Edwin A. Abbott. Flatland: A Romance of Many Dimensions. Seely & Co., 1884.

Imad Afyouni, Cyril Ray, and Christophe Claramunt. Spatial models for indoor & context-aware navigation systems: A survey. Journal of Spatial Information Science, 4:85–123, 2012.

Ricardo Pérez Aguila and Antonio Aguilera Ramírez. Classifying edges and faces as manifold or non-manifold elements in 4D orthogonal pseudo-polytopes. In WSCG'2003. UNION Agency - Science Press, February 2003.

Murad Davudovich Akhundov. Conceptions of space and time: sources, evolution, directions. MIT Press, November 1986.

Khaled K. Al-Taha, Richard T. Snodgrass, and Michael D. Soo. Bibliography on spatiotemporal databases. International Journal of Geographical Information Systems, 8(1):95–103, 1994.

N. Alam, D. Wagner, M. Wewetzer, M. Pries, and V. Coors. Towards automatic validation and healing of CityGML models for geometric and semantic consistency. In Umit Isikdag, editor, ISPRS Annals of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Proceedings of the ISPRS 8th 3DGeoInfo Conference & WG II/2 Workshop, pages 1–6, Istanbul, Turkey, 2013.

J. W. Alexander. An example of a simply connected surface bounding a region which is not simply connected. Proceedings of the National Academy of Sciences of the United States of America, 10(1):8–10, 1924.

Tyler J. Alumbaugh and Xiangmin Jiao. Compact array-based mesh data structures. In Proceedings of the 14th International Meshing Roundtable, pages 485–504, 2005.

Nina Amenta and Marshall Bern. Surface reconstruction by Voronoi filtering. In SCG '98 Proceedings of the 14th annual symposium on Computational geometry, pages 39–48. ACM, 1998.

Alexandr Andoni and Piotr Indyk. Near-optimal hashing algorithms for approximate nearest neighbor in high dimensions. Communications of the ACM, 51(1):117–122, 2008.

Marc P. Armstrong. Temporality in spatial databases. In GIS/LIS '88 : proceedings : accessing the world : third annual International Conference, Exhibits, and Workshops, pages 880–889. American Society for Photogrammetry and Remote Sensing, 1988.

Ken Arroyo Ohori. Validation and automatic repair of planar partitions using a constrained triangulation. Master's thesis, Delft University of Technology, August 2010.

Ken Arroyo Ohori, Hugo Ledoux, and Jantien Stoter. Modelling higher dimensional data for GIS using generalised maps. In B. Murgante, S. Misra, M. Carlini, C. Torre, H.Q. Nguyen, D. Taniar, B. Apduhan, and O. Gervasi, editors, Computational Science and Its Applications — ICCSA 2013. 13th International Conference, Ho Chi Minh City, Vietnam, June 24–27, 2013, Proceedings, Part I, volume 7971 of Lecture Notes in Computer Science, pages 526–539. Springer Berlin Heidelberg, Ho Chi Minh City, Vietnam, June 2013.

Emil Artin. Geometric Algebra. Nabu Press, 2011.

Marco Attene, Daniela Giorgi, Massimo Ferri, and Bianca Falcidieno. On converting sets of tetrahedra to combinatorial and PL manifolds. Computer Aided Geometric Design, 26(8):850–864, November 2009.

Marco Attene, Marcel Campen, and Leif Kobbelt. Polygon mesh repairing: An application perspectice. ACM Computing Surveys, 45(2), 2013.

Matt Austern. Why you shouldn't use set (and what you should use instead). C++ Report, 12(4), 2000.

Wael M. Badawy and Walid G. Aref. On local heuristics to speed up polygon-polygon intersection tests. In Proceedings of the 7th ACM International Symposium on Advances in Geographic Information Systems, pages 97–102. ACM, 1999.

Trevor C. Bailey and Anthony C. Gatrell. Interactive spatial data analysis. Longman, 1995.

C. L. Bajaj, V. Pascucci, and G. Rabbiolo. Hypervolume visualization: A challenge in simplicity. In IEEE Symposium on Volume Visualization. IEEE, 1998.

Chanderjit Bajaj and Tamal K. Dey. Convex decomposition of polyhedra and robustness. Technical report, Purdue University, 1990.

Dana H. Ballard. Strip trees: A hierarchical representation for curves. Communications of the ACM, 24(5):310–321, May 1981.

Ron J. Balsys and Kevin G. Suffern. Point based rendering of implicit 4-dimensional surfaces. In Computer Graphics, Imaging and Visualisation. IEEE, 2007.

C. Bradford Barber, David P. Dobkin, and Hannu Huhdanpaa. The Quickhull algorithm for convex hulls. ACM Transactions on Mathematical Software, 22(4):469–483, December 1996.

Gill Barequet and Micha Sharir. Filling gaps in the boundary of a polyhedron. Computer Aided Geometric Design, 12(2):207–229, March 1995.

Umit Basoglu and Joel Morrison. The efficient hierarchical data structure for the US historical boundary file. In Geoffrey Dutton, editor, Harvard Papers on Geographic Information Systems, volume 4. Addison-Wesley, 1978.

Bruce G. Baumgart. A polyhedron representation for computer vision. In AFIPS '75 Proceedings of the May 19-22, 1975, national computer conference and exposition, pages 589–596. ACM, 1975.

Norbert Beckmann, Hans-Peter Kriegel, Ralf Schneider, and Bernhard Seeger. The R*-tree: An efficient and robust access method for points and rectangles. In Proceedings of the 1990 ACM SIGMOD International Conference on Management of Data, number 322–330, 1990.

Jon Louis Bentley. Multidimensional binary search trees used for associative searching. Communications of the ACM, 18(9):509–517, 1975.

Lars Bernard, Benno Schmidt, and Ulrich Streit. AtmoGIS — integration of atmospheric models and GIS. In T.K. Poiker and N. Chrisman, editors, Proceedings of the 8th International Symposium on Spatial Data Handling, 1998.

Pierre Bézier. Essai de définition numérique des courbes et des surfaces experimentales: Contribution à l'étude des propriétés des courbes et des surfaces paramétriques polynomiales à coefficients vectoriels. PhD thesis, Université Pierre et Marie Curie, 1977.

H. Bieri and W. Nef. Elementary set operations with \(d\)-dimensional polyhedra. In Hartmut Noltemeier, editor, Computational Geometry and its Applications, volume 333 of Lecture Notes in Computer Science, pages 97–112. Springer Berlin Heidelberg, 1988.

Filip Biljecki, Hugo Ledoux, and Jantien Stoter. Redefining the level of detail for 3D models. GIM International, 28(11):21–23, November 2014.

Filip Biljecki, Hugo Ledoux, Jantien Stoter, and Junqiao Zhao. Formalisation of the level of detail in 3D city modelling. Computers, Environment and Urban Systems, 48:1–15, 2014.

Filip Biljecki, Hugo Ledoux, and Jantien Stoter. Improving the consistency of multi-LOD CityGML datasets by removing redundancy. In Martin Breunig, Al-Doori Mulhim, Edgar Butwilowski, Paul Vincent Kuper, Joachim Benner, and Karl-Heinz Häfele, editors, 3D Geoinformation Science. The Selected Papers of the 3D GeoInfo 2014, pages 1–17. Springer International Publishing, 2015.

Stephan Bischoff, Darko Pavic, and Leif Kobbelt. Automatic restoration of polygon models. ACM Transactions on Graphics, 24(4):1332–1352, 2005.

Denis Blackmore, Ming C. Leu, and Frank Shih. Analysis and modelling of deformed swept volumes. Computer-Aided Design, 26(4):315–326, April 1994.

Daniel K. Blandford, Guy E. Blelloch, David E. Cardoze, and Clemens Kadow. Compact representations of simplicial meshes in two and three dimensions. International Journal of Computational Geometry and Applications, 15(1):3–24, 2005.

Moshe Blank, Lena Gorelick, Eli Shechtman, Michal Irani, and Ronen Basri. Actions as space-time shapes. In Proceedings of the 10th IEEE International Conference on Computer Vision, 2005.

T. Blaschke. Object based image analysis for remote sensing. ISPRS Journal of Photogrammetry and Remote Sensing, 65(1):2–16, January 2010.

J. Bogdahn and V. Coors. Towards an automated healing of 3D urban models. In T. H. Kolbe, G. Köning, and C. Nagel, editors, Proceedings International Conference on 3D Geoinformation, volume XXXVIII–4/W15, pages 13–17, 2010.

Pawel Boguslawski and Christopher Gold. Rapid modelling of complex building interiors. In Thomas H. Kolbe, Gerhard König, and Claus Nagel, editors, Advances in 3D Geo-Information Sciences, Lecture Notes in Geoinformation and Cartography, pages 43–56. Springer, 2011.

Pawel Boguslawski, Christopher M. Gold, and Hugo Ledoux. Modelling and analysing 3D buildings with a primal/dual data structure. ISPRS Journal of Photogrammetry & Remote Sensing, 66:188–197, 2011.

Jan Helge Bøhn and Michael J. Wozny. A topology-based approach for shell-closure. In Selected and Expanded Papers from the IFIP TC5/WG5.2 Working Conference on Geometric Modeling for Product Realization, pages 297–319. North-Holland Publishing Co, 1992.

Jean-Daniel Boissonnat and Clément Maria. The simplex tree: An efficient data structure for general simplicial complexes. In Algorithms — ESA 2012, volume 7501 of Lecture Notes in Computer Science, pages 731–742. Springer Berlin Heidelberg, 2012.

Jean-Daniel Boissonnat, Olivier Devillers, Sylvain Pion, Monique Teillaud, and Mariette Yvinec. Triangulations in CGAL. Computational Geometry: Theory & Applications, 22:5–19, 2002.

János Bolyai. Appendix Scientiam Spatii Absolute Veram Exhibens. Maros-Vásárhelyini, 1832.

B. Boots. Spatial tessellations. In Paul A. Longley, Michael F. Goodchild, David J. Maguire, and David W. Rhind, editors, Geographical Information Systems, chapter 36. John Wiley & Sons, 1999.

John A. Brewer III and S. Mark Courter. Automated conversion of curvilinear wire-frame models to surface boundary models; a topological approach. In SIGGRAPH '86 Proceedings of the 13th annual conference on Computer graphics and interactive techniques, volume 20. ACM, 1986.

Erik Brisson. Representing geometric structures in \(d\) dimensions: topology and order. In Proceedings of the 5th annual symposium on Computational geometry, pages 218–227, New York, NY, USA, 1989. ACM.

Erik Brisson. Representing geometric structures in d dimensions: topology and order. Discrete & Computational Geometry, 9:387–426, 1993.

L.E.J. Brouwer. Beweis des Jordanschen Satzes für den \(n\)-dimensionalen Raum. Mathematische Annalen, 71:314–319, 1911.

Robin P. Bryant and David Singerman. Foundations of the theory of maps on surfaces with boundary. Quarterly Journal of Mathematics, 36(2):17–41, 1985.

Rizwan Bulbul and Andrew U. Frank. AHD: The alternate simplicial decomposition of nonconvex polytopes (generalization of a convex polytope based spatial data model). In Proceedings of the 17th International Conference on Geoinformatics, pages 1–6, 2009.

P.A. Burrough. Principles of geographical information systems for land resources assessment. Taylor & Francis, 1986.

Barbara P. Buttenfield and Joseph S. DeLotto. Multiple representations: Scientific report for the specialist meeting. Technical Report 89–3, National Center for Geographic Information and Analysis, 1989.

Georg Cantor. Ueber eine Eigenschaft des inbegriffs aller reellen algebraischen Zahlen. Journal für die reine und angewandte Mathematik, 77:258–262, 1874.

CEC. Corine land cover. Technical report, Commission of the European Communities, 1995.

Bernard Chazelle. Convex partitions of polyhedra: a lower bound and worst-case optimal algorithm. SIAM Journal on Computing, 13(3):488–507, 1984.

Bernard Chazelle and David Dobkin. Decomposing a polygon into its convex parts. In Proceedings of the 11th Annual ACM Symposium on Theory of Computing, pages 38–48, 1979.

Pin-Shan Chen. The entity-relationship model—toward a unified view of data. ACM Transactions on Database Systems, 1(1):9–36, 1976.

Siu-Wing Cheng, Tamal Krishna Dey, and Jonathan Richard Shewchuk. Delaunay Mesh Generation. CRC Press, 2012.

L. Paul Chew. Constrained Delaunay triangulations. Algorithmica, 4(1):97–108, 1989.

Matt Chisholm. The sphere in three dimensions and higher: Generalizations and special cases. Available at, May 2000.

Nicholas R. Chrisman. The role of quality information in the long-term functioning of a geographic information system. Cartographica, 1983.

Nicholas R. Chrisman. The risks of software innovation: A case study of the Harvard lab. The American Cartographer, 15(3):291–300, 1988.

Alan Chu, Chi-Wing Fu, Andrew J. Hanson, and Pheng-Ann Heng. GL4D: A GPU-based architecture for interactive 4D visualization. In IEEE Transactions on Visualization and Computer Graphics, volume 15, pages 1587–1594. IEEE, 2009.

Christophe Claramunt and Marius Thériault. Managing time in GIS: An event-oriented approach. In James Clifford and Alexander Tuzhilin, editors, Proceedings of the International Workshop on Temporal Databases, pages 23–42, 1995.

Christophe Claramunt, Christine Parent, Stefano Spaccapietra, and Marius Thériault. Database modelling for environmental and land use changes. In John Charles Harold Stillwell, Stan Geertman, and Stan Openshaw, editors, Geographical Information and Planning, Advances in Spatial Science, chapter 10, pages 181–202. Springer Berlin / Heidelberg, 1999.

Kenneth L. Clarkson, Kurt Mehlhorn, and Raimund Seidel. Four results on randomized incremental constructions. In Alain Finkel and Matthias Jantzen, editors, Proceedings of the 9th Annual Symposium on Theoretical Aspects of Computer Science, volume 577 of Lecture Notes in Computer Science, pages 461–474. Springer Berlin Heidelberg, 1992.

Lidija Čomić and Leila de Floriani. Modeling and Manipulating Cell Complexes in Two, Three and Higher Dimensions, volume 2 of Lecture Notes in Computational Vision and Biomechanics, chapter 4, pages 109–144. Springer, 2012.

Lidija Čomić, Leila de Floriani, Federico Iuricich, and Ulderico Fugacci. Topological modifications and hierarchical representation of cell complexes in arbitrary dimensions. Computer Vision and Image Understanding, 121:2–12, 2014.

J.H. Conway and N.J.A. Sloane. Sphere Packings, Lattices and Groups. Springer-Verlag, 1992.

J.T. Coppock and D.W. Rhind. The history of GIS. In D.J. Maguire, M.F. Goodchild, and D.W. Rhind, editors, Geographical Information Systems: Principles and Applications, volume 1, chapter 2, pages 21–43. Longman Scientific & Technical, 1991.

Robert Cori. Un code pour les graphes planaires et ses applications. Technical report, Société mathématique de France, 1975.

H. Couclelis. Space, time, geography. In Paul A. Longley, Michael F. Goodchild, David J. Maguire, and David W. Rhind, editors, Geographical Information Systems, chapter 2, pages 29–38. John Wiley & Sons, 1999.

Helen Couclelis. People manipulate objects (but cultivate fields): Beyond the raster-vector debate in GIS. In A. U. Frank, I. Campari, and U. Formentini, editors, Theories and Methods of Spatio-Temporal Reasoning in Geographic Space, volume 639 of Lecture Notes in Computer Science, pages 65–77. Springer Berlin Heidelberg, 1992.

Robert G. Cromley. Digital Cartography. Prentice Hall, 1992.

Maciej Dakowicz and Christopher M. Gold. Extracting meaningful slopes from terrain contours. International Journal of Computational Geometry and Applications, 13(4):339–357, 2003.

Boris Dalstein, Rémi Ronfard, and Michiel van de Panne. Vector graphics animation with time-varying topology. ACM Transactions of Graphics, 34(4), 2015.

Guillaume Damiand and Pascal Lienhardt. Removal and contraction for \(n\)-dimensional generalized maps. In Proceedings of the 11th Discrete Geometry for Computer Imagery, volume 2886, pages 408–419, 2003.

Guillaume Damiand and Pascal Lienhardt. Combinatorial Maps: Efficient Data Structures for Computer Graphics and Image Processing. CRC Press, 2014.

Guillaume Damiand, Samuel Peltier, and Laurent Fuchs. Computing homology generators for volumes using minimal generalized maps. In Valentin E. Brimkov, Reneta P. Barneva, and Hebert A. Hauptman, editors, Proceedings of the 12th International Workshop on Combinatorial Image Analysis, volume 4958 of Lecture Notes in Computer Science, pages 63–74. Springer, 2008.

Mark de Berg, Marc van Kreveld, René van Oostrum, and Mark Overmars. Simple traversal of a subdivision without extra storage. International Journal of Geographical Information Science, 11(4):359–374, 1997.

Mark de Berg, Marc van Kreveld, Mark Overmars, and Otfried Schwarzkopf. Computational Geometry: Algorithms and Applications. Springer-Verlag, 3rd edition, 2008.

Pierre de Fermat. Ad locos planos et solidos isagoge. Varia opera mathematica, pages 1–8, 1679.

Leila de Floriani and Annie Hui. Data structures for simplicial complexes: an analysis and a comparison. In M. Desbrunn and H. Pottmann, editors, Eurographics Symposium on Geometry Processing. The Eurographics Association, 2005.

Leila de Floriani, Leif Kobbelt, and Enrico Puppo. A survey on data structures for level-of-detail models. In Neil A. Dodgson, Michael S. Floater, and Malcolm A. Sabin, editors, Advances in Multiresolution for Geometric Modelling. Part II, Mathematics and Visualization, pages 49–74. Springer Berlin Heidelberg, 2005.

Arnaud de la Losa and Bernard Cervelle. 3D topological modeling and visualisation for 3D GIS. Computers & Graphics, 23(4):469–468, August 1999.

René Descartes. Discours de la méthode. Jan Maire, Leyde, 1637.

Olivier Devillers. Walking in a triangulation. International Journal of Foundations of Computer Science, 13(2):181–199, 2002.

Keith Devlin. The Joy of Sets: Fundamentals of Contemporary Set Theory. Springer-Verlag, 1993.

T. Devogele, J. Trevisan, and L. Raynal. Building a multi-scale database with scale-transition relationships. In Proceedings of the 7th International Symposium on Spatial Data Handling, pages 337–351, Delft, Netherlands, 1996.

A. A. Diakité, Guillaume Damiand, and D. van Maercke. Topological reconstruction of complex 3d buildings and automatic extraction of levels of detail. In Proceedings of the 2nd Eurographics Workshop on Urban Data Modelling and Visualisation, 2014.

David P. Dobkin and Michael J. Laszlo. Primitives for the manipulation of three-dimensional subdivisions. In Proceedings of the 3rd Annual Symposium on Computational Geometry, pages 86–99. ACM, 1987.

Jürgen Döllner and Henrik Buchholz. Continuous level-of-detail modeling of buildings in 3D city models. In GIS'05, pages 173–181. ACM, 2005.

Jürgen Döllner, Thomas H. Kolbe, Falko Liecke, Takis Sgouros, and Karin Teichmann. The virtual 3D city model of Berlin — managing, integrating and communicating complex urban information. In UDMS 2006, 2006.

B. Domínguez, Á.L. García, and F.R. Feito. Semantic and topological representation of building indoors: an overview. In Proceedings of the Joint ISPRS Workshop on 3D City Modelling & Applications and the 6th 3D GeoInfo Conference, volume 66, pages 209–222, 2011.

Sjors Donkers. Automatic generation of CityGML LoD3 building models from IFC models. Master's thesis, Delft University of Technology, December 2013.

David H. Douglas and Thomas K. Peucker. Algorithms for the reduction of the number of points required to represent a digitized line or its caricature. Cartographica: The International Journal for Geographic Information and Geovisualization, 10(2):112–122, December 1973.

Matthew P. Dube and Max J. Egenhofer. An ordering of convex topological relations. In Ningchuan Xiao, Mei-Po Kwan, Michael F. Goodchild, and Shashi Shekhar, editors, Geographic Information Science, volume 7478 of Lecture Notes in Computer Science, pages 72–86. Springer Berlin Heidelberg, 2012.

John Earman. How to talk about the topology of time. Noûs, 11(3):211–226, 1977.

Herbert Edelsbrunner. A Short Course in Computational Geometry and Topology. Springer Briefs in Applied Sciences and Technology. Springer, 2014.

Herbert Edelsbrunner and Ernst P. Mücke. Simulation of simplicity: A technique to cope with degenerate cases in geometric algorithms. ACM Transactions on Graphics, 9(1):66–104, 1990.

J. Edmonds. A combinatorial representation of polyhedral surfaces. Notices of the American Mathematical Society, 7, 1960.

EFI. Gutachten 2015: zu Forschung, Innovation und technologischer Leistungsfähigkeit Deutschlands. Technical report, Expertenkommission Forschung und Innovation, 2015.

Max J. Egenhofer and R. D. Franzosa. Point-set topological spatial relations. International Journal of Geographical Information Systems, 5(2):161–174, 1991.

Alberto Elduque. Vector cross products. Talk presented at the Seminario Rubio de Francia of the Universidad de Zaragoza on April 1, 2004, April 2004.

Herve Elter and Pascal Lienhardt. Cellular complexes as structured semi-simplicial sets. International Journal of Shape Modeling, 1(2), 1994.

David Eppstein. Subgraph isomorphism in planar graphs and related problems. Journal of Graph Algorithms and Applications, 3(3):1–27, 1999.

ESRI. Shapefile Technical Description. ESRI, July 1998.

ESRI. GIS Topology. ESRI, July 2005.

Leonhard Euler. Solutio problematis ad geometriam situs pertinentis. Commentarii academiae scientiarum Petropolitanae, 8:128–140, 1741.

Steven Feiner and Clifford Beshers. Visualizing \(n\)-dimensional virtual worlds with \(n\)-vision. In Proceedings of the 1990 symposium on Interactive 3D graphics, pages 37–38. ACM, 1990.

Vincenzo Ferrucci. Generalised extrusion of polyhedra. In 2nd ACM Solid Modelling '93, pages 35–42. ACM, 1993.

Waldemar Celes Filho, Luiz Henrique de Figueiredo, Marcelo Gattass, and Paulo Cezar Carvalho. A topological data structure for hierarchical planar subdivisions. Technical Report CS-95-53, Department of Computer Science, University of Waterloo, 1995.

Raphael Finkel and J.L. Bentley. Quad trees: A data structure for retrieval on composite keys. Acta Informatica, 4(1):1–9, 1974.

P. Fisher. The pixel: a snare and a delusion. International Journal of Remote Sensing, 18(3):679–685, 1997.

Richard Fitzpatrick. Euclid's Elements of Geometry. Richard Fitzpatrick, 2008.

James D. Foley, Andries van Dam, Steven K. Feiner, and John F. Hughes. Computer Graphics: Principles and Practice in C. Addison-Wesley Professional, 1995.

Thomas A. Foley and Gregory M. Nielson. Practical techniques for producing 3D graphical images. In John Black, editor, The System Engineer's Handbook: A guide to building VMEbus and VXIbus systems, chapter 19, pages 223–237. Academic Press, 1992.

David Fradin, Daniel Meneveaux, and Pascal Lienhardt. Partition de l'espace et hiérarchie de cartes généralisées: application aux complexes architecturaux. In Actes des XVèmes journées de l'Association Française d'Informatique Graphique, volume 28, 2002.

Andrew U. Frank. Spatial concepts, geometric data models, and geometric data structures. Computers & Geosciences, 18(4):409–417, 1992.

Scott M. Freundschuh and Max J. Egenhofer. Human conceptions of spaces: Implications for geographic information systems. Transactions in GIS, 2(4):361–375, 1997.

Anders Friis-Christensen and Christian S. Jensen. Object-relational management of multiply represented geographic entities. In Proceedings of the 15th International Conference on Scientific and Statistical Database Management, pages 150–159. IEEE Computer Society, 2003.

Antony Galton. Fields and objects in space, time, and space-time. Spatial Cognition and Computation, 4(1):39–68, 2004.

Michael Garland and Paul S. Heckbert. Surface simplification using quadric error metrics. In SIGGRAPH '97 Proceedings of the 24th annual conference on Computer graphics and interactive techniques, pages 209–216. ACM Press/Addison-Wesley Publishing, 1997.

Andreas Geiger, Joachim Benner, and Karl Heinz Haefele. Generalization of 3D IFC building models. In Martin Breunig, Mulhim Al-Doori, Edgar Butwilowski, Paul V. Kuper, Joachim Benner, and Karl Heinz Haefele, editors, 3D Geoinformation Science, Lecture Notes in Geoinformation and Cartography, pages 19–35. Springer International Publishing Switzerland, 2015.

Christopher M. Gold. Problems with handling spatial data—the Voronoi approach. CISM Journal, 45(1):65–80, 1991.

Christopher M. Gold. Data structures for dynamic and multidimensional GIS. In Proceedings of the 4th ISPRS Workshop on Dynamic and Multi-dimensional GIS, pages 36–41, Pontypridd, Wales, UK, 2005.

Christopher M. Gold. What is GIS and what is not? Transactions in GIS, 10(4):505–519, 2006.

David Goldberg. What every computer scientist should know about floating-point arithmetic. Computing Surveys, 23(1):5–48, March 1991.

Michael F. Goodchild. Geographical data modeling. Computers & Geosciences, 18(4):401–408, 1992.

Michael F. Goodchild. Metrics of scale in remote sensing and GIS. International Journal of Applied Earth Observation and Geoinformation, 3(2):114–120, 2001.

Stéphane Gosselin, Guillaume Damiand, and Christine Solnon. Efficient search of combinatorial maps using signatures. Theoretical Computer Science, 412(15):1392–1405, March 2011.

Miguel Granados, Peter Hachenberger, Susan Hert, Lutz Kettner, Kurt Mehlhorn, and Michael Seel. Boolean operations on 3D selective nef complexes: Data structure, algorithms and implementation. In Proceedings of the 11th Annual European Symposium on Algorithms, pages 174–186, September 2003.

Carine Grasset-Simon, Guillaume Damiand, and Pascal Lienhardt. nd generalized map pyramids: definition, representations and basic operations. Pattern Recognition, 39(4):527–538, 2006.

Gerhard Gröger and Lutz Plümer. Provably correct and complete transaction rules for updating 3D city models. Geoinformatica, 2011.

Gerhard Gröger and Lutz Plümer. How to achieve consistency for 3D city models. Geoinformatica, 15:137–165, 2011.

Gerhard Gröger, Thomas H. Kolbe, Claus Nagel, and Karl-Heiz Häfele. OGC City Geography Markup Language (CityGML) Encoding Standard. Version 2.0.0. Open Geospatial Consortium, April 2012.

André Guéziec and Francis Lazarus. Cutting and stitching: Converting sets of polygons to manifold surfaces. IEEE Transactions on Visualization and Computer Graphics, 7(2):136–151, April–June 2001.

Leonidas J. Guibas and Jorge Stolfi. Primitives for the manipulation of general subdivisions and the computation of Voronoi diagrams. ACM Transactions on Graphics, 4(2):74–123, 1985.

Oliver Günther. The arc tree: An approximation scheme to represent arbitrary curved shapes. In Efficient structures for geometric data management, volume 337 of Lecture Notes in Computer Science, chapter 6, pages 85–121. Springer Berlin Heidelberg, 1988.

E.L. Gursoz, Y. Choi, and F.B. Prinz. Vertex-based representation of non-manifold boundaries. Geometric Modeling for Product Engineering, 1990.

Ralf Hartmut Güting, Michael H. Böhlen, Martin Erwig, Christian S. Jensen, Nikos A. Lorentzos, Markus Schneider, and Michalis Vazirgiannis. A foundation for representing and querying moving objects. ACM Transactions on Database Systems, 25(1):1–42, March 2000.

Antonin Guttman. R-trees: A dynamic index structure for spatial searching. In Proceedings of the 1984 ACM SIGMOD International Conference on Management of Data, pages 47–57, 1984.

Peter Hachenberger. Boolean Operations on 3D Selective Nef Complexes Data Structure, Algorithms, Optimized Implementation, Experiments and Applications. PhD thesis, Saarland University, 2006.

Torsten Hägerstrand. What about people in regional science? Papers of the Regional Science Association, 24(1):6–21, 1970.

Mark Hampe, Karl-Heinrich Anders, and Monica Sester. MRDB applications for data revision and real-time generalisation. In Proceedings of the 21st International Cartographic Conference, pages 192–202, 2003.

Torill Hamre, Khalid Azim Mughal, and Anita Jacob. A 4D marine data model: Design and application in ice monitoring. Marine Geodesy, 20(2–3):121–136, 1997.

Patrick M. Hanrahan. Creating volume models from edge-vertex graphs. In SIGGRAPH '82 Proceedings of the 9th annual conference on Computer graphics and interactive techniques, pages 77–84. ACM, 1982.

Andrew J. Hanson. Geometry for \(n\)-dimensional graphics. In Paul S. Heckbert, editor, Graphics Gems IV, chapter II.6, pages 149–170. Academic Press Professional, 1994.

Andrew J. Hanson and Daniel Weiskopf. Visualizing relativity. Siggraph 2001 Tutorial, 2001.

Paul Hardy and Kenneth Field. Portrayal and Cartography, chapter 11, pages 323–358. Springer Handbook of Geographic Information. Springer, 2012.

Ian Hargreaves. Digital opportunity: A review of intellectural property and growth. Independent report commissioned by United Kingdom Prime Minister David Cameron, May 2011.

Allen Hatcher. Algebraic Topology. Cambridge University Press, 2002.

Felix Hausdorff. Grundzüge der Mengenlehre. Verlag von Veit & Comp., Leipzig, 1914.

Nicholas W.J. Hazelton, Lisa Marie Bennett, and Joanna Masel. Topological structures for 4-dimensional geographic information systems. Computers, Environment and Urban Systems, 16(3):227–237, May–June 1992.

N.W.J. Hazelton. Some operations requirements for a multi-temporal 4-D GIS. In M.J. Egenhofer and R.G. Golledge, editors, Spatial and Temporal Reasoning in Geographic Information Systems, pages 63–73. Oxford University Press, 1998.

N.W.J. Hazelton, F.J. Leahy, and I.P. Williamson. On the design of temporally-referenced, 3-D geographical information systems: development of four-dimensional GIS. In Proceedings of GIS/LIS'90, 1990.

Martin Held and Willi Mann. An experimental analysis of floating-point versus exact arithmetic. In Proceedings of the 23rd Canadian Conference on Computational Geometry, 2011.

Michael Henle. A Combinatorial Introduction to Topology. Dover Publications, 1994.

Franck Hétroy, Stéphanie Rey, Carlos Andújar, Pere Brunet, and Álvar Vinacua. Mesh repair with user-friendly topology control. Computer-Aided Design, 43(1):101–113, 2011.

Charles Howard Hinton. A New Era of Thought. Swan Sonnenschein & Co. Ltd., 1888.

Christoph M. Hoffmann. The problems of accuracy and robustness in geometric computation. Computer Science Technical Reports 88–771, Purdue University, 1988.

Christoph M. Hoffmann. Geometric and solid modeling. Morgan Kaufmann Publishers, 1992.

Christoph M. Hoffmann and Jianhua Zhou. Visualization of surfaces in four-dimensional space. Computer Science Technical Reports CSD TR–960, Purdue University, May 1990.

Steven Richard Hollasch. Four-space visualization of 4D objects. Master's thesis, Arizona State University, 1991.

Sébastien Horna, Guillaume Damiand, Daniel Meneveaux, and Yves Bertrand. Reconstruction topologique 3D de bâtiments. In Journées de l'Association Francophone d'Informatique Graphique, Bordeaux, 2006, 2006.

John F. Hughes, Andries van Dam, Morgan McGuire, David F. Sklar, James D. Foley, Steven K. Feiner, and Kurt Akeley. Computer Graphics: Principles and Practice. Addison-Wesley, 3rd edition, 2014.

Gary J. Hunter and Ian P. Williamson. The development of a historical cadastral database. International Journal of Geographical Information Systems, 4(2):169–179, 1990.

IEEE. IEEE Standard for Floating-Point Arithmetic. The Institute of Electrical and Electronics Engineers, 3 Park Avenue, New York, NY 10016-5997, USA, June 2008.

Darrel C. Ince, Leslie Hatton, and John Graham-Cumming. The case for open computer programs. Nature, 482:487–488, February 2012.

ISO. Geographic Information — Spatial Schema. International Organization for Standardization, February 2005.

ISO. Geographic information — Temporal schema. International Organization for Standardization, February 2005.

ISO. Geographic information — Simple feature access — Part 1: Common architecture. International Organization for Standardization, March 2006.

ISO. Geographic information — Schema for coverage geometry and functions. International Organization for Standardization, 2007.

ISO. Geographic information — Geography Markup Language (GML). International Organization for Standardization, 2007.

ISO. Industry Foundation Classes (IFC) for data sharing in the construction and facility management industries. International Organization for Standardization, March 2013.

ISO. Industrial automation systems and integration - Product data representation and exchange. International Organization for Standardization, August 2014.

ISO. Information technology — Programming languages — C++. International Organization for Standardization, 2015.

ISO/IEC. Information technology — Eiffel: Analysis, Design and Programming Language. International Organization for Standardization and International Electrotechnical Commission, 2007.

Chris L. Jackins and Steven L. Tanimoto. Quad-trees, oct-trees, and k-trees: A generalized approach to recursive decomposition of euclidean space. IEEE Transactions on Pattern Analysis and Machine Intelligence, 5(5):533–539, September 1983.

C.B. Jones and I.M. Abraham. Design considerations for a scale-independent cartographic database. In D. Marble, editor, Proceedings of the 2nd International Symposium on Spatial Data Handling, pages 384–398, 1986.

Christopher B. Jones and J. Mark Ware. Map generalisation in the web age. International Journal of Geographical Information Science, 19(8–9):859–870, 2005.

Lucas N. Joppa, Greg McInerny, Richard Harper, Lara Salido, Kenji Takeda, Kenton O'Hara, David Gavaghan, and Stephen Emmott. Troubling trends in scientific software use. Science, 340:814–815, May 2013.

M. C. Jordan. Cours d'Analyse. Gauthier-Villars, 1887.

Kenneth I. Joy, Justin Legakis, and Ron MacCracken. Data structures for multiresolution representation of unstructured meshes. In Gerard Farin, Bernd Hamann, and Hans Hagen, editors, Hierarchical and Geometrical Methods in Scientific Visualization, Mathematics and Visualization. Springer, 2003.

Tao Ju. Fixing geometric errors on polygonal models: A survey. Journal of Computer Science and Technology, 24(1):19–29, January 2009.

Tomasz Kaczynski, Konstantin Mischaikow, and Marian Mrozek. Computational Homology. Springer Berlin / Heidelberg, 2004.

Martin Kada. Scale-dependent simplification of 3D building models based on cell decomposition and primitive instancing. In COSIT 2007, volume 4736 of Lecture Notes in Computer Science, pages 222–237. Springer-Verlag Berlin Heidelberg, 2007.

Farid Karimipour, Mahmoud R. Delavar, and Andrew U. Frank. A simplex-based approach to implement dimension independent spatial analyses. Computers & Geosciences, 36(9):1123–1134, September 2010.

Michael Kazhdan, Matthew Bolitho1, and Hugues Hoppe2. Poisson surface reconstruction. In Konrad Polthier and Alla Sheffer, editors, Eurographics Symposium on Geometry Processing. The Eurographics Association, 2006.

Lutz Kettner, Kurt Mehlhorn, Sylvain Pion, Stefan Schirra, and Chee Yap. Classroom examples of robustness problems in geometric computations. Computational Geometry, 40(1):61–78, May 2008.

David Kirkpatrick, Jack Snoeyink, and Bettina Speckmann. Kinetic collision detection for simple polygons. In Proceedings of the 16th Annual Symposium on Computational Geometry, pages 322–330, 2000.

Thomas H. Kolbe, Gerhard Gröger, and Lutz Plümer. CityGML: Interoperable access to 3D city models. In Peter van Oosterom, Siyka Zlatanova, and Elfriede M. Fendel, editors, Geo-information for Disaster Management, pages 883–899. Springer Berlin Heidelberg, 2005.

Menno-Jan Kraak. The space-time cube revisited from a geovisualization perspective. In Proceedings of the 21st International Cartographic Conference, pages 1988–1996, 2003.

Pierre Kraemer, Lionel Untereiner, Thomas Jund, Sylvain Thery, and David Cazier. CGoGN: n-dimensional meshes with combinatorial maps. In J. Sarrate and M. Staten, editors, Proceedings of the 22nd International Meshing Roundtable, pages 485–503. Springer International Publishing Switzerland, 2014.

Werner Kuhn. Geospatial semantics: Why, of what, and how? Journal on Data Semantics, 2005.

P. Lancaster and K. Salkauskas. Surfaces generated by moving least squares methods. Mathematics of Computation, 37(155):141–158, July 1981.

Gail Langran and Nicholas R. Chrisman. A framework for temporal geographic informations. Cartographica, 25(3):1–14, 1988.

Charles L. Lawson. Properties of \(n\)-dimensional triangulations. Computer-Aided Design, 3(4):231–246, 1986.

Hai Ha Le. Spatio-temporal data construction. ISPRS International Journal of Geo-Information, 2:837–853, August 2013.

M. Lebesgue. Sur l'invariance du nombre de dimensions d'un espace et sur le theorème de M. Jordan relatif aux varieté fermées. Comptes rendus de l'Académie des Sciences, 152:841–844, 1911.

Hugo Ledoux. Modelling Three-dimensional Fields in Geoscience with the Voronoi Diagram and its Dual. PhD thesis, University of Glamorgan, November 2006.

Hugo Ledoux. On the validation of solids represented with the international standards for geographic information. Computer-Aided Civil and Infrastructure Engineering, 28(9):693–706, August 2013.

Hugo Ledoux and Christopher M. Gold. Modelling three-dimensional geoscientific fields with the Voronoi diagram and its dual. International Journal of Geographical Information Science, 22(5):547–574, 2008.

Hugo Ledoux and Martijn Meijers. Topologically consistent 3D city models obtained by extrusion. International Journal of Geographical Information Science, 25(4):557–574, 2011.

Hugo Ledoux, Ken Arroyo Ohori, and Martijn Meijers. A triangulation-based approach to automatically repair GIS polygons. Computers & Geosciences, 66:121–131, May 2014.

Ickjai Lee and Mark Gahegan. Interactive analysis using Voronoi diagrams: Algorithms to support dynamic update from a generic triangle-based data structure. Transactions in GIS, 6(2):89–114, 2002.

J. Lee and M.-P. Kwan. A combinatorial data model for representing topological relations among 3D geographical features in micro-spatial environments. International Journal of Geographical Information Science, 19(10):1039–1056, 2005.

J. Lee and Sisi Zlatanova. A 3D data model and topological analyses for emergency response in urban areas. In S. Zlatanova and Jonathan Li, editors, Geospatial Information Technology for Emergency Response, pages 143–168. Taylor & Francis, 2008.

Sang Hun Lee and Kunwoo Lee. Partial entity structure: A compact non-manifold boundary representation based on partial topological entities. In David C. Anderson and Kunwoo Lee, editors, SMA '01 Proceedings of the 6th ACM Symposium on Solid modeling and Applications, pages 159–170. ACM, 2001.

Yong Tsui Lee and Aristides A. G. Requicha. Algorithms for computing the volume and other integral properties of solids. I. Known methods and open issues. Communications of the ACM, 25(9):635–641, 1982.

Bruno Lévy. Dual domain extrapolation. ACM Transactions on Graphics, 22(3):364–369, July 2003.

Jos Leys, Étienne Ghys, and Aurelién Alvarez. Dimensions: une promenade mathématique. Available at, 2008.

Jyh-Ming Lien and Nancy M. Amato. Approximate convex decomposition of polygons. Computational Geometry: Theory & Applications, 35:100–123, 2006.

Pascal Lienhardt. Extension of the notion of map and subdivisions of a three-dimensional space. In Robert Cori and Martin Wirsing, editors, Proceedings of the 5th Symposium on the Theoretical Aspects of Computer Science, volume 294 of Lecture Notes in Computer Science, pages 301–311. Springer Berlin / Heidelberg, February 1988.

Pascal Lienhardt. Topological models for boundary representation: a comparison with \(n\)-dimensional generalized maps. Computer-Aided Design, 23(1):59–82, 1991.

Pascal Lienhardt. \(n\)-dimensional generalized combinatorial maps and cellular quasi-manifolds. International Journal of Computational Geometry and Applications, 4(3):275–324, 1994.

Pascal Lienhardt, Xavier Skapin, and Antoine Bergey. Cartesian product of simplicial and cellular structures. International Journal of Computational Geometry and Applications, 14(3):115–159, 2004.

Pascal Lienhardt, Laurent Fuchs, and Yves Bertrand. Combinatorial Models for Topology-Based Geometric Modeling, pages 151–198. Theory and applications of proximity, nearness and uniformity. Dipartimento di Matematica della Seconda Università di Napoli, 2009.

Peter Lindstrom and Greg Turk. Fast and memory efficient polygonal simplification. In VIS '98 Proceedings of the conference on Visualization '98, pages 279–286. IEEE Computer Society Press, 1998.

Liu Liu and Sisi Zlatanova. Generating navigation models from existing building data. In ISPRS Acquisition and Modelling of Indoor and Enclosed Environments 2013, volume XL–4/W4. ISPRS, 2013.

Yuanxin Liu and Jack Snoeyink. Faraway point: A sentinel point for Delaunay computation. International Journal of Computational Geometry and Applications, 18(4):343–355, 2008.

Nikolai Lobachevsky. Geometrische Untersuchungen zur Theorie der Parallellinien. Funcke, Berlin, 1840.

Hélio Lopes and Geovan Tavares. Structural operators for modeling 3-manifolds. In Christoph Hoffmann, Wim Bronsvoort, George Allen, Mike Pratt, and David Rosen, editors, SMA '97, Proceedings of the Fourth Symposium on Solid Modeling and Applications, pages 10–18. ACM, 1997.

María Lorenzo-Valdés, Gerardo I. Sanchez-Ortiz, Andrew G. Elkington, Raad H. Mohiaddin, and Daniel Rueckert. Segmentation of 4D cardiac MR images using a probabilistic atlas and the EM algorithm. Medical Image Analysis, 8:255–265, 2004.

David Luebke, Martin Reddy, Jonathan D. Cohen, Amitabh Varshney, Benjamin Watson, and Robert Huebner. Level of Detail for 3D Graphics. Morgan Kaufmann Publishers, 2003.

Yannis Manolopoulos, Alexandros Nanopoulos, Apostolos N. Papadopoulos, and Yannis Theodoridis. R-Trees: Theory and Applications. Advanced Information and Knowledge Processing. Springer Berlin Heidelberg, 2006.

Martti Mäntylä. An introduction to solid modeling. Computer Science Press, New York, USA, 1988.

John I. Marden. Analyzing and Modeling Rank Data, volume 64 of CRC Monographs on Statistics & Applied Probability. Chapman & Hall, August 1996.

Avraham Margalit and Gary D. Knott. An algorithm for computing the union, intersection or difference of two polygons. Computers & Graphics, 13(2):167–183, 1989.

N. C. Mason, M. A. O'Conaill, and S. B. M. Bell. Handling four-dimensional geo-referenced data in environmental GIS. International Journal of Geographical Information Systems, 8(2):191–215, 1994.

W. S. Massey. Cross products of vectors in higher dimensional Euclidean spaces. The American Mathematical Monthly, 90(10):697–701, December 1983.

Hiroshi Masuda. Topological operators and Boolean operations for complex-based non-manifold geometric models. Computer-Aided Design, 25(2), 1993.

Dan McKenney. Model quality: The key to CAD/CAM/CAE interoperability. Technical report, International TechneGroup Incorporated, 1998.

John W. McKenzie, Ian P. Williamson, and N.W.J. Hazelton. 4-D adaptive GIS: Justification and methodologies. Technical report, Department of Geomatics, The University of Melbourne, 2001.

Donald Meagher. Octree encoding: a new technique for the representation, manipulation and display of arbitrary 3-d objects by computer. Technical report, Rensselaer Polytechnic Institute, 1980.

Martijn Meijers. Variable-scale Geo-information. PhD thesis, Delft University of Technology, December 2011.

Albrecht Ludwig Friedrich Meister. Generalia de genesi figurarum planarum et inde pendentibus earum affectionibus. Novi Commentarii Societatis Reglae Scientiarum Gottingensis, 1:144–180, 1771.

Liqiu Meng and Andrea Forberg. 3D building generalisation. In W.A. Mackaness, A. Ruas, and L.T. Sarajkoski, editors, Generalisation of Geographic Information: Cartographic Modelling and Applications, pages 211–232. Elsevier, 2007.

Bertrand Meyer. Design by contract. Technical Report TR-EI-12/CO, Interactive Software Engineering, 1986.

Eric J. Miller. Towards a 4D GIS: Four-dimensional interpolation utilizing Kriging. In Zarine Kemp, editor, Innovations in GIS, chapter 13, pages 181–197. Taylor & Francis, 1997.

Hermann Minkowski. Die Grundgleichungen für die elektromagnetischen Vorgänge in bewegten Körpern. Nachrichten von der Gesellschaft der Wissenschaften zu Göttingen, Mathematisch-Physikalische Klasse, pages 53–111, 1908.

A. Morin, J. Urban, I. Foster, A. Sali, D. Baker, and P. Sliz. Shining light into black boxes. Science, 336:159–160, April 2012.

Ernst P. Mücke, Isaac Saias, and Binhai Zhu. Fast randomized point location without preprocessing in two- and three-dimensional Delaunay triangulations. Computational Geometry—Theory and Applications, 12:63–83, 1999.

D. E. Muller and F. P. Preparata. Finding the intersection of two convex polyhedra. Theoretical Computer Science, 7(2):217–236, 1978.

Nathan C. Myers. Traits: a new and useful template technique. C++ Report, June 1995.

B. Naylor. Binary space partitioning trees as an alternative representation of polytopes. Computer-Aided Design, 22(4), 1990.

Walter Nef. Beiträge zur Theorie der Polyeder: mit Anwendungen in der Computergraphik. Herbert Lang, Bern, 1978.

F.S. Nooruddin and G. Turk. Simplification and repair of polygonal models using volumetric techniques. IEEE Transactions on Visualization and Computer Graphics, 9(2):191–205, 2003.

M. A. O'Conaill, S. B. M. Bell, and N. C. Mason. Developing a prototype 4D GIS on a transputer array. ITC Journal, 1:47–54, 1992.

OGC. OpenGIS Geography Markup Language (GML) Encoding Standard. Version 3.2.1. Open Geospatial Consortium, August 2007.

OGC. OpenGIS Implementation Specification for Geographic Information - Simple Feature Access - Part 1: Common Architecture. Version 1.2.1. Open Geospatial Consortium, May 2011.

OGC. OGC Geography Markup Language — Extended schemas and encoding rules. Version 3.3.0. Open Geospatial Consortium, December 2012.

Narayan Panigrahi. Computing in Geographic Information Systems. CRC Press, 2014.

A. Paoluzzi, F. Bernardini, C. Cattani, and V. Ferrucci. Dimension-independent modeling with simplicial complexes. ACM Transactions on Graphics, 12(1):56–102, January 1993.

A. Paoluzzi, V. Pascucci, and G. Scorzelli. Progressive dimension-independent Boolean operations. In G. Elber, N. Patrikalakis, and P. Brunet, editors, ACM Symposium on Solid Modeling and Applications. ACM, 2004.

A. Pasko, V. Adzhiev, A. Sourin, and V. Savchenko. Function representation in geometric modeling: concepts, implementation and applications. The Visual Computer, 11:429–446, 1995.

Alexander Pasko and Valery Adzhiev. Constructive hypervolume modeling. Graphical Models, 63:413–442, 2001.

Tom Patterson. Getting real: Reflecting on the new look of national park service maps. Cartographic Perspectives, 43, Fall 2002.

Norbert Paul, Patrick Erik Bradley, and Martin Breunig. Integrating space, time, version and scale using Alexandrov topologies. Available at, March 2011.

Nikos Pelekis, Babis Theodoulidis, Ioannis Kopanakis, and Yannis Theodoridis. Literature review of spatio-temporal database models. The Knowledge Engineering Review, 19(3):235–274, September 2004.

Sinésio Pesco, Geovan Tavares, and Hélio Lopes. A stratification approach for modeling two-dimensional cell complexes. Computers & Graphics, 28:235–247, 2004.

Thomas K. Peucker and Nicholas R. Chrisman. Cartographic data strutures. The American Cartographer, 2(1):55–69, 1975.

Donna J. Peuquet. A conceptual framework and comparison of spatial data models. Cartographica, 21(4):66–113, 1984.

Donna J. Peuquet. It's about time: A conceptual framework for the representation of temporal dynamics in geographic information systems. Annals of the Association of American Geographers, 84(3):441–461, 1994.

Donna J. Peuquet and Niu Duan. An event-based spatiotemporal data model (ESTDM) for temporal analysis of geographical data. International Journal of Geographical Information Science, 9(1):7–24, 1995.

Sylvain Pion and Andreas Fabri. A generic lazy evaluation scheme for exact geometric computations. Science of Computer Programming, 76(4):307–323, 2011.

Lutz Plümer and Gerhard Gröger. Achieving integrity in geographic information systems—maps and nested maps. GeoInformatica, 1(4):345–367, 1997.

Joshua Podolak and Szymon Rusinkiewicz. Atomic volumes for mesh completion. In M. Desbrunn and H. Pottmann, editors, Eurographics Symposium on Geometry Processing (2005), pages 33–42, 2005.

H. Poincaré. Complément à l'analysis situs. Rendiconti del Circolo Matematico di Palermo, 13:285–343, 1899.

H. Poincaré. Second complément à l'analysis situs. Proceedings of the London Mathematical Society, 32:277–308, 1900.

Henri Poincaré. Sur la généralisation d'un théorème d'Euler relatif aux polyèdres. Comptes rendus hebdomadaires de l'Académie des sciences de Paris, 117:144–145, 1893.

M.H. Poincaré. Analysis situs. Journal de l'École polytechnique, 2(1):1–123, 1895.

Jovan Popović and Hughes Hoppe. Progressive simplicial complexes. In G. Scott Owen, Turner Whitted, and Barbara Mones-Hattal, editors, SIGGRAPH '97 Proceedings of the 24th annual conference on Computer graphics and interactive techniques, pages 217–224. ACM/Addison-Wesley Publishing, 1997.

M. Poudret, A. Arnould, Y. Bertrand, and P. Lienhardt. Cartes combinatoires ouvertes. Technical Report 2007-01, Laboratoire SIC, UFR SFA, Université de Poitiers, October 2007.

F.P. Preparata and D.E. Muller. Finding the intersection of \(n\) half-spaces in time \(O(n \log n)\). Theoretical Computer Science, 8(1):45–55, 1979.

Paul Ramsey. PostGIS: Tips for power users. Presentation at FOSS4G 2010. Available at, 2010.

Jonathan Raper, editor. Three Dimensional Applications in Geographic Information Systems. Taylor & Francis, 1989.

Jonathan Raper. Multidimensional geographic information science. Taylor & Francis, 2000.

Helmut Ratschek and Jon Rokne. New computer methods for global optimization. Ellis Horwood, 1988.

Julia Reda. Draft report on the implementation of Directive 2001/29/EC of the European Parliament and of the Council of 22 May 2001 on the harmonisation of certain aspects of copyright and related rights in the information society. Technical report, European Parliament Commitee on Legal Affairs, 2014.

A. Renolen. History graphs: conceptual modeling of spatio-temporal data. GIS Frontiers in Business and Science, 2, 1996.

A. A. G. Requicha and H. B. Voelcker. Constructive solid geometry. Technical Memorandum 25, College of Engineering & Applied Science, The University of Rochester, November 1977.

Aristides A. G. Requicha. Representations for rigid solids: Theory, methods, and systems. Computing Surveys, 12(4):437–464, December 1980.

Aristides A. G. Requicha and Robert B. Tilove. Mathematical foundations of constructive solid geometry: General topology of closed regular sets. Production Automation Project Technical Memorandum 27, University of Rochester, 1978.

B. Riemann. Ueber die Hypothesen, welche der Geometrie zu Grunde liegen. PhD thesis, Abhandlungen der Königlichen Gesellschaft der Wissenschaften zu Göttingen, 1868.

Philippe Rigaux and Michel Scholl. Multi-scale partitions: Application to spatial and statistical databases. In Max J. Egenhofer and John R. Herring, editors, Advances in Spatial Databases, volume 951 of Lecture Notes in Computer Science, pages 170–183. Springer Berlin Heidelberg, 1995.

M. Rivero and F.R. Feito. Boolean operations on general planar polygons. Computers & Graphics, 24:881–896, 2000.

Stephen J. Rock and Michael J. Wozny. Generating topological information from a ``bucket of facets''. In Solid Freeform Fabrication Symposium Proceedings, pages 251–259, 1992.

J. Rossignac and M. O'Connor. SGC: A dimension-independent model for pointsets with internal structures and incomplete boundaries. In M. Wosny, J. Turner, and K. Preiss, editors, Proceedings of the IFIP Workshop on CAD/CAM, pages 145–180, 1989.

Jarek Rossignac and David Cardoze. Matchmaker: Manifold BReps for non-manifold r-sets. Technical Report SM99–020, Georgia Institute of Technology, 1999.

Jarek Rossignac and Andrzej Szymczak. Wrap&Zip decompression of the connectivity of triangle meshes compressed with Edgebreaker. Computational Geometry: Theory & Applications, 14, 1999.

Yossi Rubner, Carlo Tomasi, and Leonidas J. Guibas. A metric for distributions with applications to image databases. In Proceedings of the 6th International Conference on Computer Vision, pages 59–66, 1998.

Jim Ruppert and Raimund Seidel. On the difficulty of triangulating three-dimensional nonconvex polyhedra. Discrete & Computational Geometry, 7(1):227–253, 1992.

V. L. Rvachev. On the analytical description of certain geometrical objects. Doklady Akademii Nauk SSSR, 153(4):765–767, 1963.

Hans Sagan. Space-Filling Curves. Springer Science+Business Media, 1994.

David Salomon. The Computer Graphics Manual, volume 2 of Texts in Computer Science. Springer London, 2011.

Hanan Samet and Markku Tamminen. Bintrees, CSG trees, and time. In Pat Cole, Robert Heilman, and Brian A. Barsky, editors, SIGGRAPH '85, volume 19, pages 121–130. ACM, 1985.

Stefan Schirra. Precision and robustness in geometric computations. In Marc van Kreveld, Jürg Nievergelt, Thomas Roos, and Peter Widmayer, editors, Algorithmic Foundations of Geographic Information Systems, volume 1340 of Lecture Notes in Computer Science, pages 255–287. Springer Berlin Heidelberg, 1997.

E. Schönhardt. Über die Zerlegung von Dreieckspolyedern in Tetraeder. Mathematische Annalen, 1:309–312, 1928.

Michael Seel. Planar Nef Polyhedra and Generic Higher-dimensional Geometry. PhD thesis, Saarland University, 2001.

Raimund Seidel. Constructing higher-dimensional convex hulls at logarithmic cost per face. In Proceedings of the 18th Annual Symposium on the Theory of Computing, pages 404–413, 1986.

Timos Sellis, Nick Roussopoulos, and Christos Faloutsos. The R+-tree: A dynamic index for multi-dimensional objects. In Proceedings of 13th International Conference on Very Large Data Bases, 1987.

SGK. Kartographische Generalisierung. Der Schweizerischen Gesellschaft für Kartographie, 1975.

Michael Ian Shamos and Dan Hoey. Geometric intersection problems. In Proceedings of the 17th Annual Symposium on the Foundations of Computer Science, pages 208–215, 1976.

Timothy M. Shead. Universal relational storage for geometric primitives. Technical report, The K-3D Project, 2010.

Xuejun Sheng and Ingo R. Meier. Generating topological structures for surface models. IEEE Computer Graphics and Applications, November 1995.

Jonathan Richard Shewchuk. Triangle: Engineering a 2D quality mesh generator and Delaunay triangulator. In Ming C. Lin and Dinesh Manocha, editors, Applied Computational Geometry: Towards Geometric Engineering, volume 1148 of Lecture Notes in Computer Science, pages 203–222. Springer-Verlag, May 1996.

Jonathan Richard Shewchuk. Robust adaptive floating-point geometric predicates. In Proceedings of the 12th Annual Symposium on Computational Geometry, pages 141–150, 1996.

Jonathan Richard Shewchuk. Adaptive precision floating-point arithmetic and fast robust geometric predicates. Discrete & Computational Geometry, 18:305–363, 1997.

Jonathan Richard Shewchuk. Sweep algorithms for constructing higher-dimensional constrained Delaunay triangulations. In Proceedings of the 16th Annual Symposium on Computational Geometry, pages 350–359, 2000.

Jonathan Richard Shewchuk. General-dimensional constrained Delaunay and constrained regular triangulations, I: Combinatorial properties. Discrete & Computational Geometry, 39(1003):580–637, March 2008.

Dave Shreiner, Graham Sellers, John Kessenich, Bill Licea-Kane, and Khronos ARB Working Group. OpenGL Programming Guide: The Official Guide to Learning OpenGL, Version 4.3. Addison-Wesley, 8th edition, 2013.

Hang Si and Klaus Gärtner. Meshing piecewise linear complexes by constrained Delaunay tetrahedralizations. In Proceedings of the 14th International Meshing Roundtable, September 2005.

Cathy Sohanpanah. Extension of a boundary representation technique for the description of \(n\) dimensional polytopes. Computers & Graphics, 13(1):17–23, 1989.

Willi-Hans Steeb. The Nonlinear Workbook. World Scientific Publishing, 5th edition, 2011.

S. S. Stevens. On the theory of scales of measurement. Science, 103(2684):677–680, 1946.

P. A. Story and Michael F. Worboys. A design support environment for spatio-temporal database applications. In Andrew U. Frank and Werner Kuhn, editors, Spatial Information Theory: A Theoretical Basis for GIS, volume 988 of Lecture Notes in Computer Science, pages 413–430. Springer Berlin / Heidelberg, 1995.

Jantien Stoter, Dirk Burghardt, Cécile Duchêne, Blanca Baella, Nico Bakker, Connie Blok, Maria Pla, Nicolas Regnauld, Guillaume Touya, and Stefan Schmid. Methodology for evaluating automated map generalization in commercial software. Computers, Environment and Urban Systems, 33(5):311–324, 2009.

Jantien Stoter, Hugo Ledoux, Martijn Meijers, and Ken Arroyo Ohori. Integrating scale and space in 3D city models. In Jacynthe Pouliot, Sylvie Daniel, Frédéric Hubert, and Alborz Zamyadi, editors, Proceedings of the 7th International 3D GeoInfo Conference, volume XXXVIII-4/C26 of International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, pages 7–10, Québec City, Canada, May 2012. ISPRS.

Jantien Stoter, Hugo Ledoux, Martijn Meijers, Ken Arroyo Ohori, and Peter van Oosterom. 5D modeling - applications and advantages. In Geospatial World Forum 2012, Amsterdam, The Netherlands, April 2012.

J.E. Stoter, M. Post, V. van Altena, R. Nijhuis, and B. Bruns. Fully automated generalisation of a 1:50k map from 1:10k data. Cartography and Geographic Information Science, 41(1):1–13, January 2014.

Wolfgang Straßer. Schnelle Kurven- und Flächendarstellung auf graphischen Sichtgeräten. PhD thesis, Technische Universität Berlin, 1974.

Jeremy Tammik. AutoCAD Nef polyhedron implementation. Available at, September 2007.

R.J. Thompson. Towards a rigorous logic for spatial data representation. PhD thesis, Delft University of Technology, 2007.

Andreas Thomsen, Martin Breunig, and Edgar Butwilowski. Towards a G-map based tool for the modelling and management of topology in multiple representation databases. Journal of Photogrammetry, Remote Sensing and Geoinformation Processing, 3:175–186, 2008.

F. Töfper and W. Pillerwizer. The principles of selection. The Cartographic Journal, 3(1):10–16, May 1966.

R.F. Tomlinson. The impact of the transition from analogue to digital cartographic representation. The American Cartographer, 15(3):249–261, July 1988.

Nectaria Tryfona and Christian S. Jensen. Conceptual data modeling for spatiotemporal applications. GeoInformatica, 3(3):245–268, 1999.

Greg Turk and Marc Levoy. Zippered polygon meshes from range images. In SIGGRAPH '94 Proceedings of the 21st annual conference on Computer graphics and interactive techniques, pages 311–318. ACM, New York, NY, USA, 1994.

L. Untereiner, P. Kraemer, D. Cazier, and D. Bechmann. CPH: A compact representation for hierarchical meshes generated by primal refinement. Computer Graphics Forum, 2015.

Dirk van Dalen. L.E.J. Brouwer — Topologist, Intuitionist, Philosopher. Springer Science+Business Media, 2013.

L. van Elfrinkhof. Eene eigenschap van de orthogonale substitutie van de vierde orde. In Handelingen van het 6e Nederlandsch Natuurkundig en Geneeskundig Congres, pages 237–240, Delft, 1897.

Marc van Kreveld. Digital elevation models and TIN algorithms. In Marc van Kreveld, Jürg Nievergelt, Thomas Roos, and Peter Widmayer, editors, Algorithmic Foundations of Geographic Information Systems, volume 1340 of Lecture Notes in Computer Science, chapter 1, pages 37–78. Springer-Verlag, Berlin, 1997.

Marc van Kreveld. Algorithms for triangulated terrains. In Proceedings of the 24th International Conference on Current Trends in Theory and Practice of Computer Science, volume 1338 of Lecture Notes in Computer Science, pages 19–36. Springer-Verlag, 1997.

Peter van Oosterom. Reactive Data Structures for Geographic Information Systems. PhD thesis, Leiden University, 1990.

Peter van Oosterom. Maintaining consistent topology including historical data in a large spatial database. In Proceedings of Auto-Carto 13, 1997.

Peter van Oosterom. Spatial access methods. In Paul A. Longley, Michael F. Goodchild, David J. Maguire, and David W. Rhind, editors, Geographical Information Systems: Principlesm Technical Issues, Management Issues and Applications, volume 1, chapter 2.3, pages 385–400. Wiley, 1999.

Peter van Oosterom. Variable-scale topological data structures suitable for progressive data transfer: The GAP-face tree and GAP-edge forest. Cartography and Geographic Information Science, 32(4):331–346, 2005.

Peter van Oosterom and Martijn Meijers. Towards a true vario-scale structure supporting smooth-zoom. In Proceedings of the 14th ICA/ISPRS Workshop on Generalisation and Multiple Representation, Paris, 2011.

Peter van Oosterom and Martijn Meijers. Vario-scale data structures supporting smooth zoom and progressive transfer of 2D and 3D data. International Journal of Geographical Information Science, 28:455–478, 2014.

Peter van Oosterom and Jantien Stoter. 5D data modelling: Full integration of 2D/3D space, time and scale dimensions. In Sara Irina Fabrikant, Tumasch Reichenbacher, Marc van Kreveld, and Christoph Schlieder, editors, Geographic Information Science: 6th International Conference, GIScience 2010, Zurich, Switzerland, September 14-17, 2010. Proceedings, pages 311–324. Springer Berlin Heidelberg, 2010.

Herman Varma, H. Boudreau, and W. Prime. A data structure for spatio-temporal databases. In Proceedings of the IHO Review, pages 1–10, 1990.

Todd L. Veldhuizen. C++ templates are turing complete. Available at, 2003.

Luiz Velho. Stellar subdivision grammars. In L. Kobbelt, P. Schröder, and H. Hoppe, editors, Eurographics Symposium on Geometry Processing. The Eurographics Association, 2003.

Remco C. Veltkamp and Michiel Hagedoorn. State of the art in shape matching. In Principles of Visual Information Retrieval, Advances in Pattern Recognition, pages 87–119. Springer London, 2001.

Kenneth James Versprille. Computer-aided design applications of the rational b-spline approximation form. PhD thesis, Syracuse University, 1975.

Georges Voronoi. Nouvelles applications des paramètres continus à la théorie des formes quadratiques. Premier mémoire. Sur quelques propriétés des formes quadratiques positives parfaites. Journal für die Reine und Angewandte Mathematik, 133:97–178, 1908.

Detlev Wagner, Mark Wewetzer, Jürgen Bogdahn, Nazmul Alam, Margitta Pries, and Volker Coors. Geometric-semantical consistency validation of CityGML models. In J. Pouliot, S. Daniel, F. Hubert, and A. Zamyadi, editors, Progress and New Trends in 3D Geoinformation Sciences, Lecture Notes in Geoinformation and Cartography. Springer Berlin Heidelberg, 2013.

Jianning Wang and Manuel M. Oliveira. Filling holes on locally smooth surfaces reconstructed from point clouds. Image and Vision Computing, 25(1):103–113, 2007.

Robert Weber, Hans-J. Schek, and Stephen Blott. A quantitative analysis and performance study for similarity-search methods in high-dimensional spaces. In Proceedings of the 24th VLDB Conference, pages 194–205. ACM, 1998.

Robert Weibel. Generalization of spatial data: Principles and selected algorithms. In Marc van Kreveld, Jürg Nievergelt, Thomas Roos, and Peter Widmayer, editors, Algorithmic Foundations of Geographic Information Systems, volume 1340 of Lecture Notes in Computer Science, pages 99–152. Springer Berlin Heidelberg, 1997.

Kevin Weiler. The radial edge data structure: a topological representation for non-manifold geometric boundary modeling. In M.J. Wozny and H.W. McLaughlin, editors, Geometric modeling for CAD applications: selected and expanded papers from the IFIP WG 5.2 working conference, pages 3–36. Elsevier, May 1988.

John D. Weld and Ming C. Leu. Geometric representation of swept volumes with application to polyhedral objects. The International Journal of Robotics Research, 9(5):105–117, 1990.

Haim J. Wolfson and Isidore Rigoutsos. Geometric hashing: An overview. IEEE Computational Science and Engineering, 4(4):10–21, October–December 1997.

M.F. Worboys. A model for spatio-temporal information. In Proceedings of the 5th International Symposium on Spatial Data Handling, pages 602–611, 1992.

Michael Worboys. The maptree: A fine-grained formal representation of space. In Ningchuan Xiao, Mei-Po Kwan, Michael F. Goodchild, and Shashi Shekhar, editors, Proceedings of the 7th International Conference GIScience 2012, volume 7478 of Lecture Notes in Computer Science, pages 298–310. Springer, 2012.

Michael Worboys and Matt Duckham. GIS: A Computational Perspective. CRC Press, 2nd edition, 2004.

Michael F. Worboys. A generic model for planar geographical objects. International Journal of Geographical Information Systems, 6(5):353–372, 1992.

Michael F. Worboys, Hilary M. Hearnshaw, and David J. Maguire. Object-oriented data modelling for spatial databases. International Journal of Geographical Information Systems, 4(4):369–383, 1990.

Mann-May Yau and Sargur N. Srihari. A hierarchical data structure for multidimensional digital images. Communications of the ACM, 26(7):504–515, 1983.

May Yuan. Wildfire conceptual modeling for building GIS space-time models. In Proceedings of GIS/LIS'94, pages 860–869, 1994.

Hui Zhang and Andrew J. Hanson. Shadow-driven 4D haptic visualization. IEEE Transactions on Visualization and Computer Graphics, 13(6):1688–1695, November/December 2007.

Xiang Zhang, Tinghua Ai, Jantien Stoter, and Xi Zhao. Data matching of building polygons at multiple map scales improved by contextual information and relaxation. ISPRS Journal of Photogrammetry and Remote Sensing, 92:147–163, June 2014.

Yeting Zhang, Qing Zhu, Gang Liu, Wenting Zheng, Zhonghua Li, and Zhiqiang Du. GeoScope: Full 3D geospatial information system case study. Geo-Spatial Information Science, 14(2):150–156, 2011.

Junqiao Zhao, Qing Zhu, Zhiqiang Du, Tiantian Feng, and Yeting Zhang. Mathematical morphology-based generalization of complex 3D building models incorporating semantic relationships. ISPRS Journal of Photogrammetry and Remote Sensing, 68:95–111, March 2012.

Junqiao Zhao, Jantien Stoter, and Hugo Ledoux. A framework for the automatic geometric repair of CityGML models. In Manfred Buchroithner, Nikolas Prechtel, and Dirk Burghardt, editors, Cartography from Pole to Pole: Selected Contributions to the XXVIth International Conference of the ICA, Dresden 2013, Lecture Notes in Geoinformation and Cartography, pages 187–202. Springer Berlin Heidelberg, 2014.

Qing Zhu, Junqiao Zhao, Xiaochun Liu, and Yeting Zhang. Perceptually guided geometrical primitive location method for 3D complex building simplification. In Thomas H. Kolbe, Hao Zhang, and Sisi Zlatanova, editors, Proceedings of GeoWeb 2009 Academic Track – Cityscapes, volume XXXVIII–3–4/C3 of The International Archives of Photogrammetry, Remote Sensing and Spatial Information Science, pages 74–79. ISPRS, 2009.

Siyka Zlatanova. 3D GIS for Urban Development. PhD thesis, Technische Universität Graz, March 2000.

Siyka Zlatanova and Daniel Holweg. 3D geo-information in emergency response: A framework. In Proceedings of the 4th International Symposium on Mobile Mapping Technology, 2004.