A triangulated spatial model for detection of spatial characteristics of GIS data

Abstract

The detection of spatial characteristics of GIS data is one of the key technologies in GIS applications. It plays an important role in such applications as spatial data mining, map generalization and spatial cognition. This paper aims at the objective to utilize the computer geometry tool Delaunay triangulated irregular network (TIN) to realize the detection of spatial structural characteristics hidden in geometry data. To formally describe the Delaunay TIN model, we denoted it as triple W <V,E,T>, in which V is a non-empty point set V = {v <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</inf> ,v <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf> ,…,v <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</inf> }, and E is a non-empty edge set E = {e <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</inf> ,e <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf> ,…,e <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</inf> }, and T is a non-empty triangle set T = {t <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</inf> ,t <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf> ,…,t <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</inf> }. Based on the formal model, we define some common operations, such as neighbor(), join(), condition(), and access() and so on, which are the basis of latter application. Also we formally define the traditional geometry object point, line and polygon based on the Delaunay TIN model. The focus of this paper is put on the application of Delaunay TIN to detect the spatial characteristics. According to different geometry form, we provide different approaches to detection different spatial structural characteristics. For point cluster, we provide Delaunay TIN and Voronoi diagram based method to extract distribution extent, distribution density and distribution skeleton; for line object, we provide the method of bend detection, which is an important structural information; for polygon object the bend and bottleneck area being important, based on Delaunay TIN model, we just need to define a visual adjacency distance, different levels of bend and bottleneck can be extracted; and for polygon group, we provide a method for clustering. For all of these methods we conduct experiments, the results are promising and satisfy the basic principle of spatial cognition.