Data structures and intersection algorithms for 3D spatial data types

Abstract

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.