Implementing Watson's algorithm in three dimensions
SCG '86 Proceedings of the second annual symposium on Computational geometry
Voronoi diagrams—a survey of a fundamental geometric data structure
ACM Computing Surveys (CSUR)
Primitives for the manipulation of general subdivisions and the computation of Voronoi
ACM Transactions on Graphics (TOG)
Convex hulls of finite sets of points in two and three dimensions
Communications of the ACM
One Step up the Abstraction Ladder: Combining Algebras - From Functional Pieces to a Whole
COSIT '99 Proceedings of the International Conference on Spatial Information Theory: Cognitive and Computational Foundations of Geographic Information Science
Delete and insert operations in Voronoi/Delaunay methods and applications
Computers & Geosciences
Primitives for computational geometry
Primitives for computational geometry
On the reconstruction of three-dimensional complex geological objects using Delaunay triangulation
Future Generation Computer Systems - Special issue: Geocomputation
Computing the 3D Voronoi Diagram Robustly: An Easy Explanation
ISVD '07 Proceedings of the 4th International Symposium on Voronoi Diagrams in Science and Engineering
A Mathematical Tool to Extend 2D Spatial Operations to Higher Dimensions
ICCSA '08 Proceeding sof the international conference on Computational Science and Its Applications, Part I
A simplicial complex-based DBMS approach to 3D topographic data modelling
International Journal of Geographical Information Science
An operation-independent approach to extend 2D spatial operations to 3D and moving objects
Proceedings of the 16th ACM SIGSPATIAL international conference on Advances in geographic information systems
Voronoi-Based curve reconstruction: issues and solutions
ICCSA'12 Proceedings of the 12th international conference on Computational Science and Its Applications - Volume Part II
Watershed delineation from the medial axis of river networks
Computers & Geosciences
Using extrusion to generate higher-dimensional GIS datasets
Proceedings of the 21st ACM SIGSPATIAL International Conference on Advances in Geographic Information Systems
Modelling higher dimensional data for GIS using generalised maps
ICCSA'13 Proceedings of the 13th international conference on Computational Science and Its Applications - Volume 1
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Many applications in geosciences need to deal with 3D objects. For this, among other requirements, 2D spatial analyses must be extended to support 3D objects. This extension is an important research topic in GIS and computational geometry. Approaches that extend an existing algorithm for a 2D spatial analysis to work for 3D or higher dimensions lead to different algorithms and implementations for different dimensions. Following such approaches the code for a package that supports spatial analyses for both 2D and 3D cases is nearly two times the code size for 2D. While dimension independent algorithms are an alternative toward generalization, they are still implemented separately for each dimension. The main reason is that each dimension is modeled using a different data structure that requires its own implementation details. In this article we use the list data structure to implement n-simplexes-as a data type that supports spatial objects of any dimension. Primitive operations on n-simplexes become manipulating functions over lists, which are independent of the number and type of the elements. We define spatial analyses as combinations of primitive operations on n-simplexes. Since the primitive operations on n-simplexes have been implemented independently of dimension, the spatial analyses are dimension independent, too. Construction of Delaunay triangulation of nD points, as the basic data structure for many geoscientific researches, is used here as the running example. The implementation results for Delaunay triangulation of some 2D and 3D points are presented and discussed. As a case study the implementations are used to calculate the area and volume of the reservoir of a dam at different water levels, which leads to a level-surface-volume diagram.