From Isovists to Visibility Graphs: A Methodology for the Analysis of Architectural Space

May combine two claims.

In the Villa Mairea, the most private spaces, such as bedrooms and study rooms, are highly clustered, whereas social spaces, such as the living rooms on each floor and ground-floor sitting rooms, offer multidirectional fields of view and therefore low C_i values.

“The figure shows that the most private spaces, such as bedrooms and study rooms, are highly clustered whereas social spaces, such as the living rooms on each floor and ground-floor sitting rooms offer multidirectional fields of view and therefore low C i , values, hinting atöwithout intruding onöthe range of the more private spaces.”

Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based). May combine two claims.

In figure 3 the coverage is not sufficient and the isovist area no longer corresponds perfectly to the neighbourhood size.

“(We assume adequate coverage of generating locations throughout the system.In figure 3 the coverage is not sufficient and the isovist area no longer corresponds perfectly to the neighbourhood size.)”

May combine two claims.

C_i values have a maximum at locations closer to the central element, which is more self-contained with almost convex visual fields, and lowest values occur further away where isovists are multidirectional.

“there is a maximum at locations closer to the central element, which is more self-contained, with almost convex visual fields.The lowest values occur further away where isovists are multidirectional”

May combine two claims.

A best-fit line through the data gives a reasonable exponential correlation between observed room occupancy and L_i, and the only significant outlier is the Tate Gallery shop, which is the only room not used as gallery space.

“A best-fit line through the data gives a reasonable exponential correlation between the two variables and it is noticeable that the only significant outlier found is the Tate Gallery shop, which is the only room that is not used as gallery space.”

• AssumptionRests on an assumption: The Tate Gallery shop is the only room that is not used as gallery space.

May combine two claims.

Although there is informational stability with respect to vertical surfaces, there are clear variations in the internal relational properties of the isovists within these spaces.

“Although there is `informational stability' with respect to vertical surfaces there are clear variations in the internal relational properties of the isovists within these spaces.”

The quote only partly states this claim.

When analysed in terms of accessibility, the core L_i values are shifted to the central space that links the two locations with the richest accessibility fields and spreads towards the far side offering views to the smaller pool and statue.

“When analysed in terms of accessibility, however, the core”

May combine two claims.

As we move towards the entrance, through the terraces, the space becomes gradually more clustered and only the central core inside the building, visible through the glass, features as an object.

“As we move towards the entrance, through the terraces, the space becomes gradually more clustered and only the central core inside the building, visible through the glass, features as an object [figure 8(b)].”

• AssumptionRests on an assumption: The external envelope of Farnsworth House is made entirely of glass.

May combine two claims.

We have shown results comparing the level of occupation of rooms found in a building with the results of an L_i analysis of that building and demonstrated that there is some quantitative correspondence between the two.

“We have shown results comparing the level of occupation of rooms found in a building with the results of an”

Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based).

The main difference in the configurational patterns generated results from the way the large pool is analysed.

“The main difference in the configurational patterns generated results from the way the large pool is analysed.”

May combine two claims.

The isovist polygon at p1 is more convex (in terms of M2 and P) than that at p2, yet the value of C_i at p2 is higher.

“The isovist polygon at p 1 is more convex (in terms of M 2 and P) than that at p 2 , yet the value of C i at p 2 is higher.”

May combine two claims.

In the Barcelona Pavilion, path length analysis produces a pattern that resembles that of neighbourhood size, or area of visual fields, and therefore is similar to Benedikt's area measurement, owing to the fact that this is a small or shallow system where the architect introduces partitions to structure the space without disturbing too much its continuity.

“In both cases, path length analysis produces a pattern that resembles that of neighbourhood size, or area of visual fields, and therefore is similar to Benedikt's area measurement, owing to the fact that this is a small or shallow system where the architect introduces partitions to structure the space without disturbing too much its continuity”

• cites BenediktNot matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

The isovist field lines are continuous, whereas the discrete generating locations used to construct the visibility graph can be seen in the second diagram.

“Note that the isovist field lines are continuous, whereas the discrete generating locations used to construct the visibility graph can be seen in the second diagram.”

Probably not a substantial claim: may not pass S4 (based).

Applications of the isovist in architectural analysis have been limited to a small number of studies.

“However, despite the elegance of Benedikt's isovist methodology, and its close relationship to theories of visual perception and spatial description, applications of the isovist in architectural analysis have been limited to a small number of studies.”

Probably not a substantial claim: may not pass S3 (load-bearing).

In a representation on a two-dimensional plane, the graph edges are undirected.

“In a representation on a two-dimensional plane, the graph edges are undirected (that is, if v 1 can see v 2 , then v 2 can see v 1 ).”

Probably not a substantial claim: may not pass S4 (based).

Visibility graph properties may be closely related to manifestations of spatial perception, such as way-finding, movement, and space use.

“Finally we show that visibility graph properties may be closely related to manifestations of spatial perception, such as way-finding, movement, and space use.”

Probably not a substantial claim: may not pass S3 (load-bearing).

The clustering coefficient and mean shortest path length have previously been used together to characterise graph systems as a whole.

“The clustering coefficient and mean shortest path length have previously been used together to characterise graph systems as a whole (see Watts and Strogatz, 1998) and we discuss how this characterisation might be applied to visibility graphs of environments in further work.”

• cites Watts and Strogatz, 1998 sourceNot checked — no full text of the source

May combine two claims.

In a closed convex area there is some potential for interaction, whereas in a junction there are numerous, but different, opportunities to form intervisible links.

“In a closed convex area there is some potential for interaction, whereas in a junction there are numerous, but different, opportunities to form intervisible links.”

Probably not a substantial claim: may not pass S4 (based).

Much of the viewshed literature still concentrates on mapping the properties of single viewsheds as fields, not on the relationships between viewsheds.

“Indeed, much of the viewshed literature still concentrates on mapping the properties of single viewsheds as fields, not on the relationships between viewsheds.”

Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based).

Many possible measures of an undirected graph are also applicable to a directed graph, including those illustrated in the paper.

“Many possible measures of an undirected graph are also applicable to a directed graph, including those we illustrate in this paper, so that the generality of the method presented is unaffected.”

Probably not a substantial claim: may not pass S3 (load-bearing).

de Arruda Campos (1997) finds good correlation with the number of axial lines intersecting at an urban space and the number of people making informal use of the square.

“In addition, de Arruda Campos (1997) finds good correlation with the number of axial lines intersecting at an urban space (implying a multidirectional visual field, that is, low C i ) and the number of people making informal use of the square”

• cites de Arruda Campos (1997)Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

Probably not a substantial claim: may not pass S3 (load-bearing).

Benedikt and Burnham (1985) show that perception of the size of a space is affected by the variance of the radials of an isovist and the perimeter.

“For example, Benedikt and Burnham (1985) show that perception of the size of a space is affected by the variance of the radials of an isovist and the perimeter (both indicators of convexity).”

• cites Benedikt and Burnham (1985)Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

Probably not a substantial claim: may not pass S3 (load-bearing).

A permeability graph is the special case of a visibility graph constructed at floor level.

“To be clear, a `permeability graph' is the special case of a visibility graph constructed at floor level.”

Probably not a substantial claim: may not pass S3 (load-bearing).

e-spaces are derived by relating space to built form, rather than derived from the space as it might be experienced.

“As a spatial description, e-spaces present a different approach to visibility graphs, primarily because they are derived by relating space to built form, rather than derived from the space as it might be experienced.”

May combine two claims.

The geometric formulation of isovist measures means that they index purely local properties of space, and the visual relationship between the current location and the whole spatial environment is missed.

“First, the geometric formulation of isovist measures means that they index purely local properties of space, and the visual relationship between the current location and the whole spatial environment is missedöincluding the fact that the internal visual relationships between locations within the isovist are ignored.”

Probably not a substantial claim: may not pass S3 (load-bearing).

In other representations visibility is not necessarily mutual.

“However, in other representations visibility is not necessarily mutualöfor example, viewshed analyses often consider viewer height.”

May combine two claims.

The clustering coefficient is potentially related to the decision-making process in way-finding and navigation and marks out key decision points within complex configurations.

“Because movement in some sense involves making decisions about which parts of one's current visual information to leave behind, the clustering coefficient is potentially related to the decisionmaking process in way-finding and navigation and certainly marks out key decision points within complex configurations.”

May combine two claims.

Finding a sufficient set by the method of choosing strategic locations and maximising viewable area is possible but not guaranteed to be a minimal covering set.

“However, although finding a sufficient set by this method is possible, it is not guaranteed to be a minimal covering set (Davis and Benedikt, 1979).”

• cites Davis and Benedikt, 1979 sourceNot checked — no full text of the source

Probably not a substantial claim: may not pass S4 (based).

The graph of mutual visibility between locations is the more general concept of a visibility graph.

“and that we are in fact invoking the more general concept of a visibility graph.”

Probably not a substantial claim: may not pass S4 (based).

If the set of generating locations covers the entire space at some uniform resolution, then this set can be thought of as equivalent to the isovist itself.

“Now if the set of generating locations covers the entire space (at some uniform resolution, so that for our purposes it fully describes the space), then this set can be thought of as equivalent to the isovist itself.”

May combine two claims.

If the isovist being considered is almost a convex polygon, then almost all the point locations within the neighbourhood will be able to see each other, and hence C_i will tend to one.

“If the isovist being considered is almost a convex polygon, then almost all the point locations within the neighbourhood will be able to see each other, and hence C i will tend to one.”

Probably not a substantial claim: may not pass S4 (based).

As isovists can be drawn at any location in space, a graph of lines-of-sight connections may be constructed easily, at any required degree of spatial resolution, by using the visual relationships between isovists.

“However, as isovists can be drawn at any location in space, a graph of lines-of-sight connections may be constructed easily, at any required degree of spatial resolution, by using the visual relationships between isovists.”

Classified as probably not a substantial claim.

The ability of axial maps to represent and quantify spatial configurations has a major drawback: each line or convex region is represented by a node in the graph, and so only a single graph measure can be defined for points along the whole length of the line, or all points within the convex region.

“Despite their general applicability, the ability of these maps to represent and quantify spatial configurations still has one major drawback: each line or convex region is represented by a node in the graph, and so only a single graph measure can be defined for points along the whole length of the line, or all points within the convex region.”

May combine two claims.

By reinterpreting the set of isovists as a graph we have made the system more amenable to a new set of analytic tools, while retaining a mapping back to the original isovist interpretation through the neighbourhood size k_i of a vertex.

“By reinterpreting the set of isovists as a graph we have made the system more amenable to a new set of analytic tools, while retaining a mapping back to the original isovist interpretation through the neighbourhood size k i of a vertex.”

Classified as probably not a substantial claim.

We have proposed two further measurements of the graph that may be useful for understanding the perception and use of architectural spaces.

“We have proposed two further measurements of the graph that may be useful for understanding the perception and use of architectural spaces.”

Probably not a substantial claim: may not pass S2 (checkable). May combine two claims.

By looking at relationships at both a local and a global level, we hope to capture the common experience of that space, and so visibility graph analysis may represent a step towards exploring the relationship between architects, as designers of spaces, and users, as architects of their own experience of space.

“However, by looking at relationships at both a local and a global level, we hope to capture the common experience of that space, and so visibility graph analysis may represent a step towards exploring the relationship between architects, as designers of spaces, and users, as architects of their own experience of space.”

Probably not a substantial claim: may not pass S2 (checkable), S3 (load-bearing), S4 (based). May combine two claims.

Any population of a space will lead to changes in the visual field which we have not considered, and members of the population will experience a space through their personal memory of the previous spaces they themselves have moved through.

“We must of course be careful to note that any population of a space will lead to changes in the visual field which we have not considered and that members of the population will experience a space through their personal memory of the previous spaces they themselves have moved through.”

Probably not a substantial claim: may not pass S4 (based). May combine two claims.

Mean shortest path length measures accessibility of every location in the spatial system, and has a significant advantage over axial and convex configurational analysis, which is unable to identify variation across open-plan layouts.

“accessibility of every location in the spatial system, it has a significant advantage over axial and convex configurational analysis, which, for example, is unable to identify variation across `open-plan' layouts.”

Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

The Barcelona Pavilion was built in 1929 for the German participation in the Barcelona exhibition and demolished afterwards; it was retrieved through photographs and plans, to be rebuilt in 1986.

“The pavilion was built in 1929 for the German participation in the Barcelona exhibition and demolished afterwards.It was retrieved through photographs and plans, to be rebuilt in 1986 (for a detailed discussion, see Futagawa and Neumeyer, 1995).”

• cites Futagawa and Neumeyer, 1995Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

May combine two claims.

The clustering coefficient is not strictly a convexity measure, but is perhaps more related to how self-contained the information in a particular isovist is.

“Hence the clustering coefficient is not strictly a convexity measure, but perhaps more related to how `self-contained' the information in a particular isovist is.”

Probably not a substantial claim: may not pass S3 (load-bearing).

Because they cannot see the top spaces of the configuration, an individual occupying that location would not know that there might be a place around the corner.

“In this case, because they cannot `see' the top spaces of the configuration, an individual occupying that location would not know that there might be a place `around the corner'.”

May combine two claims.

Although a correspondence of this sort might be expected because we are mapping a measure of centrality, it is worth demonstrating that this is not a necessary result.

“Although a correspondence of this sort might be expected in view of the fact that we are mapping a measure of centrality, it is worth demonstrating that this is not a necessary result.”

Probably not a substantial claim: may not pass S3 (load-bearing).

The comparison shows how the space has been manipulated by the architect to arrange views across the pool and the movement around it.

“The comparison shows how the space has been manipulated by the architect to arrange views across the pool and the movement around it.”

Probably not a substantial claim: may not pass S3 (load-bearing).

The clustering coefficient C_i demonstrates a local measure of the graph, since it depends only on the relation between vertices in a neighbourhood.

“The clustering coefficient C i demonstrates a local measure of the graph, since it depends only on the relation between vertices in a neighbourhood”

Probably not a substantial claim: may not pass S2 (checkable), S3 (load-bearing).

Comparing the L_i values across the visibility graph with people movement patterns may be fruitful.

“This indicates that comparing the”

Classified as probably not a substantial claim. May combine two claims.

The isovists we employ are used to derive the graph of intervisible locations and hence the visibility graph is a tool with which we can begin consciously to explore the visibility and permeability relations in spatial systems.

“The isovists we employ are used to derive the graph of intervisible locations and hence the visibility graph is a tool with which we can begin consciously to explore the visibility and permeability relations in spatial systems.”

Probably not a substantial claim: may not pass S3 (load-bearing).

The sensitivity of clustering coefficient analysis to the size of object in the environment would have a significant impact if we were to consider not just the internal relationships in Farnsworth House, but also its relationship to the surrounding environment.

“The sensitivity of clustering coefficient analysis to the size of object in the environment would have a significant impact if we were to consider not just the internal relationships in Farnsworth House, but also its relationship to the surrounding environment.”

Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

Benedikt uses the plans of the Barcelona Pavilion to investigate isovist field contour maps, demonstrating that the area of the visual field changes continuously with movement, as surfaces disappear and others come into view.

“Benedikt uses the plans of this building to investigate isovist ^field contour maps, demonstrating that the area of the visual field changes continuously with movement, as surfaces disappear and others come into view.”

• cites BenediktNot matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

Probably not a substantial claim: may not pass S3 (load-bearing).

The mean shortest path length L_i demonstrates a global measure of the graph, in that for each vertex it depends on the relative placement of all other vertices in the graph.

“whereas the mean shortest path length”

Probably not a substantial claim: may not pass S3 (load-bearing).

Conroy (2000) notes correspondence between 'junctions' and places where people pause on journeys.

“and Conroy (2000) notes correspondence between `junctions' and places where people pause on journeys.”

• cites Conroy (2000)Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

May combine two claims.

Because C_i is not just a measure of geometric spikiness but also a measure of how much objects of varying sizes disrupt the space, it may improve our understanding of how a space is perceived.

“Thus, because C i is not just a measure of geometric `spikiness', but also a measure of how much objects of varying sizes disrupt the space, it may improve our understanding of how a space is perceived.”

• AssumptionRests on an assumption: People will not usually be fooled by adding a pillar to a space; through movement they will still perceive the space as a whole.

Probably not a substantial claim: may not pass S2 (checkable), S3 (load-bearing). May combine two claims.

The measures are justified to some extent by the application of similar metrics to graphs of urban and building environments, and by their relevance to ongoing research; however, they are also intended as examples of the wider set of graph measures available.

“The measures are justified to some extent by the application of similar metrics to graphs of urban and building environments, and by their relevance to ongoing research; however, they are also intended as examples of the wider set of graph measures available.”

Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

The analysis we have made has not considered the built fabric, or the relation of the interior to the building's context.

“Further, the analysis we have made has not considered the built fabric, or the relation of the interior to the building's context.”

May combine two claims.

Any pair of mutually visible locations within the isovist area contribute to the overall C_i value; thus any system with visibility loops will display higher C_i values than those without.

“Any pair of mutually visible locations within the isovist area contribute to the overall C i value; thus any system with `visibility loops' will display higher C i values than those without.”

Probably not a substantial claim: may not pass S4 (based).

Sets of locations within the isovist of a point determine conditions of copresence of occupants and hence potential action and interaction.

“In this sense, sets of locations within the isovist of a point determine conditions of copresence of occupants and hence potential action and interaction.”

Probably not a substantial claim: may not pass S2 (checkable).

This allows us to discuss any measurement of the graph in terms of its spatial meaning.

“This allows us to discuss any measurement of the graph in terms of its spatial meaning.”

Probably not a substantial claim: may not pass S3 (load-bearing).

Average clustering coefficient and the characteristic path length have been used by Watts and Strogatz (1998) to analyse small worlds networks.

“average clustering coefficient and the characteristic path length (the average of the mean shortest path length for the whole system) have been used by Watts and Strogatz (1998) to analyse small worlds networks.”

• cites Watts and Strogatz (1998) sourceNot checked — no full text of the source

Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

According to van Fraassen's scientific empiricism, our interpretation of any graph will be limited by the ability of our measures to distinguish between different configurations, so we can only describe a graph through the number of metrics we invent to classify it.

“According to van Fraassen's scientific empiricism (1980, pages 76 ^91) our interpretation of any graph will be limited by the ability of our measures to distinguish between different configurations, so we can only describe a graph through the number of metrics we invent to classify it.”

• cites van Fraassen, 1980 sourceNot checked — no full text of the source