The topology of shapes made with points
Name
2020__EPB__TopologyPoints__Haridis.pdf
Size
2.59 MB
Format
Adobe PDF
Checksum (MD5)
6db4e9a91a65b4e1015a75ceadfd81d1
Author(s)
Haridis, Alexandros
Date Issued
February 11, 2019
Journal
Environment and Planning B: Urban Analytics and City Science
Publisher
SAGE Publications
Citation
Haridis, A. (2020). The topology of shapes made with points. Environment and Planning B: Urban Analytics and City Science, 47(7), 1279-1288.
Version
Author's final manuscript
Abstract
In architecture, city planning, visual arts, and other design areas, shapes are often made with points, or with structural representations based on point-sets. Shapes made with points can be understood more generally as finite arrangements formed with elements (i.e. points) of the algebra of shapes Ui, for i = 0. This paper examines the kind of topology that is applicable to such shapes. From a mathematical standpoint, any “shape made with points” is equivalent to a finite space, so that topology on a shape made with points is no different than topology on a finite space: the study of topological structure naturally coincides with the study of preorder relations on the points of the shape. After establishing this fact, some connections between the topology of shapes made with points and the topology of “point-free” pictorial shapes (when i > 0) are defined and the main differences between the two are summarized.
MIT Department
Massachusetts Institute of Technology. Department of Architecture
Terms of Use
Creative Commons Attribution-Noncommercial-ShareAlike
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1177/2399808319827015
