Observation}, Series = {ITC Educational Textbook Series}, Title = {Principles of Geographic Information Systems}, Year = {2009}} @incollection{Karimipour13a, Author = {Farid Karimipour and Mehran Ghandehari}, Booktitle = {Transactions on Computational Science XX}, Editor = {Marina L. Gavrilova and C. J. Kenneth Tan and Bahman Kalantari}, Pages = {138--157}, Publisher = {Springer Berlin Heidelberg}, Series = {Lecture Notes in Computer Science}, Title = {Voronoi-Based Medial Axis Approximation from Samples: Issues and Solutions}, Volume = {8110}, Year = {2013}} @article{Zapponi03, Author = {Leonardo Zapponi}, Journal = {Notices of the American Mathematical Society}, Month = {August}, Number = {7}, Pages = {788-789}, Title = {What is a Dessin d'Enfant?}, Volume = {50}, Year = {2003}} @article{Kraemer09, Author = {Pierre Kraemer and David Cazier and Dominique Bechmann}, Journal = {The Visual Computer}, Month = {January}, Number = {2}, Pages = {149--163}, Title = {Extension of half-edges for the representation of multiresolution subdivision surfaces}, Volume = {25}, Year = {2009}} @article{Coxeter34, Author = {H. S. M. Coxeter}, Journal = {Annals of Mathematics}, Month = {July}, Number = {3}, Pages = {588--621}, Title = {Discrete Groups Generated by Reflections}, Volume = {35}, Year = {1934}} @article{Bradley13, Author = {Patrick Erik Bradley and Norbert Paul}, Journal = {Geoinformatica}, Title = {Comparing {G}-maps with other topological data structures}, Year = {2013}} @article{Voronoi08a, Author = {Georges Voronoi}, Journal = {Journal f\"ur die Reine und Angewandte Mathematik}, Pages = {198--287}, Title = {Nouvelles applications des param\`etres continus \`a la th\'eorie des formes quadratiques. Deuxi\'eme M\'emoire. Recherches sur les parall\'ello\`edres primitifs}, Volume = {134}, Year = {1908}} @article{Hazelton92, Author = {Nicholas W.J. Hazelton and Lisa Marie Bennett and Joanna Masel}, Journal = {Computers, Environment and Urban Systems}, Month = {May--June}, Number = {3}, Pages = {227--237}, Title = {Topological structures for 4-dimensional geographic information systems}, Volume = {16}, Year = {1992}} @article{Chen01, Author = {Jun Chen and Chengming Li and Zhilin Li and Christopher Gold}, Journal = {International Journal of Geographical Information Science}, Number = {3}, Pages = {201--220}, Title = {A Voronoi-based 9-intersection model for spatial relations}, Volume = {15}, Year = {2001}} @article{Pundt00, Author = {Hardy Pundt and Klaus Brinkk\"otter-Runde}, Journal = {Computers \& Geosciences}, Pages = {51--56}, Title = {Visualization of spatial data for field based GIS}, Volume = {26}, Year = {2000}} @inproceedings{Stoter10, Author = {Jantien Stoter and Marcel Reuvers and George Vosselman and Joris Goos and Leon van Berlo and Sisi Zlatanova and Edward Verbree and Rick Klooster}, Booktitle = {Proceedings of the 5th International 3D GeoInfo Conference}, Title = {Towards a 3D Geo-information standard in the netherlands}, Year = {2010}} @inproceedings{Meijers13, Author = {Martijn Meijers and Hugo Ledoux}, Booktitle = {UDMS Annual 2013}, Editor = {C. Ellul and Sisi Zlatanova and M. Rumor and R. Laurini}, Pages = {107--116}, Title = {EdgeCrack: a parallel Divide-and-Conquer algorithm for building a topological data structure}, Year = {2013}} @article{Karimipour13, Author = {Farid Karimipour and Mehran Ghandehari and Hugo Ledoux}, Journal = {Computers \& Geosciences}, Month = {September}, Pages = {132--147}, Title = {Watershed delineation from the medial axis of river networks}, Volume = {59}, Year = {2013}} @inproceedings{Matijevic08, Author = {Hrvoje Matijevi\'c and Zvonko Biljecki and Stipica Pavi\v{c}i\'c, and Miodrag Roi\'c}, Booktitle = {Proceedings of the FIG Working Week 2008}, Title = {Transaction Processing on Planar Partition for Cadastral Application}, Year = {2008}} @inproceedings{Anselin89, Author = {Luc Anselin}, Booktitle = {Proceedings of the Spring 1989 Symposium on Spatial Statistics, Past, Present and Future}, Title = {What is special about spatial data? Alternative perspectives on spatial data analysis}, Year = {1989}} @article{Grunbaum03, Author = {Branko Gr\"unbaum}, Journal = {Discrete and Computational Geometry: The Goodman-Pollack Festschrift}, Pages = {461--488}, Title = {Are your polyhedra the same as my polyhedra?}, Year = {2003}} @incollection{Zlatanova06, Author = {Sisi Zlatanova and Jantien Stoter}, Booktitle = {Frontiers of Geographic Information Technology}, Chapter = {8}, Editor = {Sanjay Rana and Jayant Sharma}, Publisher = {Springer}, Title = {The role of DBMS in the new generation GIS architecture}, Year = {2006}} @techreport{Meijers08, Author = {Martijn Meijers}, Institution = {Delft University of Technology}, Title = {Variable-scale Geo-information}, Type = {PhD Research Proposal}, Year = {2008}} @inproceedings{Stanton05, Author = {Heather I. Stanton and Stephanie O'Meara and James R. Chappell and Anne R. Poole and Gregory Mack and Georgia Hybels}, Booktitle = {Proceedings of Digital Mapping Techniques '05}, Title = {Ensuring Data Quality using Topology and Attribute Validation in the Geodatabase}, Year = {2005}} @inproceedings{Wiemann10, Author = {Stefan Wiemann and Lard Bernard}, Booktitle = {Proceedings of the 13th AGILE International Conference on Geographic Information Science}, Title = {Conflation Services within Spatial Data Infrastructures}, Year = {2010}} @article{Austern00, Author = {Matt Austern}, Journal = {C++ Report}, Number = {4}, Title = {Why you shouldn't use set (and what you should use instead)}, Volume = {12}, Year = {2000}} @article{Tomlin94, Author = {C. Dana Tomlin}, Journal = {Landscape and Urban Planning}, Pages = {3--12}, Title = {Map algebra: one perspective}, Volume = {30}, Year = {1994}} @article{Bajaj90a, Author = {Chanderjit Bajaj and Tamal Dey}, Journal = {Information Processing Letters}, Pages = {23--32}, Title = {Polygon Nesting and Robustness}, Volume = {35}, Year = {1990}} @article{Laurini94, Author = {Robert Laurini and Fran\c{c}oise Milleret-Raffort}, Journal = {Computers \& Graphics}, Number = {6}, Pages = {803--813}, Title = {Topological Reorganization of Inconsistent Geographical Databases: A Step Towards Their Certification}, Volume = {18}, Year = {1994}} @article{Beard88, Author = {M. Kate Beard and Nicholas R. Chrisman}, Journal = {The American Cartographer}, Month = {April}, Number = {2}, Pages = {163--172}, Title = {Zipper: A Localized Approach to Edgematching}, Volume = {15}, Year = {1988}} @article{Rivero00, Author = {M. Rivero and F.R. Feito}, Journal = {Computers \& Graphics}, Pages = {881--896}, Title = {Boolean operations on general planar polygons}, Volume = {24}, Year = {2000}} @incollection{Schirra97, Author = {Stefan Schirra}, Booktitle = {Algorithmic Foundations of Geographic Information Systems}, Editor = {Marc van Kreveld and J\"urg Nievergelt and Thomas Roos and Peter Widmayer}, Pages = {255--287}, Publisher = {Springer Berlin Heidelberg}, Series = {Lecture Notes in Computer Science}, Title = {Precision and Robustness in Geometric Computations}, Volume = {1340}, Year = {1997}} @inproceedings{Shewchuk96a, Author = {Jonathan Richard Shewchuk}, Booktitle = {Proceedings of the 12th Annual Symposium on Computational Geometry}, Pages = {141--150}, Title = {Robust Adaptive Floating-Point Geometric Predicates}, Year = {1996}} @inproceedings{Plumer96, Author = {Lutz Pl\"umer and Gerhard Gr\"oger}, Booktitle = {Proceedings of the 4th ACM Workshop on Advances on Advances in Geographic Information Systems}, Pages = {76--83}, Title = {Nested Maps - a Formal, Provably Correct Object Model for Spatial Aggregates}, Year = {1996}} @inproceedings{Chazelle79, Author = {Bernard Chazelle and David Dobkin}, Booktitle = {Proceedings of the 11th Annual ACM Symposium on Theory of Computing}, Pages = {38--48}, Title = {Decomposing a Polygon into its Convex Parts}, Year = {1979}} @article{Gold96, Author = {C. M. Gold and J. Nantel and W. Yang}, Journal = {International Journal of Geographical Information Systems}, Number = {3}, Pages = {291--310}, Title = {Outside-in: an alternative approach to forest map digitizing}, Volume = {10}, Year = {1996}} @book{Neteler05, Author = {Markus Neteler and Helena Mitasova}, Edition = {Second}, Publisher = {Kluwer Academic Publishers}, Title = {Open Source GIS: A GRASS GIS Approach}, Year = {2005}} @article{Margalit89, Author = {Avraham Margalit and Gary D. Knott}, Journal = {Computers \& Graphics}, Number = {2}, Pages = {167--183}, Title = {An algorithm for computing the union, intersection or difference of two polygons}, Volume = {13}, Year = {1989}} @inproceedings{Ledoux10, Author = {Hugo Ledoux and Martijn Meijers}, Booktitle = {Proceedings of the 14th International Symposium on Spatial Data Handling}, Month = {May}, Title = {Validation of planar partitions using constrained triangulations}, Year = {2010}} @article{vanKreveld98, Author = {Marc van Kreveld}, Journal = {Computational Geometry}, Pages = {197--210}, Title = {On fat partitioning, fat covering and the union size of polygons}, Volume = {9}, Year = {1998}} @techreport{Davis03, Author = {Martin Davis}, Institution = {Vivid Solutions}, Title = {Java Conflation Suite}, Year = {2003}} @article{Goodchild97, Author = {Michael F. Goodchild and James Proctor}, Journal = {Geographic \& Environmental Modelling}, Number = {1}, Pages = {5--23}, Title = {Scale in a Digital Geographic World}, Volume = {1}, Year = {1997}} @inproceedings{vanOosterom02, Author = {Peter {van Oosterom} and Jantien Stoter and Wilko Quak and Sisi Zlatanova}, Booktitle = {Proceedings of the Symposium on Geospatial Theory, Processing and Applications}, Title = {The Balance Between Geometry and Topology}, Year = {2002}} @article{Scheidt87, Author = {J. K. Scheidt and C. W. Schelin}, Journal = {Computing}, Pages = {315--324}, Title = {Distributions of Floating Point Numbers}, Volume = {38}, Year = {1987}} @article{Devillers02a, Author = {Olivier Devillers}, Journal = {International Journal of Foundations of Computer Science}, Number = {2}, Pages = {181--199}, Title = {{W}alking in a triangulation}, Volume = {13}, Year = {2002}} @article{Devillers02, Author = {Olivier Devillers}, Journal = {International Journal of Foundations of Computer Science}, Number = {2}, Pages = {163--180}, Title = {{T}he {D}elaunay hierarchy}, Volume = {13}, Year = {2002}} @article{Kettner08, Author = {Lutz Kettner and Kurt Mehlhorn and Sylvain Pion and Stefan Schirra and Chee Yap}, Journal = {Computational Geometry}, Month = {May}, Number = {1}, Pages = {61--78}, Title = {Classroom Examples of Robustness Problems in Geometric Computations}, Volume = {40}, Year = {2008}} @inbook{Egenhofer91a, Author = {M. J. Egenhofer and J. R. Herring}, Chapter = {16}, Editor = {D. Maguire and M. Goodchild and D. Rhind}, Publisher = {Longman}, Title = {High-level Spatial Data Structures for GIS}, Year = {1991}} @article{Barker95, Author = {Sean Michael Barker}, Journal = {Computer-Aided Design}, Number = {4}, Pages = {311--318}, Title = {Towards a topology for computational geometry}, Volume = {27}, Year = {1995}} @article{Plumer97, Author = {Lutz Pl\"umer and Gerhard Gr\"oger}, Journal = {GeoInformatica}, Number = {4}, Pages = {345--367}, Title = {Achieving Integrity in Geographic Information Systems---Maps and Nested Maps}, Volume = {1}, Year = {1997}} @article{vanRoessel91, Author = {Jan W. {van Roessel}}, Journal = {Cartography and Geographic Information Systems}, Number = {1}, Pages = {49--67}, Title = {A New Approach to Plane-Sweep Overlay: Topological Structuring and Line-Segment Classification}, Volume = {18}, Year = {1991}} @article{Chrisman90, Author = {Nicholas R. Chrisman}, Journal = {International Journal of Geographical Information Science}, Number = {2}, Pages = {157--167}, Title = {Deficiencies of sheets and tiles: building sheetless databases}, Volume = {4}, Year = {1990}} @inproceedings{Lloyd77, Author = {Errol Lynn Lloyd}, Booktitle = {Proceedings of the 18th Annual Symposium on Foundations of Computer Science}, Pages = {228--240}, Title = {On Triangulations of a Set of Points in the Plane}, Year = {1977}} @inproceedings{Buchin13, Author = {Kevin Buchin and Olivier Devillers and Wolfgang Mulzer and Okke Schrijvers and Jonathan Shewchuk}, Booktitle = {Proceedings of the 21st European Symposium on Algorithms}, Title = {Vertex Deletion for 3D Delaunay Triangulations}, Year = {2013}} @incollection{Worboys13, Author = {Michael Worboys}, Booktitle = {Spatial Information Theory}, Editor = {Thora Tenbrink and John Stell and Antony Galton and Zena Wood}, Pages = {74--90}, Publisher = {Springer International Publishing}, Series = {Lecture Notes in Computer Science}, Title = {Using Maptrees to Characterize Topological Change}, Volume = {8116}, Year = {2013}} @article{Ledoux13, Author = {Hugo Ledoux}, Journal = {Computer-Aided Civil and Infrastructure Engineering}, Month = {August}, Number = {9}, Pages = {693--706}, Title = {On the Validation of Solids Represented with the International Standards for Geographic Information}, Volume = {28}, Year = {2013}} @inproceedings{Mahdiraji13, Author = {Alireza Rezaei Mahdiraji}, Booktitle = {Proceedings of the 39th International Conference on Very Large Data Bases}, Title = {Database Support for Unstructured Meshes}, Year = {2013}} @article{Duncan13, Author = {Edward Eric Duncan and Alias Abdul Rahman}, Journal = {International Journal of Mining, Reclamation and Environment}, Title = {3D GIS for mine development -- integrated concepts}, Year = {2013}} @article{DiCarlo13, Author = {Antonio DiCarlo and Alberto Paoluzzi and Vadim Shapiro}, Journal = {Computer-Aided Design}, Title = {Linear algebraic representation for topological structures}, Year = {2013}} @inproceedings{Kraemer14, Author = {Pierre Kraemer and Lionel Untereiner and Thomas Jund and Sylvain Thery and David Cazier}, Booktitle = {Proceedings of the 22nd International Meshing Roundtable}, Editor = {J. Sarrate and M. Staten}, Pages = {485--503}, Publisher = {Springer International Publishing Switzerland}, Title = {{CGoGN}: n-dimensional Meshes with Combinatorial Maps}, Year = {2014}} @techreport{Saalfeld87, Author = {Alan Saalfeld}, Institution = {Bureau of the Census}, Month = {October}, Number = {Census/SRD/RR-87/21}, Title = {It doesn't make me nearly as cross}, Type = {Statistical Research Division Report Series}, Year = {1987}} @article{Li13, Author = {Bo Li and Xin Zhao and Hong Qin}, Journal = {Computer Graphics Forum}, Title = {Four-Dimensional Geometry Lens: A Novel Volumetric Magnification Approach}, Year = {2013}} @inproceedings{Devillers12, Author = {Olivier Devillers}, Booktitle = {Proceedings of the 28th European Workshop on Computational Geometry}, Title = {Delaunay triangulations, theory vs practice}, Year = {2012}} @article{Le13, Author = {Hai Ha Le}, Journal = {ISPRS International Journal of Geo-Information}, Month = {August}, Pages = {837--853}, Title = {Spatio-Temporal Data Construction}, Volume = {2}, Year = {2013}} @inproceedings{Singh13, Author = {Surendra Pal Singh and Kamal Jain and V. Ravibabu Mandla}, Booktitle = {Proceedings of the 8th International 3D GeoInfo Conference}, Month = {November}, Series = {International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences}, Title = {Virtual 3D City Modeling: Techniques and Applications}, Volume = {XL-2/W2}, Year = {2013}} @article{Thomas02, Author = {Federico Thomas and Carmen Torras}, Journal = {The Visual Computer}, Month = {November}, Number = {7}, Pages = {405--414}, Title = {A projectively invariant intersection test for polyhedra}, Volume = {18}, Year = {2002}} @techreport{Eastman79, Author = {Charles M. Eastman and Kevin J. Weiler}, Institution = {Computer Science Department, School of Computer Science, Carnegie Mellon University}, Month = {January}, Number = {1587}, Title = {Geometric modeling using the Euler operators}, Type = {Research Showcase}, Year = {1979}} @article{Brisaboa13, Author = {Nieves R. Brisaboa and Miguel R. Luaces and M. Andrea Rodr\'iguez and Diego Seco}, Journal = {International Journal of Geographical Information Science}, Month = {July}, Title = {An inconsistency measure of spatial data sets with respect to topological constraints}, Year = {2013}} @book{Jordan87, Author = {M. C. Jordan}, Publisher = {Gauthier-Villars}, Title = {Cours d'Analyse}, Year = {1887}} @article{Packer08, Author = {Eli Packer}, Journal = {Computational Geometry}, Month = {August}, Number = {3}, Pages = {231--251}, Title = {Iterated Snap Rounding with Rounded Drift}, Volume = {40}, Year = {2008}} @article{Halperin02, Author = {Dan Halperin and Eli Packer}, Journal = {Computational Geometry: Theory \& Applications}, Number = {2}, Pages = {209--225}, Title = {Iterated Snap Rounding}, Volume = {23}, Year = {2002}} @incollection{Osaragi13, Author = {Toshihiro Osaragi and Sayaka Tsuda}, Booktitle = {Geographic Information Science at the Heart of Europe}, Editor = {Danny Vandenbroucke and B\'en\'edicte Bucher and Joep Crompvoets}, Pages = {307--322}, Publisher = {Springer}, Series = {Lecture Notes in Geoinformation and Cartography}, Title = {Facility Use-Choice Model with Travel Costs Incorporating Means of Transportation and Travel Direction}, Year = {2013}} @incollection{Baglatzi13, Author = {Alkyoni Baglatzi and Werner Kuhn}, Booktitle = {Geographic Information Science at the Heart of Europe}, Editor = {Danny Vandenbroucke and B\'en\'edicte Bucher and Joep Crompvoets}, Pages = {173--188}, Publisher = {Springer}, Series = {Lecture Notes in Geoinformation and Cartography}, Title = {On the Formulation of Conceptual Spaces for Land Cover Classification Systems}, Year = {2013}} @mastersthesis{Wouda11, Author = {Berend Wouda}, Month = {August}, School = {Delft University of Technology}, Title = {Visualization on a Budget for Massive LiDAR Point Clouds}, Year = {2011}} @inproceedings{Hoppe96, Author = {Hughes Hoppe}, Booktitle = {Proceedings of SIGGRAPH 1996}, Pages = {99--108}, Title = {Progressive Meshes}, Year = {1996}} @article{Wolfson97, Author = {Haim J. Wolfson and Isidore Rigoutsos}, Journal = {IEEE Computational Science and Engineering}, Month = {October--December}, Number = {4}, Pages = {10--21}, Title = {Geometric Hashing: An Overview}, Volume = {4}, Year = {1997}} @inproceedings{Huang12, Author = {Jing Huang and Suya You}, Booktitle = {Proceedings of the 2012 IEEE Computer Society Conference on Computer Vision and Pattern Recognition Workshops}, Month = {June}, Pages = {41--48}, Publisher = {IEEE}, Title = {Point Cloud Matching based on 3D Self-Similarity}, Year = {2012}} @inproceedings{Brenner05, Author = {J. Brenner and A. Geiger and K. Leinemann}, Booktitle = {Proceedings of the 1st International Workshop on Next Generation 3D City Models}, Editor = {Thomas H. Kolbe and Gerhard Gr\"oger}, Month = {June}, Pages = {17--22}, Title = {Flexible Generation of Semantic {3D} Building Models}, Year = {2005}} @article{Yin09, Author = {Xuetao Yin and Peter Wonka and Anshuman Razdan}, Journal = {IEEE Computer Graphics and Applications}, Month = {January/February}, Title = {Generating {3D} Building Models from Architectural Drawings: A Survey}, Year = {2009}} @article{Schreibmann06, Author = {Eduard Schreibmann and George T. Y. Chen and Lei Xing}, Journal = {International Journal of Radiation Oncology*Biology*Physics}, Month = {April}, Number = {5}, Pages = {1537--1550}, Title = {Image interpolation in {4D} {CT} using a {BSpline} deformable registration model}, Volume = {64}, Year = {2006}} @article{LorenzoValdes04, Author = {Mar{\'\i}a Lorenzo-Vald{\'e}s and Gerardo I. Sanchez-Ortiz and Andrew G. Elkington and Raad H. Mohiaddin and Daniel Rueckert}, Journal = {Medical Image Analysis}, Pages = {255--265}, Title = {Segmentation of {4D} cardiac {MR} images using a probabilistic atlas and the {EM} algorithm}, Volume = {8}, Year = {2004}} @article{Barequet97, Author = {Gill Barequet}, Journal = {IEEE Computational Science and Engineering}, Month = {October--December}, Number = {4}, Pages = {22--28}, Title = {Using Geometric Hashing To Repair {CAD} Objects}, Volume = {4}, Year = {1997}} @techreport{Agarwal01, Author = {Pankaj K. Agarwal and Michael T. Goodrich and S. Rao Kosaraju and Franco P. Preparata and Roberto Tamassia and Jeffrey S. Vitter}, Institution = {Brown University}, Month = {December}, Title = {Applicable and Robust Geometric Computing}, Type = {ARO Grant DAAH04-96-1-0013 Final Technical Report}, Year = {2001}} @article{Patel06, Author = {Paresh S. Patel and David L. Marcum and Michael G. Remotigue}, Journal = {International Journal for Numerical Methods in Fluids}, Month = {March}, Pages = {823--841}, Title = {Automatic {CAD} model topology generation}, Volume = {52}, Year = {2006}} @article{Pueyo13, Author = {Oriol Pueyo and Gustavo Patow}, Journal = {The Visual Computer}, Month = {April}, Title = {Structuring urban data}, Year = {2013}} @article{Bayer72, Author = {R. Bayer}, Journal = {Acta Informatica}, Month = {January}, Pages = {290--306}, Title = {Symmetric Binary B-Trees: Data Structure and Maintenance Algorithms}, Volume = {1}, Year = {1972}} @inproceedings{Damiand09, Author = {Guillaume Damiand and Colin {de la Higuera} and Jean-Christophe Janodet and \'Emilie Samuel and Christine Solnon}, Booktitle = {Proceedings of the 7th IAPR-TC-15 International Workshop on Graph-Based Representations in Pattern Recognition}, Editor = {Andrea Torsello and Francisco {Escolano Ruiz} and Luc Brun}, Pages = {102--112}, Publisher = {Springer}, Series = {Lecture Notes in Computer Science}, Title = {A Polynomial Algorithm for Submap Isomorphism---Application to Searching Patterns in Images---}, Volume = {5534}, Year = {2009}} @inproceedings{Sederberg86, Author = {Thomas W. Sederberg}, Booktitle = {Proceedings of SIGGRAPH '86}, Month = {August}, Pages = {151--160}, Title = {Free-Form Deformation of Solid Geometric Models}, Year = {1986}} @article{Masuda93, Author = {Hiroshi Masuda}, Journal = {Computer-Aided Design}, Number = {2}, Title = {Topological Operators and {B}oolean Operations for Complex-Based Non-Manifold Geometric Models}, Volume = {25}, Year = {1993}} @inproceedings{Comic13, Author = {Lidija {\v C}omi\'c and Leila {de Floriani} and Federico Iuricich}, Booktitle = {Proceedings of the 17th IAPR International Conference on Discrete Geometry for Computer Imagery}, Editor = {Rocio Gonzalez-Diaz and {Maria Jose} Jimenez and Belen Medrano}, Pages = {323--334}, Series = {Lecture Notes in Computer Science}, Title = {Multi-resolution Cell Complexes Based on Homology-Preserving Euler Operators}, Volume = {7749}, Year = {2013}} @inproceedings{vanderBrink12, Author = {Linda {van der Brink} and Jantien Stoter and Sisi Zlatanova}, Booktitle = {Proceedings of the 7th International 3D GeoInfo Conference}, Pages = {11--14}, Title = {Modeling an Application Domain Extension of CityGML in UML}, Year = {2012}} @techreport{Poudret07, Author = {M. Poudret and A. Arnould and Y. Bertrand and P. Lienhardt}, Institution = {Laboratoire SIC, UFR SFA, Universit\'e de Poitiers}, Month = {October}, Number = {2007-01}, Title = {Cartes combinatoires ouvertes}, Year = {2007}} @unpublished{Paul12, Author = {Norbert Paul}, Month = {May}, Note = {Available at \url{http://arxiv.org/abs/1205.5691}}, Title = {Signed Simplicial Decomposition and Overlay of n-D Polytope Complexes}, Year = {2012}} @unpublished{Paul11, Author = {Norbert Paul and Patrick Erik Bradley and Martin Breunig}, Month = {March}, Note = {Available at \url{http://arxiv.org/abs/1303.2595}}, Title = {Integrating Space, Time, Version and Scale Using {A}lexandrov Topologies}, Year = {2011}} @techreport{Lien06a, Author = {Jyh-Ming Lien and Nancy M. Amato}, Institution = {Parasol Lab., Department of Computer Science, Texas A\&M University}, Month = {January}, Number = {TR06-002}, Title = {Approximate Convex Decomposition of Polyhedra}, Year = {2006}} @inproceedings{Worboys12, Author = {Michael Worboys}, Booktitle = {Proceedings of the 7th International Conference GIScience 2012}, Editor = {Ningchuan Xiao and Mei-Po Kwan and Michael F. Goodchild and Shashi Shekhar}, Pages = {298--310}, Publisher = {Springer}, Series = {Lecture Notes in Computer Science}, Title = {The Maptree: A Fine-Grained Formal Representation of Space}, Volume = {7478}, Year = {2012}} @article{Afyouni11, Author = {Imad Afyouni and Cyril Ray and Christophe Claramunt}, Journal = {Journal of Spatial Information Science}, Pages = {85--123}, Title = {Spatial Models for Indoor \& Context-Aware Navigation Systems: A Survey}, Volume = {4}, Year = {2012}} @inproceedings{Shi13, Author = {Yunfei Shi and Biao He}, Booktitle = {Proceedings of the 6th IFIP WG 5.14 International Conference}, Editor = {Diaoliang Li and Yingyi Chen}, Pages = {203--210}, Series = {IFIP Advances in Information and Communication Technology}, Title = {Creating Topologically Consistent 3D City Models of LOD+ with Extrusion}, Volume = {393}, Year = {2013}} @inproceedings{Horna07, Author = {Sebastien Horna and Guillaume Damiand and Daniel Meneveaux and Yves Bertrand}, Booktitle = {Proceedings of the 2nd International Conference on Computer Graphics Theory and Applications}, Month = {March}, Pages = {37--44}, Title = {Building 3D Indoor Scenes Topology from 2D Architectural Plans}, Year = {2007}} @incollection{Weiler88a, Author = {Kevin Weiler}, Booktitle = {Geometric modeling for CAD applications: selected and expanded papers from the IFIP WG 5.2 working conference}, Editor = {M.J. Wozny and H.W. McLaughlin}, Month = {May}, Pages = {37--66}, Publisher = {Elsevier}, Title = {Boundary Graph Operators for Non-Manifold Geometric Modeling Topology Representations}, Year = {1988}} @inproceedings{Isenburg06, Author = {Martin Isenburg and Yuanxin Liu and Jonathan Shewchuk and Jack Snoeyink}, Booktitle = {Proceedings of SIGGRAPH 2006}, Month = {July}, Pages = {1049--1056}, Title = {Streaming Computation of Delaunay Triangulations}, Year = {2006}} @inproceedings{Kirkpatrick00, Author = {David Kirkpatrick and Jack Snoeyink and Bettina Speckmann}, Booktitle = {Proceedings of the 16th Annual Symposium on Computational Geometry}, Pages = {322--330}, Title = {Kinetic Collision Detection for Simple Polygons}, Year = {2000}} @inproceedings{Shamos76, Author = {Michael Ian Shamos and Dan Hoey}, Booktitle = {Proceedings of the 17th Annual Symposium on the Foundations of Computer Science}, Pages = {208--215}, Title = {Geometric Intersection Problems}, Year = {1976}} @inproceedings{Shea89, Author = {Shea, K S and McMaster, R B}, Booktitle = {Proceedings of Auto-Carto 9}, Pages = {56--67}, Title = {Cartographic generalization in a digital environment: When and how to generalize}, Year = {1989}} @article{Aronov89, Author = {Boris Aronov}, Journal = {Algorithmica}, Pages = {109--140}, Title = {On the Geodesic Voronoi Diagram of Point Sites in a Simple Polygon}, Volume = {4}, Year = {1989}} @inproceedings{Pacheco09, Author = {Ana Pacheco and Pedro Real}, Booktitle = {Proceedings of the 14th Iberoamerican Congress on Pattern Recognition}, Editor = {Eduardo Bayro-Corrochano and Jan-Olof Eklundh}, Pages = {279--286}, Publisher = {Springer Berlin / Heidelberg}, Series = {Lecture Notes in Computer Science}, Title = {Getting Topological Information for a 80-Adjacency Doxel-Based 4D Volume through a Polytopal Cell Complex}, Volume = {5856}, Year = {2009}} @article{Alayrangues08, Author = {Sylvie Alayrangues and Xavier Daragon and Jacques-Olivier Lachaud and Pascal Lienhardt}, Journal = {Journal of Mathematical Imaging and Vision}, Pages = {1--22}, Title = {Equivalence between Closed Connected n-G-Maps without Multi-Incidence and n-Surfaces}, Volume = {32}, Year = {2008}} @article{Peltier09, Author = {Samuel Peltier and Laurent Fuchs and Pascal Lienhardt}, Journal = {Discrete Applied Mathematics}, Pages = {542--557}, Title = {Simploidals sets: Definitions, operations and comparison with simplicial sets}, Volume = {157}, Year = {2009}} @article{Skapin01, Author = {Xavier Skapin and Pascal Lienhardt}, Journal = {Journal of Visualization and Computer Animation}, Pages = {131--144}, Title = {Using Cartesian product for animation}, Volume = {12}, Year = {2001}} @unpublished{Mazur07, Author = {Barry Mazur}, Month = {June}, Note = {Available at \url{http://www.math.harvard.edu/~mazur/preprints/when_is_one.pdf}}, Title = {When is one thing equal to some other thing?}, Year = {2007}} @incollection{Albrecht98, Author = {Jochen Albrecht}, Booktitle = {Geographic Information Research: Transatlantic Perspectives}, Editor = {Massimo Craglia and Harlan Onsrud}, Pages = {577--591}, Publisher = {CRC Press}, Title = {Universal analytical GIS operations---a task-oriented systematization of data structure-independent GIS functionality}, Year = {1998}} @techreport{Biljecki13, Author = {Filip Biljecki}, Institution = {Delft University of Technology}, Month = {February}, Number = {62}, Title = {The concept of level of detail in {3D} city models}, Type = {PhD proposal}, Year = {2013}} @inproceedings{Shewchuk03, Author = {Jonathan Richard Shewchuk}, Booktitle = {Proceedings of the 19th Annual Symposium on Computational Geometry}, Month = {June}, Pages = {181--190}, Title = {Updating and Constructing Constrained Delaunay and Constrained Regular Triangulations by Flips}, Year = {2003}} @book{Okabe00, Author = {Atsuyuki Okabe and Barry Boots and Kokichi Sugihara and Sung Nok Chiu}, Publisher = {John Wiley \& Sons}, Title = {Spatial Tessellations: Concepts and Applications of Voronoi Diagrams}, Year = {2000}} @article{Coors03, Author = {Volker Coors}, Journal = {Computers, Environment and Urban Systems}, Pages = {345--357}, Title = {{3D-GIS} in networking environments}, Volume = {27}, Year = {2003}} @article{NguyenGia12, Author = {Tuan Anh {Nguyen Gia}}, Journal = {International Journal of Computer and Electrical Engineering}, Month = {December}, Number = {6}, Pages = {962--966}, Title = {Propose New Primitives for Urban Data Model}, Volume = {4}, Year = {2012}} @article{Schleicher07, Author = {Dierk Schleicher}, Journal = {American Mathematical Monthly}, Month = {June--July}, Number = {6}, Pages = {509--528}, Title = {Hausdorff Dimension, Its Properties, and Its Surprises}, Volume = {114}, Year = {2007}} @article{Zhang13, Author = {Lingling Zhang and Yunfei Shi and Changlin Mi}, Journal = {Applied Mechanics and Materials}, Month = {February}, Pages = {1129--1133}, Title = {Survey of Research Progress on Three Dimensional Topological Data Structure}, Volume = {303--306}, Year = {2013}} @inproceedings{Shewchuk13, Author = {Jonathan Richard Shewchuk and Brielin C. Brown}, Booktitle = {Proceedings of the 29th ACM Symposium on Computational Geometry}, Title = {Fast Segment Insertion and Incremental Construction of Constrained Delaunay Triangulations}, Year = {2013}} @article{Fortune97, Author = {Steven Fortune}, Journal = {Computer-Aided Design}, Number = {2}, Pages = {123--133}, Title = {Polyhedral modelling with multiprecision integer arithmetic}, Volume = {29}, Year = {1997}} @article{Edelsbrunner93a, Author = {Herbert Edelsbrunner and Raimund Seidel and Micha Sharir}, Journal = {SIAM Journal on Computing}, Month = {April}, Number = {2}, Pages = {418--429}, Title = {On the Zone Theorem for Hyperplane Arrangements}, Volume = {22}, Year = {1993}} @article{Edelsbrunner86, Author = {Herbert Edelsbrunner and J. O'Rourke and R. Seidel}, Journal = {SIAM Journal on Computing}, Month = {May}, Number = {2}, Pages = {341--363}, Title = {Constructing Arrangements of Lines and Hyperplanes with Applications}, Volume = {15}, Year = {1986}} @book{Engelking77, Author = {Rysxard Engelking}, Publisher = {Polish Scientific Publishers}, Title = {General Topology}, Year = {1977}} @inproceedings{Clementini93, Author = {Eliseo Clementini and Paolino {di Felice} and Peter {van Oosterom}}, Booktitle = {Proceedings of the 3rd International Symposium on Advances in Spatial Databases}, Pages = {277--295}, Title = {A Small Set of Formal Topological Relationships Suitable for End-User Interaction}, Year = {1993}} @book{Itskov13, Author = {Mikhail Itskov}, Edition = {3rd}, Publisher = {Springer}, Series = {Mathematical Engineering}, Title = {Tensor Algebra and Tensor Analysis for Engineers}, Volume = {15}, Year = {2013}} @incollection{Zhao14, Author = {Junqiao Zhao and Jantien Stoter and Hugo Ledoux}, Booktitle = {Cartography from Pole to Pole: Selected Contributions to the XXVIth International Conference of the ICA, Dresden 2013}, Editor = {Manfred Buchroithner and Nikolas Prechtel and Dirk Burghardt}, Pages = {187--202}, Publisher = {Springer Berlin Heidelberg}, Series = {Lecture Notes in Geoinformation and Cartography}, Title = {A Framework for the Automatic Geometric Repair of {CityGML} Models}, Year = {2014}} @incollection{Thompson11a, Author = {Rodney James Thompson and Peter {van Oosterom}}, Booktitle = {Advances in 3D Geo-Information Sciences}, Editor = {Thomas H. Kolbe and Gerhard K\"onig and Claus Nagel}, Pages = {179--196}, Publisher = {Springer}, Series = {Lecture Notes in Geoinformation and Cartography}, Title = {Integrated Representation of (Potentially Unbounded) {2D} and {3D} Spatial Objects for Rigorously Correct Query and Manipulation}, Year = {2011}} @incollection{Halbwachs00, Author = {Yvon Halbwachs and {\O}yving Hjelle}, Booktitle = {Advances in Software Tools for Scientific Computing}, Editor = {Langtangen, Hans P. and Bruaset, Are M. and Quak, Ewald}, Pages = {339--356}, Publisher = {Springer}, Series = {Lecture Notes in Computational Science and Engineering}, Title = {Generalized Maps in Geological Modeling: Object-Oriented Design of Topological Kernels}, Volume = {10}, Year = {2000}} @techreport{Fradin05, Author = {D. Fradin and D. Meneveaux and P. Lienhardt}, Institution = {Signal Image Communication Laboratory, CNRS, University of Poitiers}, Number = {4}, Title = {Hierarchy of Generalized Maps for Modeling and Rendering Complex Indoor Scenes}, Year = {2005}} @inproceedings{Govindaraju04, Author = {Naga K. Govindaraju and Ming C. Lin and Dinesh Manocha}, Booktitle = {Proceedings of the 11th ACM Symposium on Virtual Reality Software and Technology}, Title = {Fast and Reliable Collision Culling Using Graphics Processors}, Year = {2004}} @unpublished{Erickson09, Author = {Jeff Erickson}, Note = {Lecture notes from CS 598: Computational Topology}, Title = {CS 598: Computational Topology}, Year = {2009}} @phdthesis{Zlatanova00, Author = {Siyka Zlatanova}, Month = {March}, School = {Technische Universit\"at Graz}, Title = {3D GIS for Urban Development}, Year = {2000}} @article{McInerney95, Author = {Tim McInerney and Demetri Terzopoulos}, Journal = {Computerized Medical Imaging and Graphics}, Number = {1}, Pages = {69--83}, Title = {A dynamic finite element surface model for segmentation and tracking in multidimensional medical images with application to cardiac {4D} image analysis}, Volume = {19}, Year = {1995}} @inproceedings{Kim03, Author = {Sung-Soo Kim and Seong-Ho Lee and Kyong-Ho Kim and Jong-Hun Lee}, Booktitle = {Proceedings of the IEEE 2003 International Geoscience and Remote Sensing Symposium}, Pages = {3715--3717}, Title = {A Unified Visualization Framework for Spatial and Temporal Analysis in 4D GIS}, Volume = {6}, Year = {2003}} @inproceedings{Bendix99, Author = {J\"org Bendix and Frank Berthmann and Christoph Reudenbach}, Booktitle = {Proceedings of the IEEE 1999 International Geoscience and Remote Sensing Symposium}, Pages = {2235--2237}, Title = {NOAA-AVHRR and 4D GIS --- towards a more realistic view of fog clearance}, Year = {1999}} @incollection{vanOosterom12a, Author = {Peter van Oosterom and Martijn Meijers}, Booktitle = {Jaarverslag 2011}, Publisher = {Nederlandse Commissie voor Geodesie}, Title = {Vario-scale data structures supporting smooth zoom and progressive transfer of {2D} and {3D} data}, Year = {2012}} @article{Gueziec99, Author = {Andr\'e Gu\'eziec and Frank Bossen and Gabriel Taubin and Claudio Silva}, Journal = {Computational Geometry: Theory \& Applications}, Pages = {137--166}, Title = {Efficient compression of non-manifold polygonal meshes}, Volume = {14}, Year = {1999}} @book{Luebke03, Author = {David Luebke and Martin Reddy and Jonathan D. Cohen and Amitabh Varshney and Benjamin Watson and Robert Huebner}, Editor = {Brian A. Barsky}, Publisher = {Morgan Kaufmann Publishers}, Title = {Level of Detail for 3D Graphics}, Year = {2003}} @article{Hagbi10, Author = {Nate Hagbi and Jihad El-Sana}, Journal = {Computer-Aided Design}, Pages = {67--75}, Title = {Carving for topology simplification of polygonal meshes}, Volume = {42}, Year = {2010}} @article{Soille03, Author = {Pierre Soille and J\"urgen Vogt and Roberto Colombo}, Journal = {Water Resources Research}, Number = {12}, Title = {Carving and adaptive drainage enforcement of grid digital elevation models}, Volume = {39}, Year = {2003}} @article{Garbrecht97, Author = {Jurgen Garbrecht and Lawrence W. Martz}, Journal = {Journal of Hydrology}, Pages = {204--213}, Title = {The assignment of drainage direction over flat surfaces in raster digital elevation models}, Volume = {193}, Year = {1997}} @article{Prat05, Author = {Sylvain Prat and Patrick Giola and Yves Bertrand and Daniel Meneveaux}, Journal = {The Visual Computer}, Month = {September}, Number = {8--10}, Pages = {876--885}, Title = {Connectivity Compression in Arbitrary Dimension}, Volume = {21}, Year = {2005}} @inproceedings{Alumbaugh05, Author = {Tyler J. Alumbaugh and Xiangmin Jiao}, Booktitle = {Proceedings of the 14th International Meshing Roundtable}, Pages = {485--504}, Title = {Compact Array-Based Mesh Data Structures}, Year = {2005}} @phdthesis{Damiand10, Author = {Guillaume Damiand}, Month = {September}, School = {Universit\'e Claude Bernard Lyon 1}, Title = {Contributions aux Cartes Combinatoires et Cartes G\'en\'eralis\'ees : Simplification, Mod\`eles, Invariants Topologiques et Applications}, Type = {Habilitation}, Year = {2010}} @phdthesis{Damiand01, Author = {Guillaume Damiand}, Month = {December}, School = {Universit\'e Montpellier II}, Title = {D\'efinition et \'etude d'un mod\`ele topologique minimal de repr\'esentation d'images 2d et 3d}, Year = {2001}} @inproceedings{Damiand08, Author = {Guillaume Damiand and Samuel Peltier and Laurent Fuchs}, Booktitle = {Proceedings of the 12th International Workshop on Combinatorial Image Analysis}, Editor = {Valentin E. Brimkov and Reneta P. Barneva and Hebert A. Hauptman}, Pages = {63--74}, Publisher = {Springer}, Series = {Lecture Notes in Computer Science}, Title = {Computing Homology Generators for Volumes Using Minimal Generalized Maps}, Volume = {4958}, Year = {2008}} @inproceedings{Cicerone12, Author = {Serafino Cicerone and Matteo Cermignani}, Booktitle = {Proceedings of the International Conference on Computational Science and Its Applications 2012}, Editor = {Beriamino Murgante and Osvaldo Gervasi and Sanjay Misra and Nadia Nedjah and Ana Maria A. C. Rocha and David Taniar and Bernady O. Apduhan}, Pages = {267--279}, Series = {Lecture Notes in Computer Science}, Title = {Fast and Simple Approach for Polygon Schematization}, Volume = {7333}, Year = {2012}} @inproceedings{Cicerone09, Author = {S. Cicerone and A. Orlandi and B. Archambeault and S. Connor and J. Fan and J.L. Drewniak}, Booktitle = {Proceedings of the 20th International Zurich Symposium on EMC}, Pages = {253--256}, Title = {Cavities' Identification Algorithm for Power Integrity Anaysis of Complex Boards}, Year = {2009}} @mastersthesis{Rastelli11, Author = {Michele Rastelli}, School = {Universit\`a degli Studi dell-Aquila}, Title = {BusOnAir - Un sistema informativo per transporti pubblici: modelli, algoritmi e tecnologie}, Year = {2011}} @article{Elter94, Author = {Herve Elter and Pascal Lienhardt}, Journal = {International Journal of Shape Modeling}, Number = {2}, Title = {Cellular complexes as structured semi-simplicial sets}, Volume = {1}, Year = {1994}} @article{Lienhardt04, Author = {Pascal Lienhardt and Xavier Skapin and Antoine Bergey}, Journal = {International Journal of Computational Geometry and Applications}, Number = {3}, Pages = {115--159}, Title = {Cartesian product of simplicial and cellular structures}, Volume = {14}, Year = {2004}} @inbook{Hardy12, Author = {Paul Hardy and Kenneth Field}, Chapter = {11}, Editor = {Wolfgang Kresse and David M. Danko}, Pages = {323--358}, Publisher = {Springer}, Series = {Springer Handbook of Geographic Information}, Title = {Portrayal and Cartography}, Year = {2012}} @inproceedings{He12, Author = {S. He and G. Besuievsky and V. Tourre and G. Patow and G. Moreau}, Booktitle = {Proceedings of 3U3D2012: Usage, Usability, and Utility of 3D City Models}, Title = {All range and heterogeneous multi-scale 3D city models}, Year = {2012}} @inproceedings{Feng12, Author = {Xin Feng and Yuanzhen Wang and Yanlin Weng and Yiying Tong}, Booktitle = {Proceedings of the 1st International Conference on Computational Visual Media}, Editor = {Shi-Min Hu and Ralph R. Martin}, Pages = {194--201}, Series = {Lecture Notes in Computer Science}, Title = {Compact combinatorial maps in 3D}, Volume = {7633}, Year = {2012}} @inproceedings{Wang10, Author = {Lvdi Wang and Kun Zhou and Yizhou Yu and Baining Guo}, Booktitle = {Proceedings of SIGGRAPH 2011}, Number = {4}, Series = {ACM Transactions on Graphics}, Title = {Vector Solid Textures}, Volume = {29}, Year = {2010}} @inproceedings{Wang11, Author = {Lvdi Wang and Yizhou Yu and Kun Zhou and Baining Guo}, Booktitle = {Proceedings of SIGGRAPH Asia 2011}, Month = {December}, Number = {6}, Series = {ACM Transactions on Graphics}, Title = {Multiscale Vector Volumes}, Volume = {30}, Year = {2011}} @article{Goetz12, Author = {Marcus Goetz}, Journal = {International Journal of Geographical Information Science}, Month = {September}, Pages = {1--21}, Title = {Towards generating highly detailed 3D CityGML models from OpenStreetMap}, Volume = {iFirst}, Year = {2012}} @article{Gosselin11, Author = {St\'ephane Gosselin and Guillaume Damiand and Christine Solnon}, Journal = {Theoretical Computer Science}, Month = {March}, Number = {15}, Pages = {1392--1405}, Title = {Efficient search of combinatorial maps using signatures}, Volume = {412}, Year = {2011}} @mastersthesis{Baas12, Author = {Bart Baas}, School = {Delft University of Technology}, Title = {NoSQL Spatial: Neo4j versus PostGIS}, Year = {2012}} @book{Bellman57, Author = {Richard Ernest Bellman}, Publisher = {Princeton University Press}, Title = {Dynamic programming}, Year = {1957}} @inbook{Comic12, Author = {Lidija {\v C}omi\'c and Leila {de Floriani}}, Chapter = {4}, Editor = {V.E. Brimkov and R.P. Barneva}, Number = {2}, Pages = {109--144}, Publisher = {Springer}, Series = {Lecture Notes in Computational Vision and Biomechanics}, Title = {Modeling and Manipulating Cell Complexes in Two, Three and Higher Dimensions}, Volume = {2}, Year = {2012}} @inproceedings{Meijers11b, Address = {Delft, The Netherlands}, Author = {Martijn Meijers}, Booktitle = {Proceedings of the 28th Urban Data Management Symposium}, Editor = {Elfriede M. Fendel and Hugo Ledoux and M. Rumor and Sisi Zlatanova}, Pages = {95--101}, Publisher = {ISPRS Archives}, Title = {The space-scale cube: an integrated model for 2D polygonal areas and scale}, Volume = {XXXVIII-4/C21}, Year = {2011}} @article{Thomsen08, Author = {Andreas Thomsen and Martin Breunig and Edgar Butwilowski}, Journal = {Journal of Photogrammetry, Remote Sensing and Geoinformation Processing}, Pages = {175--186}, Title = {Towards a {G}-Map Based Tool for the Modelling and Management of Topology in Multiple Representation Databases}, Volume = {3}, Year = {2008}} @article{Coxeter30, Author = {H.S.M. Coxeter}, Journal = {Philosophical Transactions of the Royal Society of London. Series A, Containing Papers of a Mathematical or Physical Character}, Pages = {329--425}, Title = {The Polytopes with Regular-Prismatic Vertex Figures}, Volume = {229}, Year = {1930}} @inproceedings{Zhu09, Author = {Qing Zhu and Junqiao Zhao and Xiaochun Liu and Yeting Zhang}, Booktitle = {Proceedings of GeoWeb 2009 Academic Track -- Cityscapes}, Editor = {Thomas H. Kolbe and Hao Zhang and Sisi Zlatanova}, Pages = {74--79}, Publisher = {ISPRS}, Series = {The International Archives of Photogrammetry, Remote Sensing and Spatial Information Science}, Title = {Perceptually Guided Geometrical Primitive Location Method for {3D} Complex Building Simplification}, Volume = {XXXVIII--3--4/C3}, Year = {2009}} @article{Zhu10, Author = {Qing Zhu and Junqiao Zhao and Zhiqiang Du and Yeting Zhang}, Journal = {Computers \& Graphics}, Month = {February}, Number = {1}, Pages = {55--65}, Title = {Quantitative analysis of discrete 3D geometrical detail levels based on perceptual metric}, Volume = {34}, Year = {2010}} @article{Amenta01, Author = {Nina Amenta and Sunghee Choi and Ravi Krishna Kolluri}, Journal = {Computational Geometry: Theory \& Applications}, Number = {2--3}, Pages = {127--153}, Title = {The power crust, unions of balls, and the medial axis transform}, Volume = {19}, Year = {2001}} @article{Andoni08, Author = {Alexandr Andoni and Piotr Indyk}, Journal = {Communications of the ACM}, Number = {1}, Pages = {117--122}, Title = {Near-optimal Hashing Algorithms for Approximate Nearest Neighbor in High Dimensions}, Volume = {51}, Year = {2008}} @article{Arya98, Author = {Sunil Arya and David M. Mount and Nathan S. Netanyahu and Ruth Silverman and Angela Y. Wu}, Journal = {Journal of the ACM}, Pages = {891--923}, Title = {An Optimal Algorithm for Approximate Nearest Neighbor Searching in Fixed Dimensions}, Volume = {45}, Year = {1998}} @inproceedings{Bellet10, Author = {Thomas Bellet and Mathieu Poudret and Agnes Arnould and Laurent Fuchs}, Booktitle = {Proceedings of the Shape Modeling International Conference 2010}, Pages = {100--112}, Title = {Designing a topological modeler kernel: a rule-based approach}, Year = {2010}} @inproceedings{Desbarats03, Author = {Pascal Desbarats and Stefka Gueorguieva}, Booktitle = {Proceedings of the International Conference on Computational Science and Its Applications 2003}, Pages = {498--507}, Series = {Lecture Notes in Computer Science}, Title = {CW Complexes: Topological Mainframe for Numerical Representations of Objects}, Volume = {2669}, Year = {2003}} @techreport{Illetschko06a, Author = {Thomas Illetschko and Adrian Ion and Yll Haxhimusa and Walter G. Kropatsch}, Institution = {Vienna University of Technology}, Month = {October}, Number = {106}, Title = {Effective Programming of Combinatorial Maps using COMA - A C++ Framework for Combinatorial Maps}, Year = {2006}} @inproceedings{Illetschko06, Author = {Thomas Illetschko and Adrian Ion and Yll Haxhimusa and Walter G. Kropatsch}, Booktitle = {Proceedings of the 30th Annual Workshop of the Austrian Association for Pattern Recognition}, Editor = {F. Lenzen and O. Scherzer and M. Vincze}, Title = {Collapsing 3D Combinatorial Maps}, Year = {2006}} @article{Vince83, Author = {Andrew Vince}, Journal = {Journal of Combinatorial Theory, Series B}, Month = {February}, Number = {1}, Pages = {1--21}, Title = {Combinatorial Maps}, Volume = {34}, Year = {1983}} @article{Rottensteiner03, Author = {Franz Rottensteiner}, Journal = {3D Reconstruction and Visualization}, Number = {6}, Pages = {42--50}, Title = {Automatic Generation of High-Quality Building Models from Lidar Data}, Volume = {23}, Year = {2003}} @inproceedings{Ledoux09, Author = {Hugo Ledoux and Martijn Meijers}, Booktitle = {UDMS Annual 2009: Proceedings of the Urban Data Management Society Symposium 2009}, Editor = {Alenka Krek and Massimo Rumor and Sisi Zlatanova}, Pages = {39--48}, Title = {Extruding building footprints to create topologically consistent 3D city models}, Year = {2009}} @inproceedings{Meijers11a, Author = {Martijn Meijers}, Booktitle = {Proceedings of the 14th {ICA}/{ISPRS} Workshop on Generalisation and Multiple Representation}, Title = {Cache-friendly progressive data streaming with variable-scale data structures}, Year = {2011}} @phdthesis{Meijers11, Author = {Martijn Meijers}, Month = {December}, School = {Delft University of Technology}, Title = {Variable-scale Geo-information}, Year = {2011}} @inproceedings{vanOosterom12, Author = {Peter {van Oosterom} and Jantien Stoter}, Booktitle = {Proceedings of the Geospatial World Forum 2012}, Title = {Principles of 5D modeling, full integration of 3D space, time and scale}, Year = {2012}} @article{Requicha80, Author = {Aristides A. G. Requicha}, Journal = {Computing Surveys}, Month = {December}, Number = {4}, Pages = {437--464}, Title = {Representations for Rigid Solids: Theory, Methods, and Systems}, Volume = {12}, Year = {1980}} @article{Ledoux11a, Author = {Hugo Ledoux and Martijn Meijers}, Journal = {International Journal of Geographical Information Science}, Number = {4}, Pages = {557--574}, Title = {Topologically consistent {3D} city models obtained by extrusion}, Volume = {25}, Year = {2011}} @article{Myers95, Author = {Nathan C. Myers}, Journal = {C++ Report}, Month = {June}, Title = {Traits: a new and useful template technique}, Year = {1995}} @inproceedings{deBerg97a, Author = {Mark {de Berg} and Matthew J. Katz and A. Frank {van der Stappen} and Jules Vleugels}, Booktitle = {Proceedings of the 13th Annual Symposium on Computational Geometry}, Pages = {294--303}, Title = {Realistic Input Models for Geometric Algorithms}, Year = {1997}} @book{Boots86, Address = {Norwich, United Kingdom}, Author = {B. N. Boots}, Publisher = {W. H. Hutchkins \& Sons}, Series = {Concepts and Techniques in Modern Geography}, Title = {Voronoi (Thiessen) Polygons}, Volume = {45}, Year = {1986}} @article{Fabri00, Author = {Andreas Fabri and Geert-Jan Giezeman and Lutz Kettner and Stefan Schirra and Sven Sch\"onherr}, Journal = {Software: Practice and Experience}, Number = {11}, Pages = {1167--1202}, Title = {On the design of CGAL, a computational geometry algorithms library}, Volume = {30}, Year = {2000}} @article{Zomorodian02, Author = {Afra Zomorodian and Herbert Edelsbrunner}, Journal = {International Journal of Computational Geometry and Applications}, Pages = {143--172}, Title = {Fast Software for Box Intersections}, Volume = {12}, Year = {2002}} @inproceedings{Boots74, Author = {Boots, Barry}, Booktitle = {Proceedings, Association of American Geographers, 6}, Pages = {26--29}, Title = {{D}elaunay triangles, an alternative approach to point pattern analysis}, Year = {1974}} @unpublished{Tammik07, Author = {Jeremy Tammik}, Month = {September}, Note = {Available at \url{http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.89.6020&rep=rep1&type=pdf}}, Title = {{AutoCAD} {N}ef Polyhedron Implementation}, Year = {2007}} @inproceedings{Dupas08, Author = {Alexandre Dupas and Guillaume Damiand}, Booktitle = {Proceedings of the 14th IAPR International Conference on Discrete Geometry for Computer Imagery}, Pages = {507--518}, Series = {Lecture Notes in Computer Science}, Title = {First Results for 3D Image Segmentation with Topological Map}, Volume = {4992}, Year = {2008}} @inproceedings{vanOosterom04, Author = {Peter {van Oosterom} and Quak, Wilko and Tijssen, Theo}, Booktitle = {Proceedings of the 11th International Symposium on Spatial Data Handling}, Editor = {Fisher, Peter F.}, Pages = {1--16}, Publisher = {Springer}, Title = {About invalid, valid and clean polygons}, Year = {2004}} @inproceedings{Thiemann10, Author = {Frank Thiemann and Monika Sester and Joachim Bobrich}, Booktitle = {Proceedings of the Joint International Conference on Theory, Data Handling and Modelling in GeoSpatial Information Science}, Pages = {558--563}, Title = {Automatic Derivation of Land-Use from Topographic Data}, Volume = {38}, Year = {2010}} @article{Yuan99, Author = {Shuxin Yuan and Chuang Tao}, Journal = {Geoinformatics and Socioinformatics}, Month = {June}, Pages = {1--13}, Title = {Development of Conflation Components}, Year = {1999}} @inproceedings{vanOosterom03, Author = {Peter {van Oosterom} and Wilko Quak and Theo Tijssen}, Booktitle = {Proceedings of the ISPRS Joint Workshop on Spatial, Temporal and Multi-Dimensional Data Modelling and Analysis}, Month = {October}, Title = {Polygons: The unstable foundation of spatial modeling}, Year = {2003}} @book{Hatcher02, Author = {Allen Hatcher}, Publisher = {Cambridge University Press}, Title = {Algebraic Topology}, Year = {2002}} @inbook{Congote12, Author = {John Congote and Luis Kabongo and Aitor Moreno and Alvaro Segura and Andoni Beristain and Jorge Posada and Oscar Ruiz}, Chapter = {9}, Editor = {Nobuhiko Mukai}, Month = {March}, Pages = {157--178}, Publisher = {InTech}, Series = {Computer Graphics}, Title = {Volume Ray Casting in WebGL}, Year = {2012}} @inproceedings{Escalona07, Author = {Francisco Escalona and Ruy Fabila-Monroy and Jorge Urrutia}, Booktitle = {Proceedings of the 23rd European Workshop on Computational Geometry}, Month = {March}, Pages = {12--16}, Title = {Hamiltonian Tetrahedralizations with Steiner Points}, Year = {2007}} @article{El-Mekawy12, Author = {Mohamed El-Mekawy and Anders Ostman and Ihab Hijazi}, Journal = {ISPRS International Journal of Geo-Information}, Month = {July}, Pages = {120--145}, Title = {A Unified Building Model for 3D Urban GIS}, Volume = {1}, Year = {2012}} @incollection{Boguslawski11, Author = {Pawel Boguslawski and Christopher Gold}, Booktitle = {Advances in 3D Geo-Information Sciences}, Editor = {Kolbe, Thomas H. and K\"{o}nig, Gerhard and Nagel, Claus}, Pages = {43--56}, Publisher = {Springer}, Series = {Lecture Notes in Geoinformation and Cartography}, Title = {Rapid Modelling of Complex Building Interiors}, Year = {2011}} @unpublished{Edelsbrunner06, Author = {Herbert Edelsbrunner}, Note = {Lecture notes from CPS296.1: COMPUTATIONAL TOPOLOGY}, Title = {CPS296.1: Computational Topology}, Year = {2006}} @inbook{Lienhardt09, Author = {Pascal Lienhardt and Laurent Fuchs and Yves Bertrand}, Editor = {Giuseppe Di Malo and Somashekhar Naimpally}, Pages = {151--198}, Publisher = {Dipartimento di Matematica della Seconda Universit\`a di Napoli}, Series = {Theory and applications of proximity, nearness and uniformity}, Title = {Combinatorial Models for Topology-Based Geometric Modeling}, Year = {2009}} @article{Mallet04, Author = {Jean-Laurent Mallet}, Journal = {Mathematical Geology}, Month = {January}, Number = {1}, Pages = {1--32}, Title = {Space--Time Mathematical Framework for Sedimentary Geology}, Volume = {36}, Year = {2004}} @article{Tossebro11, Author = {Erlend T{\o}ssebro and Mads Nyg{\aa}rd}, Journal = {Geoinformatica}, Pages = {633--661}, Title = {Representing topological relationships for spatiotemporal objects}, Volume = {15}, Year = {2011}} @inproceedings{Hansen01, Author = {Henning Sten Hansen}, Booktitle = {Proceedings of the 1st International Symposium on Digital Earth Moving}, Pages = {48--59}, Series = {Lecture Notes in Computer Science}, Title = {A Quasi-Four Dimensional Database for the Built Environment}, Volume = {2181}, Year = {2001}} @article{Pion11, Author = {Sylvain Pion and Andreas Fabri}, Journal = {Science of Computer Programming}, Number = {4}, Pages = {307--323}, Title = {A Generic Lazy Evaluation Scheme for Exact Geometric Computations}, Volume = {76}, Year = {2011}} @inproceedings{Held11, Author = {Martin Held and Willi Mann}, Booktitle = {Proceedings of the 23rd Canadian Conference on Computational Geometry}, Title = {An Experimental Analysis of Floating-Point Versus Exact Arithmetic}, Year = {2011}} @book{Manolopoulos06, Author = {Yannis Manolopoulos and Alexandros Nanopoulos and Apostolos N. Papadopoulos and Yannis Theodoridis}, Publisher = {Springer Berlin Heidelberg}, Series = {Advanced Information and Knowledge Processing}, Title = {R-Trees: Theory and Applications}, Year = {2006}} @inproceedings{Guttman84, Author = {Antonin Guttman}, Booktitle = {Proceedings of the 1984 ACM SIGMOD International Conference on Management of Data}, Pages = {47--57}, Title = {R-trees: A dynamic index structure for spatial searching}, Year = {1984}} @inproceedings{Beckmann90, Author = {Norbert Beckmann and Hans-Peter Kriegel and Ralf Schneider and Bernhard Seeger}, Booktitle = {Proceedings of the 1990 ACM SIGMOD International Conference on Management of Data}, Number = {322--330}, Title = {The {R}*-tree: An Efficient and Robust Access Method for Points and Rectangles}, Year = {1990}} @article{Bradley10, Author = {Patrick Erik Bradley and Norbert Paul}, Journal = {The Computer Journal}, Number = {1}, Pages = {69--89}, Title = {Using the Relational Model to Capture Topological Information of Spaces}, Volume = {53}, Year = {2010}} @inproceedings{Fradin02, Author = {David Fradin and Daniel Meneveaux and Pascal Lienhardt}, Booktitle = {Actes des XV\`emes journ\'ees de l'Association Fran\c{c}aise d'Informatique Graphique}, Number = {2}, Title = {Partition de l'espace et hi\'erarchie de cartes g\'en\'eralis\'ees: application aux complexes architecturaux}, Volume = {28}, Year = {2002}} @inproceedings{Paul10, Author = {N. Paul and M. Breunig and E Butwilowski and A. Thomsen}, Booktitle = {Proceedings of the 6th International Conference GIScience 2010}, Title = {n-D-Topological Data Structures: Some Theoretical and Pragmatic Considerations for GI-Science}, Year = {2010}} @inproceedings{Edelsbrunner85, Author = {Herbert Edelsbrunner and Raimund Seidel}, Booktitle = {Proceedings of the 1st Annual Symposium on Computational Geometry}, Pages = {251--262}, Title = {Voronoi diagrams and arrangements}, Year = {1985}} @article{Edelsbrunner90, Author = {Herbert Edelsbrunner and Ernst P. M\"ucke}, Journal = {ACM Transactions on Graphics}, Number = {1}, Pages = {66--104}, Title = {Simulation of Simplicity: A Technique to Cope with Degenerate Cases in Geometric Algorithms}, Volume = {9}, Year = {1990}} @inproceedings{Hert01, Author = {Susan Hert and Michael Hoffmann and Lutz Kettner and Sylvain Pion and Michael Seel}, Booktitle = {Proceedings of the Workshop on Algorithm Engineering}, Pages = {79--90}, Publisher = {Springer-Verlag}, Series = {Lecture Notes in Computer Science}, Title = {An Adaptable and extensible geometry kernel}, Volume = {2141}, Year = {2001}} @article{Thompson11, Author = {Rodney James Thompson and Peter {van Oosterom}}, Journal = {Geoinformatica}, Pages = {223-246}, Title = {Connectivity in the regular polytope representation}, Volume = {15}, Year = {2011}} @inproceedings{Rossignac96, Author = {Jarek R. Rossignac}, Booktitle = {SIGGRAPH 1996 Course Notes}, Title = {Specification, representation, and construction of non-manifold geometric structures}, Year = {1996}} @inproceedings{Stoter07, Author = {Jantien Stoter and Wilko Quak and Peter {van Oosterom} and Martijn Meijers and Rob Lemmens and Harry Uitermark}, Booktitle = {Proceedings of the 2nd International Symposium on Generalization of Information}, Pages = {1--18}, Title = {Considerations for the design of a semantic data model for a multi-representation topographical database}, Year = {2007}} @incollection{vanOosterom99, Author = {Peter {van Oosterom}}, Booktitle = {Geographical Information Systems: Principlesm Technical Issues, Management Issues and Applications}, Chapter = {2.3}, Editor = {Paul A. Longley and Michael F. Goodchild and David J. Maguire and David W. Rhind}, Pages = {385--400}, Publisher = {Wiley}, Title = {Spatial Access Methods}, Volume = {1}, Year = {1999}} @article{Kirkpatrick83, Author = {David Kirkpatrick}, Journal = {SIAM Journal on Computing}, Month = {February}, Number = {1}, Pages = {28--35}, Title = {Optimal Seach in Planar Subdivisions}, Volume = {12}, Year = {1983}} @inproceedings{Snoeyink97a, Author = {Jack Snoeyink and Marc {van Kreveld}}, Booktitle = {Proceedings of the 7th Annual European Symposium on Algorithms}, Pages = {459--471}, Publisher = {Springer-Verlag}, Series = {Lecture Notes in Computer Science}, Title = {Linear-time reconstruction of Delaunay triangulations with applications}, Volume = {1284}, Year = {1997}} @inproceedings{Snoeyink97, Author = {Jack Snoeyink and Marc {van Kreveld}}, Booktitle = {Proceedings of the 13th ACM Symposium on Computational Geometry}, Pages = {400--402}, Title = {Good orders for incremental (re)construction}, Year = {1997}} @inproceedings{vanKreveld97a, Author = {Marc van Kreveld}, Booktitle = {Proceedings of the 24th International Conference on Current Trends in Theory and Practice of Computer Science}, Pages = {19--36}, Publisher = {Springer-Verlag}, Series = {Lecture Notes in Computer Science}, Title = {Algorithms for Triangulated Terrains}, Volume = {1338}, Year = {1997}} @incollection{vanKreveld97, Address = {Berlin}, Author = {Marc van Kreveld}, Booktitle = {Algorithmic Foundations of Geographic Information Systems}, Chapter = {1}, Editor = {Marc van Kreveld and J\"urg Nievergelt and Thomas Roos and Peter Widmayer}, Pages = {37--78}, Publisher = {Springer-Verlag}, Series = {Lecture Notes in Computer Science}, Title = {Digital Elevation Models and {TIN} Algorithms}, Volume = {1340}, Year = {1997}} @article{Lien06, Author = {Jyh-Ming Lien and Nancy M. Amato}, Journal = {Computational Geometry: Theory \& Applications}, Pages = {100--123}, Title = {Approximate convex decomposition of polygons}, Volume = {35}, Year = {2006}} @inproceedings{Bulbul09a, Author = {Rizwan Bulbul and Andrew U. Frank}, Booktitle = {Proceedings of the 17th International Conference on Geoinformatics}, Pages = {1--6}, Title = {{AHD}: The Alternate Simplicial Decomposition of Nonconvex Polytopes (Generalization of a Convex Polytope Based Spatial Data Model)}, Year = {2009}} @phdthesis{Hachenberger06, Author = {Peter Hachenberger}, School = {Saarland University}, Title = {Boolean Operations on 3D Selective Nef Complexes Data Structure, Algorithms, Optimized Implementation, Experiments and Applications}, Year = {2006}} @techreport{Dobrint93, Author = {Katrin Dobrint and Kurt Mehlhorn and Mariette Yvinec}, Institution = {INRIA}, Month = {August}, Number = {2023}, Title = {A Complete and Efficient Algorithm for the Intersectionof a General and a Convez Polyhedron}, Year = {1993}} @phdthesis{Seel01, Author = {Michael Seel}, School = {Saarland University}, Title = {Planar Nef Polyhedra and Generic Higher-dimensional Geometry}, Year = {2001}} @inproceedings{Granados03, Author = {Miguel Granados and Peter Hachenberger and Susan Hert and Lutz Kettner and Kurt Mehlhorn and Michael Seel}, Booktitle = {Proceedings of the 11th Annual European Symposium on Algorithms}, Month = {September}, Pages = {174--186}, Title = {Boolean Operations on {3D} Selective Nef Complexes: Data Structure, Algorithms and Implementation}, Year = {2003}} @article{Paoluzzi93, Author = {A. Paoluzzi and F. Bernardini and C. Cattani and V. Ferrucci}, Journal = {ACM Transactions on Graphics}, Month = {January}, Number = {1}, Pages = {56--102}, Title = {Dimension-Independent Modeling with Simplicial Complexes}, Volume = {12}, Year = {1993}} @phdthesis{Pilouk96, Address = {The Netherlands}, Author = {Pilouk, Morakot}, School = {ITC}, Title = {Integrated modelling for {3D} {GIS}}, Year = {1996}} @incollection{vanOosterom10, Author = {Peter van Oosterom and Stoter, Jantien}, Booktitle = {Geographic Information Science: 6th International Conference, GIScience 2010, Zurich, Switzerland, September 14-17, 2010. Proceedings}, Editor = {Sara Irina Fabrikant and Tumasch Reichenbacher and Marc van Kreveld and Christoph Schlieder}, Pages = {311--324}, Publisher = {Springer Berlin Heidelberg}, Title = {{5D} Data Modelling: Full Integration of {2D}/{3D} Space, Time and Scale Dimensions}, Year = {2010}} @article{Stoter11a, Author = {Jantien Stoter and George Vosselman and Joris Goos and Sisi Zlatanova and Edward Verbree and Rick Klooster and Marcel Reuvers}, Journal = {Journal of Photogrammetry, Remote Sensing and Geoinformation Processing}, Pages = {405--420}, Title = {Towards a national {3D} Spatial Data Infrastructure: case of the Netherlands}, Volume = {6}, Year = {2011}} @inproceedings{Penninga05, Author = {Friso Penninga}, Booktitle = {Spatial Information Theory, COSIT 2005}, Pages = {409--425}, Title = {{3D} Topographic Data Modelling: Why Rigidity Is Preferable to Pragmatism}, Year = {2005}} @article{Torquato09, Author = {S. Torquato and Y. Jiao}, Journal = {Nature}, Pages = {876--879}, Title = {Dense packings of the Platonic and Archimedean solids}, Volume = {460}, Year = {2009}} @article{Muigg11, Author = {Phillip Muigg and Markus Hadwiger and Helmut Doleisch and Eduard Gr\"oller}, Journal = {IEEE Transactions on Visualization and Computer Graphics}, Month = {December}, Number = {12}, Pages = {2115--2124}, Title = {Interactive Volume Visualization of General Polyhedral Grids}, Volume = {17}, Year = {2011}} @incollection{Mesmoudi05, Author = {M. Mostefa Mesmoudi and Leila {de Floriani} and Franco Morando and Enrico Puppo}, Booktitle = {Advances in Multiresolution for Geometric Modelling}, Pages = {75--87}, Publisher = {Springer Berlin / Heidelberg}, Title = {An Algorithm for Decomposing Multi-dimensional Non-manifold Objects into Nearly Manifold Components}, Year = {2005}} @inproceedings{deFloriani02, Author = {Leila {de Floriani} and Mostefa Mohammed Mesmoudi and Franco Morando and Enrico Puppo}, Booktitle = {Proceedings of the 10th International Conference of Discrete Geometry for Computer Imagery}, Pages = {69--80}, Series = {Lecture Notes in Computer Science}, Title = {Non-manifold Decomposition in Arbitrary Dimensions}, Year = {2002}} @inproceedings{Lienhardt97, Author = {Pascal Lienhardt}, Booktitle = {Proceedings of the 7th International Workshop on Discrete Geometry for Computer Imagery}, Pages = {33--48}, Series = {Lecture Notes in Computer Science}, Title = {Aspects in topology-based geometric modeling. Possible tools for discrete geometry?}, Volume = {1347}, Year = {1997}} @inproceedings{Goodchild87, Author = {Michael F. Goodchild}, Booktitle = {Proceedings of the International GIS Symposium}, Pages = {66--77}, Title = {Towards an enumeration and classification of {GIS} functions}, Volume = {2}, Year = {1987}} @article{Burrough92, Author = {P. A. Burrough}, Journal = {Computers \& Geosciences}, Number = {4}, Pages = {395--400}, Title = {Are {GIS} data structures too simple minded?}, Volume = {18}, Year = {1992}} @inproceedings{Bru08, Author = {Antoine Bru and Monique Teillaud}, Booktitle = {Abstracts of the 24th European Workshop on Computational Geometry}, Pages = {95--98}, Title = {Generic Implementation of a Data Structure for 3D Regular Complexes}, Year = {2008}} @inproceedings{Damiand03, Author = {Guillaume Damiand and Pascal Lienhardt}, Booktitle = {Proceedings of the 11th Discrete Geometry for Computer Imagery}, Pages = {408--419}, Title = {Removal and Contraction for $n$-Dimensional Generalized Maps}, Volume = {2886}, Year = {2003}} @article{Grasset-Simon06, Author = {Carine Grasset-Simon and Guillaume Damiand and Pascal Lienhardt}, Journal = {Pattern Recognition}, Number = {4}, Pages = {527--538}, Title = {nD generalized map pyramids: definition, representations and basic operations}, Volume = {39}, Year = {2006}} @book{Kaczynski04, Author = {Tomasz Kaczynski and Konstantin Mischaikow and Marian Mrozek}, Publisher = {Springer Berlin / Heidelberg}, Title = {Computational Homology}, Year = {2004}} @inproceedings{Alayrangues09, Author = {Sylvie Alayrangues and Samuel Peltier and Guillaume Damiand and Pascal Lienhardt}, Booktitle = {Proceedings of the 15th International Conference on Discrete Geometry for Computer Imagery}, Pages = {300--312}, Series = {Lecture Notes in Computer Science}, Title = {Border Operator for Generalized Maps}, Volume = {5810}, Year = {2009}} @article{Dahmen82, Author = {Wolfgang A. Dahmen and Charles A. Micchelli}, Journal = {SIAM Journal on Numerical Analysis}, Number = {5}, Pages = {993--1012}, Title = {On the Linear Independence of Multivariate B-Splines, I. Triangulations of Simploids}, Volume = {19}, Year = {1982}} @inproceedings{Lienhardt99, Author = {Pascal Lienhardt and Laurent Fuchs and Yves Bertrand}, Booktitle = {Proceedings of the Eurographics Workshop on Graphics and Visualization Education}, Pages = {39--44}, Title = {A course in Topology-based Geometric Modeling}, Year = {1999}} @article{Pearson01, Author = {Karl Pearson}, Journal = {Philosophical Magazine}, Number = {6}, Pages = {559-572}, Title = {On Lines and Planes of Closest Fit to Systems of Points in Space}, Volume = {2}, Year = {1901}} @inproceedings{vanOosterom97, Author = {Peter {van Oosterom}}, Booktitle = {Proceedings of Auto-Carto 13}, Title = {Maintaining Consistent Topology Including Historical Data in a Large Spatial Database}, Year = {1997}} @inproceedings{vanOosterom06a, Author = {Peter {van Oosterom} and Hendrik Ploeger and Jantien Stoter and Rod Thompson and Christiaan Lemmen}, Booktitle = {Proceedings of the XXIII International FIG congress}, Title = {Aspects of a 4D Cadastre: A First Exploration}, Year = {2006}} @article{Goodchild92, Author = {Michael F. Goodchild}, Journal = {Computers \& Geosciences}, Number = {4}, Pages = {401--408}, Title = {Geographical Data Modeling}, Volume = {18}, Year = {1992}} @phdthesis{Ledoux06, Author = {Hugo Ledoux}, Month = {November}, School = {University of Glamorgan}, Title = {Modelling Three-dimensional Fields in Geoscience with the Voronoi Diagram and its Dual}, Year = {2006}} @phdthesis{Penninga08, Author = {F. Penninga}, School = {Delft University of Technology}, Title = {{3D} Topography A Simplicial Complex Solution-based Solution in a Spatial {DBMS}}, Year = {2008}} @phdthesis{Thompson07, Author = {R.J. Thompson}, School = {Delft University of Technology}, Title = {Towards a rigorous logic for spatial data representation}, Year = {2007}} @inproceedings{Pigot91, Author = {Simon Pigot}, Booktitle = {Proceedings of Auto-Carto 10}, Pages = {368--392}, Title = {Topological Models for {3D} Spatial Information Systems}, Year = {1991}} @article{Arens05, Author = {C\v{a}lin Arens and Jantien Stoter and Peter {van Oosterom}}, Journal = {Computers \& Geosciences}, Pages = {165--177}, Title = {Modelling {3D} spatial objects in a geo-{DBMS} using a {3D} primitive}, Volume = {31}, Year = {2005}} @manual{Shapefile, Author = {{ESRI}}, Month = {July}, Organization = {{ESRI}}, Title = {Shapefile Technical Description}, Year = {1998}} @manual{SimpleFeatures2, Author = {{OGC}}, Month = {August}, Organization = {{Open Geospatial Consortium}}, Title = {{OpenGIS} Implementation Specification for Geographic Information - Simple Feature Access - Part 2: SQL option. Version 1.2.1}, Year = {2010}} @manual{CityGML2, Author = {Gerhard Gr\"oger and Thomas H. Kolbe and Claus Nagel and Karl-Heiz H\"afele}, Month = {April}, Organization = {Open Geospatial Consortium}, Title = {{OGC} {C}ity {G}eography {M}arkup {L}anguage {(CityGML)} Encoding Standard. Version 2.0.0}, Year = {2012}} @manual{KML, Author = {{OGC}}, Edition = {2.2.0}, Month = {April}, Organization = {{Open Geospatial Consortium}}, Title = {OGC KML}, Year = {2008}} @manual{SimpleFeatures1, Author = {{OGC}}, Month = {May}, Organization = {{Open Geospatial Consortium}}, Title = {{OpenGIS} Implementation Specification for Geographic Information - Simple Feature Access - Part 1: Common Architecture. Version 1.2.1}, Year = {2011}} @article{Jacques70, Author = {A. Jacques}, Journal = {Combinatorial Theory and Applications}, Pages = {657-673}, Title = {Constellations et Graphes Topologiques}, Volume = {2}, Year = {1970}} @inproceedings{Kriegel91, Author = {Hans-Peter Kriegel and Holger Horn and Michael Schiwietz}, Booktitle = {Proceedings of the 2nd International Symposium on Advances in Spatial Databases}, Title = {The Performance of Object Decomposition Techniques for Spatial Query Processing}, Year = {1991}} @inproceedings{Bulbul09, Author = {Rizwan Bulbul and Farid Karimipour and Andrew U. Frank}, Booktitle = {Proceedings of Geocomputation 2009}, Title = {A Simplex based Dimension Independent Approach for Convex Decomposition of Nonconvex polytopes}, Year = {2009}} @book{Grunbaum67, Author = {Branko Gr\"unbaum}, Publisher = {John Wiley}, Title = {Convex polytopes}, Year = {1967}} @inproceedings{Hazelton90, Author = {N.W.J. Hazelton and F.J. Leahy and I.P. Williamson}, Booktitle = {Proceedings of GIS/LIS'90}, Title = {On the design of temporally-referenced, 3-{D} geographical information systems: development of four-dimensional {GIS}}, Year = {1990}} @phdthesis{Chazelle80, Author = {Bernard Chazelle}, School = {Yale University}, Title = {Computational Geometry and Complexity}, Year = {1980}} @article{Chazelle84, Author = {Bernard Chazelle}, Journal = {SIAM Journal on Computing}, Number = {3}, Pages = {488--507}, Title = {Convex partitions of polyhedra: a lower bound and worst-case optimal algorithm}, Volume = {13}, Year = {1984}} @techreport{Bajaj90, Author = {Chanderjit Bajaj and Tamal K. Dey}, Institution = {Purdue University}, Title = {Convex Decomposition of Polyhedra and Robustness}, Year = {1990}} @incollection{Chazelle85, Author = {Bernard Chazelle and David P. Dobkin}, Booktitle = {Computational Geometry}, Pages = {63--133}, Publisher = {Elsevier}, Title = {Optimal Convex Decompositions}, Year = {1985}} @article{Voelcker77, Author = {H.B. Voelcker and A.A.G. Requicha}, Journal = {Computer}, Number = {12}, Pages = {48--57}, Title = {Geometric Modeling of Mechanical Parts and Processes}, Volume = {10}, Year = {1977}} @manual{ISO19107:2003, Author = {{ISO}}, Month = {March}, Organization = {{International Organization for Standardization}}, Title = {Geographic Information --- Spatial Schema}, Year = {2003}} @phdthesis{Albrecht95, Author = {Jochen Albrecht}, School = {University of Vechta}, Title = {Universal Analytical GIS Operations. A Task-Oriented Systematization of Data Structure-Independent GIS Functionality Leading Towards a Geographic Modeling Language}, Year = {1995}} @article{Dollner00, Author = {J\"urgen D\"ollner and Klaus Hinrichs}, Journal = {Computers \& Geosciences}, Month = {February}, Number = {1}, Pages = {67--76}, Title = {An object-oriented approach for integrating {3D} visualization systems and {GIS}}, Volume = {26}, Year = {2000}} @article{Schon09, Author = {Bianca Sch\"on and Debra Laefer and Sean W. Morrish and Michela Bertolotto}, Journal = {Recent Patents on Computer Science}, Pages = {21--31}, Title = {Three-Dimensional Spatial Information Systems: State of the Art Review}, Volume = {2}, Year = {2009}} @article{Karimipour10, Author = {Farid Karimipour and Mahmoud R. Delavar and Andrew U. Frank}, Journal = {Computers \& Geosciences}, Month = {September}, Number = {9}, Pages = {1123--1134}, Title = {A simplex-based approach to implement dimension independent spatial analyses}, Volume = {36}, Year = {2010}} @article{Ellul06, Author = {Claire Ellul and Muki Haklay}, Journal = {Transactions in GIS}, Month = {March}, Number = {2}, Pages = {157--175}, Title = {Requirements for Topology in {3D} {GIS}}, Volume = {10}, Year = {2006}} @article{vanOosterom09, Author = {Peter {van Oosterom}}, Journal = {Computers, Environment and Urban Systems}, Number = {5}, Pages = {303--310}, Title = {Research and development in geo-information generalisation and multiple representation}, Volume = {33}, Year = {2009}} @inproceedings{Stoter03, Author = {Jantien Stoter and Siyka Zlatanova}, Booktitle = {Proceedings of the ISPRS Joint Workshop on Spatial, Temporal and Multi-Dimensional Data Modelling and Analysis}, Month = {October}, Title = {{3D} {GIS}, where are we standing?}, Year = {2003}} @incollection{Tet-Khuan07, Author = {Chen Tet-Khuan and Alias Abdul-Rahman and Sisi Zlatanova}, Booktitle = {Computational Science and Its Applicaction --- ICCSA 2007}, Pages = {151--163}, Publisher = {Springer Berlin / Heidelberg}, Series = {Lecture Notes in Computer Science}, Title = {{3D} Spatial Operations in Geo {DBMS} Environment for {3D} {GIS}}, Volume = {4705}, Year = {2007}} @article{Bentley75, Author = {Jon Louis Bentley}, Journal = {Communications of the ACM}, Number = {9}, Pages = {509--517}, Title = {Multidimensional binary search trees used for associative searching}, Volume = {18}, Year = {1975}} @article{Finkel74, Author = {Raphael Finkel and J.L. Bentley}, Journal = {Acta Informatica}, Number = {1}, Pages = {1--9}, Title = {Quad Trees: A Data Structure for Retrieval on Composite Keys}, Volume = {4}, Year = {1974}} @article{Hales92, Author = {Thomas C. Hales}, Journal = {Journal of Computational and Applied Mathematics}, Month = {December}, Number = {1}, Pages = {41--76}, Title = {The sphere packing problem}, Volume = {44}, Year = {1992}} @phdthesis{vanOosterom90, Author = {Peter {van Oosterom}}, School = {Leiden University}, Title = {Reactive Data Structures for Geographic Information Systems}, Year = {1990}} @article{Stoter11, Author = {Jantien Stoter and Thomas Visser and Peter {van Oosterom} and Wilko Quak and Nico Bakker}, Journal = {International Journal of Geographical Information Science}, Number = {5}, Pages = {739--763}, Title = {A semantic-rich multi-scale information model for topography}, Volume = {25}, Year = {2011}} @article{Frank94, Author = {Andrew U. Frank and Sabine Timpf}, Journal = {Computers \& Graphics}, Number = {6}, Pages = {823--829}, Title = {Multiple representations for cartographic objects in a multi-scale tree: An intelligent graphical zoom}, Volume = {18}, Year = {1994}} @article{Stoter09, Author = {Jantien Stoter and Dirk Burghardt and C\'ecile Duch\^ene and Blanca Baella and Nico Bakker and Connie Blok and Maria Pla and Nicolas Regnauld and Guillaume Touya and Stefan Schmid}, Journal = {Computers, Environment and Urban Systems}, Number = {5}, Pages = {311--324}, Title = {Methodology for evaluating automated map generalization in commercial software}, Volume = {33}, Year = {2009}} @article{Douglas73, Author = {David H. Douglas and Thomas K. Peucker}, Journal = {Cartographica: The International Journal for Geographic Information and Geovisualization}, Month = {December}, Number = {2}, Pages = {112--122}, Title = {Algorithms for the reduction of the number of points required to represent a digitized line or its caricature}, Volume = {10}, Year = {1973}} @phdthesis{Cecconi03, Author = {Alessandro Cecconi}, School = {University of Zurich}, Title = {Integration of Cartographic Generalization and Multi-Scale Databases for Enhanced Web Mapping}, Year = {2003}} @article{Haunert09, Author = {Jan-Henrik Haunert and Arta Dilo and Peter {van Oosterom}}, Journal = {Computers \& Geosciences}, Pages = {2191--2203}, Title = {Constrained set-up of the {tGAP} structure for progressive vector data transfer}, Volume = {35}, Year = {2009}} @article{Shaw02, Author = {Gary Shaw and Dimitris Manolakis}, Journal = {IEEE Signal Processing Magazine}, Month = {January}, Number = {1}, Pages = {12--16}, Title = {Signal processing for hyperspectral image exploitation}, Volume = {19}, Year = {2002}} @article{Schultz01, Author = {Roger A. Schultz and Thomas Nielsen and Jeff R. Zavaleta and Raynal Ruch and Robert Wyatt and Harold R. Garner}, Journal = {Cytometry}, Month = {April}, Number = {4}, Pages = {239--247}, Title = {Hyperspectral imaging: A novel approach for microscopic analysis}, Volume = {43}, Year = {2001}} @inproceedings{Corbett75, Author = {James P. Corbett}, Booktitle = {Proceedings of Auto-Carto II}, Pages = {61--65}, Title = {Topological Principles in Cartography}, Year = {1975}} @article{Frank92, Author = {Frank, Andrew U.}, Journal = {Computers \& Geosciences}, Number = {4}, Pages = {409--417}, Title = {Spatial concepts, geometric data models, and geometric data structures}, Volume = {18}, Year = {1992}} @article{Peuquet94, Author = {Donna J. Peuquet}, Journal = {Annals of the Association of American Geographers}, Number = {3}, Pages = {441--461}, Title = {It's About Time: A Conceptual Framework for the Representation of Temporal Dynamics in Geographic Information Systems}, Volume = {84}, Year = {1994}} @book{Akhundov86, Author = {Murad Davudovich Akhundov}, Month = nov, Publisher = {MIT Press}, Title = {Conceptions of space and time: sources, evolution, directions}, Year = {1986}} @book{Peuquet02, Author = {Donna J. Peuquet}, Publisher = {Guilford Press}, Title = {Representations of Space and Time}, Year = {2002}} @incollection{Abdul-Rahman08, Author = {Alias Abdul-Rahman and Morakot Pilouk}, Booktitle = {Spatial data modelling for 3D GIS}, Chapter = {2}, Pages = {15--23}, Publisher = {Springer Berlin / Heidelberg}, Title = {An Overview of {3D} {GIS} Development}, Year = {2008}} @article{Zhang11, Author = {Yeting Zhang and Qing Zhu and Gang Liu and Wenting Zheng and Zhonghua Li and Zhiqiang Du}, Journal = {Geo-Spatial Information Science}, Number = {2}, Pages = {150--156}, Title = {{GeoScope}: Full {3D} geospatial information system case study}, Volume = {14}, Year = {2011}} @book{Lee99, Author = {Kunwoo Lee}, Publisher = {Prentice Hall}, Title = {Principles of {CAD}/{CAM}/{CAE}}, Year = {1999}} @book{Kalay04, Author = {Yehuda E. Kalay}, Publisher = {MIT Press}, Title = {Architecture's New Media: Principles, Theories and Methods of Computer-Aided Design}, Year = {2004}} @article{Gold06, Author = {Christopher M. Gold}, Journal = {Transactions in GIS}, Number = {4}, Pages = {505--519}, Title = {What is {GIS} and What is Not?}, Volume = {10}, Year = {2006}} @book{Jowett98, Author = {Plato}, Editor = {Jowett, Benjamin}, Publisher = {Project Gutemberg}, Title = {Plato's Timaeus}, Year = {1998}} @article{Chrisman88, Author = {Nicholas R. Chrisman}, Journal = {The American Cartographer}, Number = {3}, Pages = {291--300}, Title = {The Risks of Software Innovation: A Case Study of the {H}arvard Lab}, Volume = {15}, Year = {1988}} @article{Tomlinson88, Author = {R.F. Tomlinson}, Journal = {The American Cartographer}, Month = {July}, Number = {3}, Pages = {249--261}, Title = {The Impact of the Transition From Analogue to Digital Cartographic Representation}, Volume = {15}, Year = {1988}} @article{Dupin26, Author = {Charles Dupin}, Journal = {Jobard}, Title = {Carte figurative de l'instruction populaire de la {F}rance}, Year = {1826}} @article{Braid75, Author = {I.C. Braid}, Journal = {Communications of the ACM}, Number = {4}, Pages = {209--216}, Title = {The Synthesis of Solids Bounded by Many Faces}, Volume = {18}, Year = {1975}} @article{Harrell92, Author = {James E. Harrell and V. Max Brown}, Journal = {Journal of the American Research Center in Egypt}, Pages = {81--105}, Title = {The oldest surviving topographical map from ancient Egypt (Turin Papyri 1879, 1899 and 1969)}, Volume = {29}, Year = {1992}} @article{Finkel95, Author = {I.L. Finkel}, Journal = {British Museum Magazine: the-5}, Pages = {26--27}, Title = {A join to the Map of the World: a notable discovery}, Volume = {Winter}, Year = {1995}} @incollection{Coppock91, Author = {J.T. Coppock and D.W. Rhind}, Booktitle = {Geographical Information Systems: Principles and Applications}, Chapter = {2}, Editor = {Maguire, D.J. and Goodchild, M.F. and Rhind, D.W.}, Pages = {21--43}, Publisher = {Longman Scientific \& Technical}, Title = {The History of {GIS}}, Volume = {1}, Year = {1991}} @article{Li94, Author = {Zhilin Li}, Journal = {The Cartographic Journal}, Number = {1}, Pages = {50--51}, Title = {Reality in time-scale systems and cartographic representation}, Volume = {31}, Year = {1994}} @article{Muller78, Author = {D. E. Muller and F. P. Preparata}, Journal = {Theoretical Computer Science}, Number = {2}, Pages = {217--236}, Title = {Finding the intersection of two convex polyhedra}, Volume = {7}, Year = {1978}} @article{Rambau05, Author = {J\"org Rambau}, Journal = {Combinatorial and Computational Geometry}, Pages = {501--516}, Title = {On a Generalization of Sch\"onhardt's Polyhedron}, Volume = {52}, Year = {2005}} @inproceedings{Isenburg00, Author = {Martin Isenburg and Jack Snoeyink}, Booktitle = {Proceedings of SIGGRAPH 2000}, Month = {July}, Pages = {263--270}, Title = {Face Fixer: Compressing Polygon Meshes with Properties}, Year = {2000}} @inproceedings{Amenta03, Address = {San Diego, USA}, Author = {Amenta, Nina and Choi, Sunghee and Rote, G\"unter}, Booktitle = {Proceedings 19th Annual Symposium on Computational Geometry}, Pages = {211--219}, Publisher = {ACM Press}, Title = {{I}ncremental constructions con {BRIO}}, Year = {2003}} @article{Worboys90, Author = {Michael F. Worboys and Hilary M. Hearnshaw and David J. Maguire}, Journal = {International Journal of Geographical Information Systems}, Number = {4}, Pages = {369--383}, Title = {Object-Oriented Data Modelling for Spatial Databases}, Volume = {4}, Year = {1990}} @incollection{Claramunt99, Author = {Christophe Claramunt and Christine Parent and Stefano Spaccapietra and Marius Th\'eriault}, Booktitle = {Geographical Information and Planning}, Chapter = {10}, Editor = {John Charles Harold Stillwell and Stan Geertman and Stan Openshaw}, Pages = {181--202}, Publisher = {Springer Berlin / Heidelberg}, Series = {Advances in Spatial Science}, Title = {Database Modelling for Environmental and Land Use Changes}, Year = {1999}} @article{Worboys94a, Author = {Michael F. Worboys}, Journal = {International Journal of Geographical Information Science}, Number = {4}, Pages = {385--399}, Title = {Object-oriented approaches to geo-referenced information}, Volume = {8}, Year = {1994}} @article{Chen76, Author = {Pin-Shan Chen}, Journal = {ACM Transactions on Database Systems}, Number = {1}, Pages = {9--36}, Title = {The Entity-Relationship Model---Toward a Unified View of Data}, Volume = {1}, Year = {1976}} @inproceedings{Story95, Author = {P. A. Story and Michael F. Worboys}, Booktitle = {Spatial Information Theory: A Theoretical Basis for GIS}, Editor = {Andrew U. Frank and Werner Kuhn}, Pages = {413--430}, Publisher = {Springer Berlin / Heidelberg}, Series = {Lecture Notes in Computer Science}, Title = {A design support environment for spatio-temporal database applications}, Volume = {988}, Year = {1995}} @article{Tryfona99, Author = {Nectaria Tryfona and Christian S. Jensen}, Journal = {GeoInformatica}, Number = {3}, Pages = {245--268}, Title = {Conceptual Data Modeling for Spatiotemporal Applications}, Volume = {3}, Year = {1999}} @article{Renolen96, Author = {A. Renolen}, Journal = {GIS Frontiers in Business and Science}, Title = {History graphs: conceptual modeling of spatio-temporal data}, Volume = {2}, Year = {1996}} @inproceedings{Claramunt95, Author = {Christophe Claramunt and Marius Th\'eriault}, Booktitle = {Proceedings of the International Workshop on Temporal Databases}, Editor = {James Clifford and Alexander Tuzhilin}, Pages = {23--42}, Title = {Managing Time in {GIS}: An Event-Oriented Approach}, Year = {1995}} @inproceedings{Yuan94, Author = {May Yuan}, Booktitle = {Proceedings of GIS/LIS'94}, Pages = {860--869}, Title = {Wildfire Conceptual Modeling for Building {GIS} Space-Time Models}, Year = {1994}} @article{Peuquet95, Author = {Donna J. Peuquet and Niu Duan}, Journal = {International Journal of Geographical Information Science}, Number = {1}, Pages = {7--24}, Title = {An event-based spatiotemporal data model {(ESTDM)} for temporal analysis of geographical data}, Volume = {9}, Year = {1995}} @article{Hunter90, Author = {Gary J. Hunter and Ian P. Williamson}, Journal = {International Journal of Geographical Information Systems}, Number = {2}, Pages = {169--179}, Title = {The development of a historical cadastral database}, Volume = {4}, Year = {1990}} @article{Galton04, Author = {Galton, Antony}, Journal = {Spatial Cognition and Computation}, Number = {1}, Pages = {39--68}, Title = {Fields and objects in space, time, and space-time}, Volume = {4}, Year = {2004}} @inproceedings{Snodgrass85, Author = {Richard T. Snodgrass and Ilso Ahn}, Booktitle = {Proceedings of the 1985 ACM SIGMOD International Conference on Management of Data}, Title = {A taxonomy of time databases}, Year = {1985}} @article{Chrisman83, Author = {Nicholas R. Chrisman}, Journal = {Cartographica}, Title = {The Role of Quality Information in the Long-term Functioning of a Geographic Information System}, Year = {1983}} @article{Peucker75, Author = {Thomas K. Peucker and Nicholas R. Chrisman}, Journal = {The American Cartographer}, Number = {1}, Pages = {55--69}, Title = {Cartographic Data Strutures}, Volume = {2}, Year = {1975}} @article{Bolour83, Author = {A. Bolour and L. J. Dekeyser}, Journal = {Information Systems}, Number = {1}, Pages = {41--49}, Title = {Abstractions in temporal information}, Volume = {8}, Year = {1983}} @article{Al-Taha94, Author = {Khaled K. Al-Taha and Richard T. Snodgrass and Michael D. Soo}, Journal = {International Journal of Geographical Information Systems}, Number = {1}, Pages = {95--103}, Title = {Bibliography on spatiotemporal databases}, Volume = {8}, Year = {1994}} @incollection{Basoglu78, Author = {Umit Basoglu and Joel Morrison}, Booktitle = {Harvard Papers on Geographic Information Systems}, Editor = {Geoffrey Dutton}, Publisher = {Addison-Wesley}, Title = {The efficient hierarchical data Structure for the {US} Historical Boundary File}, Volume = {4}, Year = {1978}} @book{Muehrcke78, Author = {Phillip C. Muehrcke}, Publisher = {JP Publications}, Title = {Map Use}, Year = {1978}} @article{Langran88, Author = {Gail Langran and Nicholas R. Chrisman}, Journal = {Cartographica}, Number = {3}, Pages = {1--14}, Title = {A Framework for Temporal Geographic Informations}, Volume = {25}, Year = {1988}} @article{Groger11, Author = {Gerhard Gr\"oger and Lutz Pl\"umer}, Journal = {Geoinformatica}, Title = {Provably correct and complete transaction rules for updating {3D} city models}, Year = {2011}} @article{Egenhofer91, Author = {Max J. Egenhofer and R. D. Franzosa}, Journal = {International Journal of Geographical Information Systems}, Number = {2}, Pages = {161--174}, Title = {Point-set topological spatial relations}, Volume = {5}, Year = {1991}} @techreport{Egenhofer94, Author = {Max J. Egenhofer and David M. Mark and John Herring}, Institution = {National Center for Geographic Information and Analysis}, Number = {94-1}, Title = {The 9-Intersection: Formalism and its Use for Natural-Language Spatial Predicates}, Year = {1994}} @inproceedings{Cheng99, Author = {Siu-Wing Cheng and Tamal K. Dey and Herbert Edelsbrunner and Michael A. Facello and Shang-Fua Teng}, Booktitle = {Proceedings of the 15th Annual Symposium on Computational Geometry}, Title = {Sliver Exudation}, Year = {1999}} @inproceedings{Rossignac89, Author = {J. Rossignac and M. O'Connor}, Booktitle = {Proceedings of the IFIP Workshop on CAD/CAM}, Editor = {M. Wosny and J. Turner and K. Preiss}, Pages = {145--180}, Title = {{SGC}: A Dimension-Independent Model for Pointsets with Internal Structures and Incomplete Boundaries}, Year = {1989}} @article{Sohanpanah89, Author = {Cathy Sohanpanah}, Journal = {Computers \& Graphics}, Number = {1}, Pages = {17--23}, Title = {Extension of a Boundary Representation Technique for the Description of $n$ Dimensional Polytopes}, Volume = {13}, Year = {1989}} @incollection{Weiler88, Author = {Kevin Weiler}, Booktitle = {Geometric modeling for CAD applications: selected and expanded papers from the IFIP WG 5.2 working conference}, Editor = {M.J. Wozny and H.W. McLaughlin}, Month = {May}, Pages = {3--36}, Publisher = {Elsevier}, Title = {The radial edge data structure: a topological representation for non-manifold geometric boundary modeling}, Year = {1988}} @article{Johnson84, Author = {W. Johnson and J. Lindenstrauss}, Journal = {Contemporary Mathematics}, Pages = {189--206}, Title = {Extensions of Lipschitz mappings into a Hilbert space}, Volume = {26}, Year = {1984}} @inproceedings{Si06, Author = {Hang Si}, Booktitle = {Proceedings of the 15th International Meshing Roundtable}, Pages = {509--528}, Title = {On Refinement of Constrained {D}elaunay Tetrahedralizations}, Year = {2006}} @inproceedings{Si05, Author = {Hang Si and Klaus G\"artner}, Booktitle = {Proceedings of the 14th International Meshing Roundtable}, Month = {September}, Title = {Meshing Piecewise Linear Complexes by Constrained {D}elaunay Tetrahedralizations}, Year = {2005}} @incollection{Lee91, Author = {Carl W. Lee}, Booktitle = {Applied Geometry and Discrete Mathematics: The Victor Klee Festschrift}, Editor = {P. Gritzmann and B. Sturmfels}, Pages = {443--456}, Publisher = {American Mathematical Society}, Series = {DIMACS Series in Discrete Mathematics}, Title = {Regular Triangulations of Convex Polytopes}, Volume = {4}, Year = {1991}} @inproceedings{Edelsbrunner92, Author = {Herbert Edelsbrunner and N. R. Shah}, Booktitle = {Proceedings of the 8th Annual Symposium on Computational Geometry}, Pages = {43--52}, Publisher = {ACM}, Title = {Incremental topological flipping works for regular triangulations}, Year = {1992}} @incollection{Clarkson92, Author = {Kenneth L. Clarkson and Kurt Mehlhorn and Raimund Seidel}, Booktitle = {Proceedings of the 9th Annual Symposium on Theoretical Aspects of Computer Science}, Editor = {Finkel, Alain and Jantzen, Matthias}, Pages = {461--474}, Publisher = {Springer Berlin Heidelberg}, Series = {Lecture Notes in Computer Science}, Title = {Four results on randomized incremental constructions}, Volume = {577}, Year = {1992}} @incollection{Agarwal05, Author = {Pankaj K. Agarwal and Lars Arge and Ke Yi}, Booktitle = {Proceedings of the 13th Annual European Symposium}, Editor = {Brodal, Gerth and Leonardi, Stefano}, Pages = {355--366}, Publisher = {Springer Berlin / Heidelberg}, Series = {Lecture Notes in Computer Science}, Title = {{I/O}-Efficient Construction of Constrained {D}elaunay Triangulations}, Volume = {3669}, Year = {2005}} @article{Murphy01, Author = {Michael Murphy and David M. Mount and Carl W. Gable}, Journal = {International Journal of Computational Geometry and Applications}, Number = {6}, Pages = {669--682}, Title = {A Point-Placement Strategy for Conforming Delaunay Tetrahedralization}, Volume = {11}, Year = {2001}} @article{Cohen-Steiner04, Author = {David Cohen-Steiner and \'Eric Colin {de Verdi\`ere} and Mariette Yvinec}, Journal = {Computational Geometry: Theory \& Applications}, Pages = {217--233}, Title = {Conforming {D}elaunay Triangulations in 3D}, Volume = {28}, Year = {2004}} @inproceedings{Shewchuk98a, Author = {Jonathan Richard Shewchuk}, Booktitle = {Proceedings of the 14th Annual Symposium on Computational Geometry}, Month = {June}, Pages = {86--95}, Publisher = {ACM}, Title = {Tetrahedral mesh generation by Delaunay refinement}, Year = {1998}} @inproceedings{Saalfeld91, Author = {A. Saalfeld}, Booktitle = {Proceedings of the 3rd Canadian Conference on Computational Geometry}, Pages = {33--36}, Title = {Delaunay edge refinements}, Year = {1991}} @article{Dirichlet50, Author = {Gustav Lejeune Dirichlet}, Journal = {Journal f\"ur die Reine und Angewandte Mathematik}, Pages = {209--227}, Title = {\"Uber die {R}eduktion der positiven quadratischen {F}ormen mit drei unbestimmten ganzen {Z}ahlen}, Volume = {40}, Year = {1850}} @article{Voronoi08, Author = {Georges Voronoi}, Journal = {Journal f\"ur die Reine und Angewandte Mathematik}, Pages = {97--178}, Title = {Nouvelles applications des param\`etres continus \`a la th\'eorie des formes quadratiques. {P}remier M\'emoire. {S}ur quelques propri\'et\'es des formes quadratiques positives parfaites}, Volume = {133}, Year = {1908}} @article{Delaunay34, Author = {Boris N. Delaunay}, Journal = {Otdelenie Matematicheskikh i Estestvennykh Nauk}, Pages = {793--800}, Title = {Sur la sph\`ere vide}, Volume = {6}, Year = {1934}} @article{Hansen92, Author = {Andrew J. Hansen and Peter L. Levin}, Journal = {Advances in Engineering Software}, Pages = {129--135}, Title = {On Conforming Delaunay Mesh Generation}, Volume = {14}, Year = {1992}} @article{Edelsbrunner93, Author = {Herbert Edelsbrunner and Tiow Seng Tan}, Journal = {Discrete \& Computational Geometry}, Number = {2}, Pages = {197--213}, Title = {An Upper Bound for Conforming {D}elaunay Triangulations}, Volume = {10}, Year = {1993}} @article{Brown79, Author = {K. Q. Brown}, Journal = {Information Processing Letters}, Number = {5}, Pages = {223--228}, Title = {Voronoi diagrams from convex hulls}, Volume = {9}, Year = {1979}} @article{Guibas92, Author = {Leonidas J. Guibas and Donald E. Knuth and Micha Sharir}, Journal = {Algorithmica}, Pages = {381--413}, Title = {Randomized Incremental Construction of Delaunay and Voronoi Diagrams}, Volume = {7}, Year = {1992}} @article{Green78, Author = {P. J. Green and R. Sibson}, Journal = {The Computer Journal}, Number = {2}, Pages = {168--173}, Title = {Computing {D}irichlet Tessellations in the Plane}, Volume = {21}, Year = {1978}} @inproceedings{Seidel86, Author = {Raimund Seidel}, Booktitle = {Proceedings of the 18th Annual Symposium on the Theory of Computing}, Pages = {404--413}, Title = {Constructing Higher-Dimensional Convex Hulls at Logarithmic Cost per Face}, Year = {1986}} @article{Dwyer91, Author = {Rex A. Dwyer}, Journal = {Discrete \& Computational Geometry}, Pages = {343--367}, Title = {Higher-Dimensional {V}oronoi Diagrams in Linear Expected Time}, Volume = {6}, Year = {1991}} @article{Dwyer87, Author = {Rex A. Dwyer}, Journal = {Algorithmica}, Number = {1--4}, Pages = {137--151}, Title = {A Faster Divide-and-Conquer Algorithm for Constructing {D}elaunay Triangulations}, Volume = {2}, Year = {1987}} @article{Tanemura83, Author = {Masaharu Tanemura and Tohru Ogawa and Naofumi Ogita}, Journal = {Journal of Computational Physics}, Number = {2}, Pages = {191--207}, Title = {A new algorithm for three-dimensional Voronoi tessellation}, Volume = {51}, Year = {1983}} @inproceedings{Devillers98, Author = {Olivier Devillers}, Booktitle = {Proceedings of the 14th Annual Symposium on Computational Geometry}, Pages = {106--115}, Title = {Improved Incremental Randomized {D}elaunay Triangulation}, Year = {1998}} @article{Lee80, Author = {D. T. Lee and B. J. Schachter}, Journal = {International Journal of Computer and Information Sciences}, Number = {3}, Pages = {219--242}, Title = {Two Algorithms for Constructing a Delaunay Triangulation}, Volume = {9}, Year = {1980}} @inproceedings{Mucke96, Address = {New York, NY, USA}, Author = {Ernst P. M\"ucke and Isaac Saias and Binhai Zhu}, Booktitle = {Proceedings of the 12th Annual Symposium on Computational Geometry}, Pages = {274--283}, Publisher = {ACM}, Title = {Fast Randomized Point Location Without Preprocessing in Two- and Three-dimensional Delaunay Triangulations}, Year = {1996}} @article{Boissonnat02, Author = {Jean-Daniel Boissonnat and Olivier Devillers and Sylvain Pion and Monique Teillaud and Mariette Yvinec}, Journal = {Computational Geometry: Theory \& Applications}, Pages = {5--19}, Title = {Triangulations in {CGAL}}, Volume = {22}, Year = {2002}} @article{Barber96, Author = {C. Bradford Barber and David P. Dobkin and Hannu Huhdanpaa}, Journal = {ACM Transactions on Mathematical Software}, Month = {December}, Number = {4}, Pages = {469--483}, Title = {The {Q}uickhull Algorithm for Convex Hulls}, Volume = {22}, Year = {1996}} @inproceedings{Su95, Author = {Peter Su and Robert L. Scott Drysdale}, Booktitle = {Proceedings of the 11th Annual Symposium on Computational Geometry}, Month = {June}, Pages = {61--70}, Publisher = {ACM}, Title = {A Comparison of Sequential Delaunay Triangulation Algorithms}, Year = {1995}} @article{Ruppert95, Author = {Jim Ruppert}, Journal = {Journal of Algorithms}, Month = {May}, Number = {3}, Pages = {548--585}, Title = {A Delaunay Refinement Algorithm for Quality 2-Dimensional Mesh Generation}, Volume = {18}, Year = {1995}} @article{Chew89, Author = {L. Paul Chew}, Journal = {Algorithmica}, Number = {1}, Pages = {97--108}, Title = {Constrained {D}elaunay Triangulations}, Volume = {4}, Year = {1989}} @book{Rana06, Editor = {Sanjay Rana}, Publisher = {John Wiley \& Sons}, Title = {Topological Data Structures for Surfaces: An Introduction to Geographical Information Science}, Year = {2006}} @article{Yamaguchi95, Author = {Yamaguchi, Yasushi and Kimura, Fumihiko}, Journal = {IEEE Computer Graphics and Applications}, Number = {1}, Pages = {42--50}, Title = {Nonmanifold Topology Based on Coupling Entities}, Volume = {15}, Year = {1995}} @inproceedings{Varma90, Author = {Varma, Herman and Boudreau, H. and Prime, W.}, Booktitle = {Proceedings of the IHO Review}, Pages = {1--10}, Title = {A data structure for spatio-temporal databases}, Year = {1990}} @book{Raper00, Author = {Raper, Jonathan}, Publisher = {Taylor \& Francis}, Title = {Multidimensional geographic information science}, Year = {2000}} @article{Oconaill92, Author = {O'Conaill, M. A. and Bell, S. B. M. and Mason, N. C.}, Journal = {ITC Journal}, Pages = {47--54}, Title = {Developing a prototype {4D} {GIS} on a transputer array}, Volume = {1}, Year = {1992}} @inproceedings{Molenaar90, Author = {Molenaar, Martien}, Booktitle = {Proceedings of the 4th International Symposium on Spatial Data Handling}, Pages = {830--843}, Title = {A Formal Data Structure for three dimensional vector maps}, Year = {1990}} @article{Schonhardt28, Author = {E. Sch\"onhardt}, Journal = {Mathematische Annalen}, Pages = {309--312}, Title = {{\"U}ber die {Z}erlegung von {D}reieckspolyedern in {T}etraeder}, Volume = {1}, Year = {1928}} @article{Lienhardt94, Author = {Pascal Lienhardt}, Journal = {International Journal of Computational Geometry and Applications}, Number = {3}, Pages = {275--324}, Title = {$N$-dimensional Generalized Combinatorial Maps and Cellular Quasi-Manifolds}, Volume = {4}, Year = {1994}} @article{Edmonds60, Author = {J. Edmonds}, Journal = {Notices of the American Mathematical Society}, Title = {A Combinatorial Representation of Polyhedral Surfaces}, Volume = {7}, Year = {1960}} @article{Mason94, Author = {Mason, N. C. and O'Conaill, M. A. and Bell, S. B. M.}, Journal = {International Journal of Geographical Information Systems}, Number = {2}, Pages = {191--215}, Title = {{H}andling four-dimensional geo-referenced data in environmental {GIS}}, Volume = {8}, Year = {1994}} @inproceedings{Gold05, Address = {Pontypridd, Wales, UK}, Author = {Gold, Christopher M.}, Booktitle = {Proceedings of the 4th ISPRS Workshop on Dynamic and Multi-dimensional GIS}, Pages = {36--41}, Title = {Data structures for dynamic and multidimensional {GIS}}, Year = {2005}} @inproceedings{deFloriani03, Address = {Aachen, Germany}, Author = {De Floriani, Leila and Hui, Annie}, Booktitle = {Proceedings of the 1st Eurographics Symposium on Geometry Processing}, Pages = {72--82}, Title = {A scalable data structure for three-dimensional non-manifold objects}, Year = {2003}} @article{Blandford05, Author = {Blandford, Daniel K. and Blelloch, Guy E. and Cardoze, David E. and Kadow, Clemens}, Journal = {International Journal of Computational Geometry and Applications}, Number = {1}, Pages = {3--24}, Title = {Compact representations of simplicial meshes in two and three dimensions}, Volume = {15}, Year = {2005}} @book{Munkres75, Author = {James Raymond Munkres}, Publisher = {Prentice-Hall, Inc.}, Title = {Topology: A First Course}, Year = {1975}} @inproceedings{Stoter08, Author = {J.E. Stoter and J.M. Morales and R.L.G. Lemmens and B.M. Meijers and P.J.M van Oosterom and C.W. Quak and H.T. Uitermark and L. van den Brink}, Booktitle = {Proceedings of the 13th International Symposium on Spatial Data Handling}, Pages = {233--254}, Series = {Lecture Notes in Geoinformation and Cartography}, Title = {A Data Model for Multi-scale Topographical Data}, Year = {2008}} @inproceedings{Friis-Christensen03, Author = {Anders Friis-Christensen and Christian S. Jensen}, Booktitle = {Proceedings of the 15th International Conference on Scientific and Statistical Database Management}, Pages = {150--159}, Publisher = {IEEE Computer Society}, Title = {Object-Relational Management of Multiply Represented Geographic Entities}, Year = {2003}} @article{Worboys94, Author = {Michael F. Worboys}, Journal = {The Computer Journal}, Number = {1}, Pages = {26--34}, Title = {A Unified Model for Spatial and Temporal Information}, Volume = {37}, Year = {1994}} @article{Pelekis04, Author = {Pelekis, Nikos and Theodoulidis, Babis and Kopanakis, Ioannis and Theodoridis, Yannis}, Journal = {The Knowledge Engineering Review}, Month = {September}, Number = {3}, Pages = {235--274}, Title = {Literature review of spatio-temporal database models}, Volume = {19}, Year = {2004}} @article{Hornsby00, Author = {Kathleen Hornsby and Max J. Egenhofer}, Journal = {International Journal of Geographical Information Science}, Pages = {207--224}, Title = {Identity-Based Change: A Foundation for Spatio-Temporal Knowledge Representation}, Volume = {14}, Year = {2000}} @article{Hamilton05, Author = {Andy Hamilton and Hongxia Wang and Ali Murat Tanyer and Yusuf Arayci and Xiaonan Zhang and Yonghui Song}, Journal = {Journal of Information Technology in Construction}, Month = {April}, Pages = {55--67}, Title = {Urban information model for city planning}, Volume = {10}, Year = {2005}} @article{Kettner99, Author = {Kettner, Lutz}, Journal = {Computational Geometry --- Theory and Applications}, Month = {May}, Number = {1}, Pages = {65--90}, Title = {Using generic programming for designing a data structure for polyhedral surfaces}, Volume = {13}, Year = {1999}} @article{Shewchuk07, Author = {Jonathan Richard Shewchuk}, Journal = {Discrete \& Computational Geometry}, Month = {March}, Number = {1003}, Pages = {580--637}, Title = {General-Dimensional Constrained {D}elaunay and Constrained Regular Triangulations, {I}: Combinatorial Properties}, Volume = {39}, Year = {2008}} @book{deBerg08, Author = {Mark {de Berg} and Marc {van Kreveld} and Mark Overmars and Otfried Schwarzkopf}, Edition = {3rd}, Publisher = {Springer-Verlag}, Title = {Computational Geometry: Algorithms and Applications}, Year = {2008}} @article{Fortune87, Author = {Steven Fortune}, Journal = {Algorithmica}, Number = {1--4}, Pages = {153--174}, Title = {A sweepline algorithm for {V}oronoi diagrams}, Volume = {2}, Year = {1987}} @article{Ruppert92, Author = {Jim Ruppert and Raimund Seidel}, Journal = {Discrete \& Computational Geometry}, Number = {1}, Pages = {227--253}, Title = {On the difficulty of triangulating three-dimensional Nonconvex Polyhedra}, Volume = {7}, Year = {1992}} @inproceedings{Shewchuk98, Author = {Jonathan Richard Shewchuk}, Booktitle = {Proceedings of the 14th Annual Symposium on Computational Geometry}, Pages = {76--85}, Publisher = {ACM}, Title = {A condition guaranteeing the existence of higher-dimensional constrained Delaunay triangulations}, Year = {1998}} @book{Mantyla88, Address = {New York, USA}, Author = {M\"{a}ntyl\"{a}, Martti}, Publisher = {Computer Science Press}, Title = {An introduction to solid modeling}, Year = {1988}} @phdthesis{Levy99, Address = {France}, Author = {L\'{e}vy, Bruno}, School = {INPL, Universit\'e de Nancy}, Title = {{T}opologie algorithmique : {C}ombinatoire et plongement (\emph{in French})}, Year = {1999}} @incollection{Bieri88, Author = {H. Bieri and W. Nef}, Booktitle = {Computational Geometry and its Applications}, Editor = {Hartmut Noltemeier}, Pages = {97--112}, Publisher = {Springer Berlin Heidelberg}, Series = {Lecture Notes in Computer Science}, Title = {Elementary set operations with $d$-dimensional polyhedra}, Volume = {333}, Year = {1988}} @article{Ansaldi85, Author = {Silvia Ansaldi and Leila {de Floriani} and Bianca Falcidieno}, Journal = {IEEE Computer Graphics and Applications}, Number = {3}, Pages = {131--139}, Title = {Geometric modeling of solid objects by using a face adjacency graph representation}, Volume = {19}, Year = {1985}} @article{Mantyla82, Author = {Martti Mantyla and Reijo Sulonen}, Journal = {IEEE Computer Graphics and Applications}, Month = {September}, Number = {7}, Pages = {17--31}, Title = {{GWB}: A Solid Modeler with Euler Operators}, Volume = {2}, Year = {1982}} @article{Spehner91, Author = {Jean-Claude Spehner}, Journal = {Theoretical Computer Science}, Number = {2}, Pages = {205--232}, Title = {Merging in maps and in pavings}, Volume = {86}, Year = {1991}} @article{Weiler85, Author = {K. Weiler}, Journal = {IEEE Computer Graphics and Applications}, Number = {1}, Pages = {21--40}, Title = {Edge-Based Data Structures for Solid Modeling in Curved-Surface Environments}, Volume = {5}, Year = {1985}} @inproceedings{Baumgart75, Author = {Bruce G. Baumgart}, Booktitle = {AFIPS '75 Proceedings of the May 19-22, 1975, national computer conference and exposition}, Pages = {589--596}, Publisher = {ACM}, Title = {A polyhedron representation for computer vision}, Year = {1975}} @inproceedings{Levy01, Address = {San Diego, CA, USA}, Author = {L\'{e}vy, Bruno and Caumon, Guillaume and Conreaux, St\'ephane and Cavin, Xavier}, Booktitle = {Proceedings of the IEEE Visualization Conference 2001}, Publisher = {IEEE Computer Society}, Title = {{C}ircular {I}ncident {E}dge {L}ist: {A} data structure for rendering complex unstructured grids}, Year = {2001}} @article{deBerg97, Author = {de Berg, Mark and van Kreveld, Marc and van Oostrum, Ren\'e and Overmars, Mark}, Journal = {International Journal of Geographical Information Science}, Number = {4}, Pages = {359--374}, Title = {Simple traversal of a subdivision without extra storage}, Volume = {11}, Year = {1997}} @incollection{Lienhardt88, Author = {Pascal Lienhardt}, Booktitle = {Proceedings of the 5th Symposium on the Theoretical Aspects of Computer Science}, Editor = {Cori, Robert and Wirsing, Martin}, Month = {February}, Pages = {301--311}, Publisher = {Springer Berlin / Heidelberg}, Series = {Lecture Notes in Computer Science}, Title = {Extension of the Notion of Map and Subdivisions of a Three-Dimensional Space}, Volume = {294}, Year = {1988}} @article{Putnam86, Author = {L.K. Putnam and P.A. Subrahmanyam}, Journal = {IEEE Computer Graphics and Applications}, Month = {June}, Number = {6}, Pages = {43--51}, Title = {Boolean Operations on n-Dimensional Objects}, Volume = {6}, Year = {1986}} @article{Lawson86, Author = {Charles L. Lawson}, Journal = {Computer-Aided Design}, Number = {4}, Pages = {231--246}, Title = {Properties of $n$-dimensional triangulations}, Volume = {3}, Year = {1986}} @article{Lienhardt91, Author = {Pascal Lienhardt}, Journal = {Computer-Aided Design}, Number = {1}, Pages = {59--82}, Title = {Topological models for boundary representation: a comparison with $n$-dimensional generalized maps}, Volume = {23}, Year = {1991}} @inproceedings{Lienhardt89, Author = {Pascal Lienhardt}, Booktitle = {Proceedings of the 5th annual symposium on Computational geometry}, Pages = {228--236}, Publisher = {ACM}, Title = {Subdivisions of n-dimensional spaces and n-dimensional generalized maps}, Year = {1989}} @inproceedings{Dobkin87, Author = {David P. Dobkin and Michael J. Laszlo}, Booktitle = {Proceedings of the 3rd Annual Symposium on Computational Geometry}, Pages = {86--99}, Publisher = {ACM}, Title = {Primitives for the Manipulation of Three-Dimensional Subdivisions}, Year = {1987}} @article{Gray97, Author = {Jim Gray and Surajit Chaudhuri and Adam Bosworth and Andrew Layman and Don Reichart and Murali Venkatrao and Frank Pellow and Hamid Pirahesh}, Journal = {Data Mining and Knowledge Discovery}, Number = {1}, Pages = {29--53}, Title = {Data Cube: A Relational Aggregation Operator Generalizing Group-By, Cross-Tab and Sub-Totals}, Volume = {1}, Year = {1997}} @inproceedings{Casali03, Author = {Alain Casali and Rosine Cicchetti and Lotfi Lakhal}, Booktitle = {Proceedings of the 3rd {SIAM} International Conference on Data Mining}, Pages = {304--308}, Title = {Cube Lattices: a Framework for Multidimensional Data Mining}, Year = {2003}} @article{Goldberg91, Author = {David Goldberg}, Journal = {Computing Surveys}, Month = {March}, Number = {1}, Pages = {5--48}, Title = {What Every Computer Scientist Should Know About Floating-Point Arithmetic}, Volume = {23}, Year = {1991}} @article{Watson81, Author = {D.F. Watson}, Journal = {The Computer Journal}, Number = {2}, Pages = {167--182}, Title = {Computing the n-dimensional Delaunay tessellation with application to Voronoi polytopes}, Volume = {24}, Year = {1981}} @article{Shewchuk97, Author = {Jonathan Richard Shewchuk}, Journal = {Discrete \& Computational Geometry}, Pages = {305-363}, Title = {Adaptive Precision Floating-Point Arithmetic and Fast Robust Geometric Predicates}, Volume = {18}, Year = 1997} @article{Guibas85, Author = {Leonidas J. Guibas and Jorge Stolfi}, Journal = {ACM Transactions on Graphics}, Number = {2}, Pages = {74--123}, Title = {Primitives for the manipulation of general subdivisions and the computation of {V}oronoi diagrams}, Volume = {4}, Year = {1985}} @inproceedings{Shewchuk00, Author = {Shewchuk, Jonathan Richard}, Booktitle = {Proceedings of the 16th Annual Symposium on Computational Geometry}, Pages = {350--359}, Title = {Sweep Algorithms for Constructing Higher-Dimensional Constrained {D}elaunay Triangulations}, Year = {2000}} @incollection{Shewchuk96, Author = {Shewchuk, Jonathan Richard}, Booktitle = {Applied Computational Geometry: Towards Geometric Engineering}, Editor = {Ming C. Lin and Dinesh Manocha}, Month = {May}, Pages = {203--222}, Publisher = {Springer-Verlag}, Series = {Lecture Notes in Computer Science}, Title = {Triangle: Engineering a {2D} Quality Mesh Generator and {D}elaunay Triangulator}, Volume = {1148}, Year = {1996}} @article{vanOosterom05, Author = {Peter {van Oosterom}}, Journal = {Cartography and Geographic Information Science}, Number = {4}, Pages = {331--346}, Title = {Variable-scale Topological Data Structures Suitable for Progressive Data Transfer: The {GAP}-face Tree and {GAP}-edge Forest}, Volume = {32}, Year = {2005}} @inproceedings{vanOosterom11, Author = {Peter van Oosterom and Meijers, Martijn}, Booktitle = {Proceedings of the 14th {ICA}/{ISPRS} Workshop on Generalisation and Multiple Representation, Paris}, Title = {Towards a true vario-scale structure supporting smooth-zoom}, Year = {2011}} @techreport{Levy99a, Author = {L\'{e}vy, Bruno and Mallet, Jean-Laurent}, Institution = {ISA-GOCAD}, Title = {Cellular modeling in arbitrary dimension using generalized maps}, Year = {1999}} @incollection{Thomsen07, Author = {Andreas Thomsen and Martin Breunig and Edgar Butwilowski and Bj\"orn Broscheit}, Booktitle = {Advances in 3D Geoinformation Systems}, Chapter = {14}, Editor = {P. van Oosterom and S. Zlatanova and F. Penninga and E. Fendel}, Pages = {229--246}, Publisher = {Springer Berlin / Heidelberg}, Series = {Lecture Notes in Geoinformation and Cartography}, Title = {Modelling and Managing Topology in {3D} Geoinformation Systems}, Year = {2008}} @inproceedings{vanOosterom06, Author = {Peter {van Oosterom}}, Booktitle = {Proceedings of the {INSPIRE} Multiple- Representation and Data Consistency Workshop, Ispra}, Editor = {K. Toth and A. Illert and K. Murray}, Month = {November}, Title = {The {tGAP} structure: minimizing redundancy and maximizing consistency and offering access at any {LoD}}, Year = {2006}} @article{Delafontaine07, Author = {M. Delafontaine and G. Nolf and N. {van de Weghe} and M. Antrop and Ph. de Maeyer}, Journal = {International Journal of Geographical Information Science}, Month = {September}, Number = {6}, Pages = {719--735}, Title = {Assessment of sliver polygons in geographical vector data}, Volume = {23}, Year = {2007}} @incollection{Weibel97, Author = {Weibel, Robert}, Booktitle = {Algorithmic Foundations of Geographic Information Systems}, Editor = {van Kreveld, Marc and Nievergelt, J\"urg and Roos, Thomas and Widmayer, Peter}, Pages = {99--152}, Publisher = {Springer Berlin Heidelberg}, Series = {Lecture Notes in Computer Science}, Title = {Generalization of spatial data: Principles and selected algorithms}, Volume = {1340}, Year = {1997}} @article{Mackaness06, Author = {William A. Mackaness}, Journal = {Cartography and Geographic Information Science}, Number = {4}, Pages = {245--256}, Title = {Automated Cartography in a Bush of Ghosts}, Volume = {33}, Year = {2006}} @article{Jones05, Author = {Christopher B. Jones and J. Mark Ware}, Journal = {International Journal of Geographical Information Science}, Number = {8--9}, Pages = {859--870}, Title = {Map Generalisation in the Web Age}, Volume = {19}, Year = {2005}} @inproceedings{Brisson89, Address = {New York, NY, USA}, Author = {Brisson, Erik}, Booktitle = {Proceedings of the 5th annual symposium on Computational geometry}, Pages = {218--227}, Publisher = {ACM}, Title = {Representing geometric structures in $d$ dimensions: topology and order}, Year = {1989}}