PAPER REF # 8041 Proceedings: Eighth International Space Syntax Symposium Edited by M. Greene, J. Reyes and A. Castro. Santiago de Chile: PUC, 2012.
VIEW AND VIEWED ANALYSIS AUTHOR:
Takashi TANIGUCHI Graduate School of Science and Technology, Keio University, Japan e‐mail:
[email protected] Yuto TAKAHASHI Graduate School of Science and Technology, Keio University, Japan Tatsuya KISHIMOTO Faculty of Science and Technology, Keio University, Japan e‐mail:
[email protected]
KEYWORDS:
Visibility Accessibility Problem, Visibility Graph Analysis, Isovist, View and Viewed Analysis
THEME:
Methodological Development and Modeling
Abstract
The visibility accessibility problem is one of the problems in analyzing architectural spatial structures in space syntax. This problem occurs when there are objects such as glass walls, wire fences, ponds and voids disabling direct access to some space you can observe. Straightening the problem, this paper resolves the existing method into accessibility analysis and visibility analysis. Accessibility analysis regards glass walls and ponds as blocks, considering accessibility only. On the other hand, visibility analysis regards ponds as grounds and excludes glass walls, not considering accessibility but considering visibility. These analyses have contradiction to human spatial perception not a little. This paper proposes a method of spatial analysis using space syntax theory named view and viewed analysis which rests on the 2 premises: when we want to observe a space we need to reach another space which we can observe the purpose space directly; a space of a void and a space over a pond are not able to be reached but able to be observed. With this method, we can measure easiness of observing other spaces and being observed from other spaces, considering accessibility. One characteristic of the method is the way of calculating depth considering accessibility and visibility at the same time, and the method calculates 2 types of depth: view depth and viewed depth. View depth is the amount of steps necessary to observe a space from another space, and viewed depth is the amount of steps necessary that a space is observed from another space. For each depth, the method calculates view integration value and viewed integration value in ordinary way. Proving effectiveness of the method, a case study of spatial analysis is conducted at the Barcelona Pavilion, designed by Ludwig Mies van der Rohe and characterized by its glass walls and ponds. The paper divides the architectural space into cells, and setting of the cells rests on the grid system which Ludwig Mies van der Rohe proposed. Data of photographing spots and photographed spots is based on 500 photographs brought from the online photo sharing application Flickr.com. The correlation of the view integration value with the data of photographing spots and the correlation of the viewed integration value with the data of photographed spots are examined. Comparing the proposed method with the existing method, the correlation of the accessibility integration value with the data of photographing spots and the correlation of the visibility integration value with the data of photographed spots are examined too. The result shows that view and viewed analysis has higher correlation to the image conception of space, compared to the existing method.
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1.
INTRODUCTION
Space syntax (Hillier and Hanson 1984; Hillier, Penn et al. 1993; Hillier 1996; Hillier. B 1999) is a spatial analysis methodology which usefulness has been proven. Incorporating the idea of Isovist into space syntax, visibility graph analysis (Turner, A., Doxa, M., et al. 2001) extended space syntax field, but then it caused the visibility accessibility problem. The visibility accessibility problem occurs when we make a graph of architectural spatial structures which has objects such as glass walls, wire fences, ponds and voids disabling direct access to some space we can observe. The essence of the problem is whether we should draw edges between spaces which have such objects between them or not. Space syntax originally drew graphs based on connection of spaces, and there are basically two kinds of connection such as visibility and accessibility. These two are largely different if the problem objects like glass walls and the problem spaces like voids have important role in architectural spaces. Following the definition of Isovist, we should draw graphs based on visibility only, but such graphs include paths which are impossible to walk along. Passing through a glass wall and walking over a void or a pond are some examples. This paper resolves the existing method into accessibility analysis and visibility analysis to straighten the problem. Accessibility analysis regards glass walls and ponds as opaque blocks, and we draw graphs excluding the problem edges which include glass walls or voids between the nodes with this method. Accessibility analysis is a right way to show characteristics of spaces considering accessibility only, but it cannot consider visual effect of architectural elements such as transparency of glass walls. On the other hand, visibility analysis regards ponds as grounds and excludes glass walls, and we draw graphs including the problem edges with this method. Visibility analysis makes graphs including impossible paths to walk along, because it does not consider accessibility. Under the present circumstances, analyzers variously interpret the visibility accessibility problem. Some papers practiced only accessibility analysis, some did only visibility analysis, and others did both of them and compared the results of each analysis (Ruchi C., Yeonsook H. and Sonit B. 2007). Application programs which perform visibility graph analysis like Depthmap (Turner A. 2003, Turner A. 2004) do not cope with the problem. If we want to practice visibility analysis we have to remove glass walls and regard voids and ponds as floors. To solve the problem, layered graphs (Dalton S. and Dalton R. 2009) which add depth of accessibility analysis (accessibility depth) and depth of visibility analysis (visibility depth) in a proportion has been proposed, however a method of determining the proportion has not been proposed. 2.
PROPOSAL OF VIEW AND VIEWED ANALYSIS
The previous section described the visibility accessibility problem and defined accessibility analysis and visibility analysis, but is it correct to separate accessibility from visibility? When we want to observe a space which we cannot observe directly from where we stand we need to reach another space which we can observe the purpose space directly. We cannot divide accessibility and visibility considering human spatial perception, and visibility analysis is deficient in accessibility. This chapter proposes a method of spatial analysis using the space syntax theory named view analysis which considers both accessibility and visibility in accordance with human action of spatial perception. This analysis shows easiness of observing other spaces based on the amount of steps necessary for observing a space
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actually. On the other hand, a space of a void and a space over a pond are not able to be accessed but able to be observed from other spaces (Figure 1), so this paper also proposes viewed analysis which is based on the amount of steps necessary for a space to be observed from another space. View and viewed analysis clearly defines the way of drawing graphs of architectural spatial structures with the problem objects and spaces; therefore this method can be a solution of the visibility accessibility problem.
Figure 1 Section Model Including a Void
One characteristic of view and viewed analysis is the way of calculating depth, and it is different from simple shortest path problem. Comparing the proposed method with the existing method, this chapter explains the way of calculating depth with the all methods: accessibility analysis, visibility analysis, view analysis and viewed analysis. To explain view and viewed analysis this paper defines 2 types of edges: accessibility edges and visibility edges. Accessibility edges are edges between nodes on the floor without the problem objects and spaces. On the other hand, visibility edges include the problem objects and spaces between the nodes (Figure 2).
Figure 2 Accessibility Edge and Visibility Edge
Take Figure 3 for example. Shown in the illustration is a plane spatial model with 12 cells named A to L, and there is a transparent wall between A and B. F is a space of a void, and there are no objects disabling direct access between E and J, G and J, and H and I.
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Figure 3 Plane Model Including a Transparent Wall and a Void
Accessibility analysis makes paths considering accessibility only. As shown in Figure 4, accessibility depth from A to E and I are 1. The depth from A to H, J and K are 2. The depth from A to D, G and L are 3. The depth from A to B and C are 4. Furthermore the depth from A to F is infinity because we cannot reach to voids. Visibility analysis makes paths through transparent walls and voids because it is based on visibility only. As Figure 4 shows, visibility depth from A to B, C, D, E, I and J are 1. The depth from A to F, G, H, K and L are 2.
Figure 4 Depth from A
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View analysis rests on a premise: when we want to observe a space we need to reach another space which we can observe the purpose space directly, so this analysis calculates the amount of steps necessary to observe a space from another space actually. As shown in Figure 4, view depth from A to B, C, D, E, I and J are 1. The depth from A to F, G, H and K are 2 because they are able to be accessed or observed from E or I which are able to be reached from A with 1 step. Finally, the depth from A to L is 3 because L is able to be reached and observed from H which is able to be reached from A with 2 steps. Thus view analysis can add a new edge to a path including accessibility edges only. As green arrows of Figure 5 shows, the path A→D→L does not exist because we cannot reach to D from A directly. Viewed analysis rests on the same premise as view analysis’s and calculates the amount of steps necessary for a space to be observed from another space. As shown in Figure 4, viewed depth from A to B, C, D, E, I, and J are 1. The depth from A to G, H, K and L are 2. In addition, the depth from A to F is infinity because we cannot stand on voids. Thus viewed analysis can use a visibility edge as 1st step only since the premise. As green arrows of Figure 5 shows, the path A←E←H is wrong because we cannot access to E from H directly.
Figure 5 Wrong Paths from A
Table 1 and Table 2 show all depth, k (the amount of nodes included in graph from each node), total depth (TD) and integration values (Int.V) of view analysis and viewed analysis. The way of calculating TD and integration value is completely same as existing method. With the existing method, asymmetric matrix of depth appears only if there are one‐way equipments like escalators. In contrast, matrixes of view depth and viewed depth become asymmetric when the subjected space has objects disabling direct access to some space you can observe. For example, view depth from A to L is 3 (Figure 4) because we have to reach H to observe L, and view depth from L to A is 2 since we can directly observe A from D through the transparent wall. Comparing view depth and viewed depth, we can discover that view depth from x to y is same as viewed depth from y to x. Thus we can get viewed depth from view depth automatically. Describing k, viewed analysis makes different k between each node. Take table 2, k of F is 12 because F can be observed from all other nodes and viewed analysis graph of F includes all nodes. On the other hand, view k of other nodes are 11 since F is a void and other nodes cannot be observed from F. Thus we should use integration value which excludes influence of difference of k. As shown above, there are differences with calculating depth and k between the proposed method and existing method, but the depth of each analysis are completely same if the subjected space does not have objects disabling direct access to some space you can observe. Thus view and viewed analysis does not contradict the existing method especially accessibility analysis.
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Proceedings: Eighth International Space Syntax Symposium. Santiago de Chile: PUC, 2012. Table 1 Result of View Analysis (depth, k, TD, Int. V) A
B
C
D
E
F
G
H
I
J
K
L
k
TD
Int.V
A
0
1
1
1
1
2
2
2
1
1
2
3
12
17
2.611
B
1
0
1
1
3
3
3
2
3
3
2
2
12
24
1.205
C
1
1
0
1
3
3
3
2
3
3
2
2
12
24
1.205
D
1
1
1
0
2
2
2
1
2
2
1
1
12
16
3.134
E
1
2
2
2
0
1
1
1
1
1
1
3
12
16
3.134
F
∞
∞
∞
∞
∞
0
∞
∞
∞
∞
∞
∞
1
∞
0.000
G
2
3
3
2
1
1
0
1
1
1
1
2
12
18
2.238
H
2
2
2
1
1
1
1
0
1
1
2
1
12
15
3.917
I
1
2
2
2
1
1
1
1
0
1
1
2
12
15
3.917
J
1
3
3
2
1
1
1
1
1
0
1
2
12
17
2.611
K
2
2
2
1
1
1
1
2
1
1
0
2
12
16
3.134
L
2
2
2
1
2
2
2
1
2
2
2
0
12
20
1.741
Table 2 Result of Viewed Analysis (depth, k, TD, Int. V)
3.
A
B
C
D
E
F
G
H
I
J
K
L
k
TD
Int.V
A
0
1
1
1
1
∞
2
2
1
1
2
2
11
14
3.318
B
1
0
1
1
2
∞
3
2
2
3
2
2
11
19
1.474
C
1
1
0
1
2
∞
3
2
2
3
2
2
11
19
1.474
D
1
1
1
0
2
∞
2
1
2
2
1
1
11
14
3.318
E
1
3
3
2
0
∞
1
1
1
1
1
2
11
16
2.212
F
2
3
3
2
1
0
1
1
1
1
1
2
12
18
2.238
G
2
3
3
2
1
∞
0
1
1
1
1
2
11
17
1.896
H
2
2
2
1
1
∞
1
0
1
1
2
1
11
14
3.318
I
1
3
3
2
1
∞
1
1
0
1
1
2
11
16
2.212
J
1
3
3
2
1
∞
1
1
1
0
1
2
11
16
2.212
K
2
2
2
1
1
∞
1
2
1
1
0
2
11
15
2.654
L
3
2
2
1
3
∞
2
1
2
2
2
0
11
20
1.327
THE WAY OF CALCULATING VIEW AND VIEWED DEPTH ON SOFTWARE
To perform the existing method, software calculates depth with Dijksta’s algorithm: an algorithm to solve the shortest path problem. Dijkstra’s algorithm adds edges to paths regarded as the shortest ways to calculate the shortest paths one after another. Contrary to this, view and viewed analysis has 2 types of edges: accessibility edge and visibility edge, and functions of these edges are different. Thus we have to put something in the algorithm, and this chapter explains the way of calculating view and viewed depth on application software.
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3.1.
The Way of Calculating View Depth
With view analysis, a path including visibility edge can be the shortest path, but we cannot add a new edge to such paths. Thus we have to prepare 2 types of memories: memory to memorize depth of paths not including visibility edges (depth memory); memory to memorize depth of paths including visibility edges (v‐ depth memory). The data of depth memory are renewed when shorter paths not including visibility edges are presented, and the data of v‐depth memory are renewed when shorter paths including visibility edges are presented. Other memories and operations are same as Dijkstra’s algorithm basically. When the renewal of the data of depth memory and v‐depth memory has been finished, the program compares the data of both memories and collects smaller data as view depth. On the occasion, we can get accessibility depth from the data of depth memory before comparing. In the following C++ source cord shows how to calculate view depth, and the number of nodes: n, the weight of edges: weight[1..n][1..n] and the type of edges: weight_type[1..n][1..n] are given. If there is no direct connection from i to j, weight[i][j] = INT_MAX. weight_type[i][j] = 0 means that both nodes of the edge are on the floor and the edge from i to j is accessibility edge: there is no object between i and j. weight_type[i][j] = 1 means that the node i is on the floor and the edge from i to j is visibility edge: there are some problem objects like glass walls and voids between the nodes. int main () { #define FALSE 0 #define TRUE 1 int START, i, j, next, min; char visited[n+1]; int prev[n+1]; int v‐prev[n+1] for (START = 1; START