A Structural Perspective on Visibility Patterns with a Topographic Surface
Abstract
A topographic surface can be modeled as a graph, a visibility graph in terms of how each point location is visible to every other. This paper demonstrates various structural properties of visibility patterns with a topographic surface from a graph perspective, which could be important for landscape planning. This paper illustrates the fact that the visibility graph with a topographic surface is a small-world. This finding implies that the average visual separation between any two point locations with a surface is very short (i.e. a small separation), and the visible locations to a given location have a high possibility of being visible to each other (i.e. a high clustering level). Additionally we show that the visibility graph exhibits an exponential distribution rather than a power law distribution, i.e. it is not scale-free, in contrast to many other real world networks.
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SNVG has an exponential distribution rather than a power law.
“Findings on the SNVG that has an exponential distribution rather than a power law, confirms and reinforces the existing knowledge on visibility graphs (Jiang 2005).”
From A Network Approach to Link Visibility and Urban Activity Location (2018) · cites this paper as Jiang 2005
Cites
From Isovists to Visibility Graphs: A Methodology for the Analysis of Architectural Space
Turner, A., Doxa, M., O'Sullivan, D., & Penn, A. (2001) · Environment and Planning B: Planning and Design · doi:10.1068/b2684 · Cited by 969 · cited 2× · see citing works
“In this connection, it would be better to use the individual nodes of a metric surface network ( Pfaltz 1976 ) rather than those of a TIN for the computation of visibilities with a surface.”
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A Network Approach to Link Visibility and Urban Activity Location
Natapov, A., Czamanski, D., & Fisher-Gewirtzman, D. (2018) · Networks and Spatial Economics · doi:10.1007/s11067-018-9411-4 · Cited by 11 · see citing works
“…package, Gephi (Jacomy et al. 2009), using the probability of links distribution equal to: pi ¼ 2E N N−1ð Þ ð5Þ The calculations of L and C in actual and random graphs were performed in the same package and for the regular graphs it is straightforward following Jiang (2005) (see supporting files).”
MethodResult
- Authors
- Jiang, B.
- Affiliations
- University of Gävle (SE)
- Corresponding author
- Jiang, Bin
- ORCID
- Jiang, Bin
- Venue
- Transactions in GIS
- Publisher
- Wiley
- Published
- 2005-10
- Volume
- 9
- Issue
- 4
- Pages
- 475-488
- ISSN
- 1361-1682 (ISSN-L)
- 1467-9671
- OpenAlex
- W2147695953
- Cited by
- 11
- References
- 1
- Citations by year
- 2021: 1 · 2020: 1 · 2019: 2 · 2018: 1 · 2014: 1 · 2013: 1
- FWCI
- 5.48
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Transactions in GIS (publishedVersion)
- Topics
- Physical Sciences › Engineering › Building and Construction › Urban Design and Spatial Analysis
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Complex Network Analysis Techniques
- Physical Sciences › Computer Science › Computer Vision and Pattern Recognition › Graph Theory and Algorithms
- Keywords
- visibility graph, topographic surfaces, small-world networks, clustering coefficient, exponential degree distribution, scale-free networks, landscape planning, graph structure
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