An optimal algorithm for intersecting three-dimensional convex polyhedra
SIAM Journal on Computing
Handbook of discrete and computational geometry
Fast Detection of Polyhedral Intersections
Proceedings of the 9th Colloquium on Automata, Languages and Programming
A Complete and Efficient Algorithm for the Intersection of a General and a Convex Polyhedron
WADS '93 Proceedings of the Third Workshop on Algorithms and Data Structures
An abstract model of three-dimensional spatial data types
Proceedings of the 12th annual ACM international workshop on Geographic information systems
Spatial Data Modelling for 3D GIS
Spatial Data Modelling for 3D GIS
3D spatial operations in geo DBMS environment for 3D GIS
ICCSA'07 Proceedings of the 2007 international conference on Computational science and its applications - Volume Part I
Similarity in (spatial, temporal and) spatio-temporal datasets
Proceedings of the 15th International Conference on Extending Database Technology
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Apart from visualization tasks, three-dimensional (3D) data management features are not or only hardly available in current spatial database systems and Geographic Information Systems (GIS). But the increasing demands from application domains like urban planning, geoscience, and soil engineering call for systems that are capable of storing, retrieving, querying, and manipulating the underlying 3D spatial data. Current 3D data models are tailored to specific applications and simple 3D spatial objects only, and available 3D data structures are restricted to main memory representations; thus they lack the ability of handling general and complex 3D spatial objects in a database context. Available algorithms, especially intersection algorithms for 3D objects, usually require special properties like convexity or monotonicity. Therefore, universal intersection algorithms that are capable of handling general 3D spatial objects are currently unknown. This paper proposes a paradigm called slice representation as a general data representation method for complex 3D spatial data types. In particular, data structures are developed applying the paradigm to point3D, line3D, surface, and volume data types. Two intersection algorithms that involve one argument of type point3D are introduced and show the benefit of the slice representation.