Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/19751
Title: Basic topological models for spatial entities in 3-dimensional space
Authors: Li, Z 
Li, Y
Chen, YQ 
Keywords: Raster space
Spatial entities
Topological models
Topological properties
Vector space
Issue Date: 2000
Source: GeoInformatica, 2000, v. 4, no. 4, p. 419-433 How to cite?
Journal: GeoInformatica 
Abstract: In recent years, models of spatial relations, especially topological relations, have attracted much attention from the GIS community. In this paper, some basic topologic models for spatial entities in both vector and raster spaces are discussed. It has been suggested that, in vector space, an open set in 1-D space may not be an open set any more in 2-D and 3-D spaces. Similarly, an open set in 2-D vector space may also not be an open set any more in 3-D vector spaces. As a result, fundamental topological concepts such as boundary and interior are not valid any more when a lower dimensional spatial entity is embedded in higher dimensional space. For example, in 2-D, a line has no interior and the line itself (not its two end-points) forms a boundary. Failure to recognize this fundamental topological property will lead to topological paradox. It has also been stated that the topological models for raster entities are different in Z2 and R2. There are different types of possible boundaries depending on the definition of adjacency or connectedness. If connectedness is not carefully defined, topological paradox may also occur. In raster space, the basic topological concept in vector space-connectedness-is implicitly inherited. This is why the topological properties of spatial entities can also be studied in raster space. Study of entities in raster (discrete) space could be a more efficient method than in vector space, as the expression of spatial entities in discrete space is more explicit than that in connected space.
URI: http://hdl.handle.net/10397/19751
ISSN: 1384-6175
DOI: 10.1023/A:1026570130172
Appears in Collections:Journal/Magazine Article

Access
View full-text via PolyU eLinks SFX Query
Show full item record

SCOPUSTM   
Citations

13
Last Week
0
Last month
0
Citations as of Feb 24, 2017

Page view(s)

23
Last Week
0
Last month
Checked on Feb 19, 2017

Google ScholarTM

Check

Altmetric



Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.