Implementing Watson's algorithm in three dimensions
SCG '86 Proceedings of the second annual symposium on Computational geometry
Marching cubes: A high resolution 3D surface construction algorithm
SIGGRAPH '87 Proceedings of the 14th annual conference on Computer graphics and interactive techniques
Topological considerations in isosurface generation extended abstract
VVS '90 Proceedings of the 1990 workshop on Volume visualization
Computers & Geosciences - Special issue on GIS design models
Why is the 3D Delaunay triangulation difficult to construct?
Information Processing Letters
ACM Computing Surveys (CSUR)
Selected papers from the 12th annual symposium on Computational Geometry
ACM Transactions on Mathematical Software (TOMS)
The Quadtree and Related Hierarchical Data Structures
ACM Computing Surveys (CSUR)
Three Dimensional Applications in Geographical Information Systems
Three Dimensional Applications in Geographical Information Systems
Environmental Modeling with GIS
Environmental Modeling with GIS
Perturbations and vertex removal in a 3D delaunay triangulation
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
People Manipulate Objects (but Cultivate Fields): Beyond the Raster-Vector Debate in GIS
Proceedings of the International Conference GIS - From Space to Territory: Theories and Methods of Spatio-Temporal Reasoning on Theories and Methods of Spatio-Temporal Reasoning in Geographic Space
GIS: A Computing Perspective, 2nd Edition
GIS: A Computing Perspective, 2nd Edition
On the reconstruction of three-dimensional complex geological objects using Delaunay triangulation
Future Generation Computer Systems - Special issue: Geocomputation
Computational Geometry: Theory and Applications
Urban Data Visualization with Voronoi Diagrams
ICCSA '08 Proceeding sof the international conference on Computational Science and Its Applications, Part I
Moving Phenomenon: Aggregation and Analysis of Geotime-Tagged Contents on the Web
W2GIS '09 Proceedings of the 9th International Symposium on Web and Wireless Geographical Information Systems
Proceedings of the 2011 conference on Information Modelling and Knowledge Bases XXII
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Fields as found in the geosciences have properties that are not usually found in other disciplines: the phenomena studied are often three-dimensional (3D), they tend to change continuously over time, and the collection of samples to study the phenomena is problematic, which often results in highly anisotropic distributions of samples. In the geographical information system (GIS) community, raster structures (voxels or octrees) are the most popular solutions, but, as we show in this paper, they have shortcomings for modelling and analysing 3D geoscientific fields. As an alternative to using rasters, we propose a new spatial model based on the Voronoi diagram (VD) and its dual the Delaunay tetrahedralisation (DT), and argue that they have many advantages over other tessellations. We discuss the main properties of the 3D VD/DT, present some GIS operations that are greatly simplified when the VD/DT is used, and, to analyse two or more fields, we also present a variant of the map algebra framework where all the operations are performed directly on VDs. The usefulness of this Voronoi-based spatial model is demonstrated with a series of potential applications.