Topology for 3D spatial objects

Abstract

Topology is one of the mechanisms to describe relationships between spatial objects and thus the basics for many spatial operations. In this paper, we present models that are built on the topological properties of the spatial objects. They are usually called topological models and are considered by many the best suited for complex spatial analysis (i.e shortest path, line of view). There are a number of topological models that are utilized for 2D and 2.5D spatial objects by experimental and commercial software. However, when we move to the next dimension (i.e 3D), many difficulties are encountered in establishing the topology for the objects (consisting of points, lines, faces, and solids). This paper describes some existing topological models and a comparison between them is made. The advantages and disadvantages of the models and the recent experiments by the authors towards formalizing a 3D topology for 3D objects are discussed. The paper considers the models in object-oriented (OO) environment as well. Finally, we summarize the application of the 3D topological model, highlight the current approaches and the outlook of the works.