カテゴリー Ⅰ 日本建築学会計画系論文集第 80 巻第 717 号,2735-2741,2015 年 11 月 J. Archit. Plann., AIJ, Vol. 80 No. 717, 2735-2741, Nov., 2015 DOI http://doi.org/10.3130/aija.80.2735 建築空間の分節に関連する遮蔽縁の判別方法 A METHOD TO DISCRIMINATE OCCLUDING EDGES RELATED TO SPATIAL DIVISION 山岡馨 *, 中村航 ** ***, 隈研吾 Kaoru YAMAOKA, Ko NAKAMURA and Kengo KUMA Architectural spaces can be divided into smaller spaces such as, but not limited to living rooms, entrance, and corridor. Then, a room connectivity graph can be constructed. However, a robust algorithm to construct the graph from a shape of architectural space has not been established. Before constructing the room connectivity graph, specifying dividing lines and occluding edges corresponding to the lines are needed. In this paper, We propose a method to discriminate occluding edges which are corresponding to the divisions from others such as a tiny relieves or decorations. Compared to previous method, Our method is robust against the addition of trivial vertices, or orientation of vertices of shapes. Using our method, true positive rate of the discrimination is 86%, and true negative rate is 85%. Keywords:Space Syntax, Spatial Division, Occluding Edge, Algorithmic Design, Shape Analysis, Computational Geometry. * ** *** 東京大学工学系研究科都市工学専攻 大学院生 工修 東京大学工学系研究科建築学専攻 助教 工博 東京大学工学系研究科建築学専攻 教授 工博 Grad. Stud., Dept. of Urban Engineering, Faculty of Engineering, The University of Tokyo, M. Eng. Assist. Prof., Dept. of Architecture, Faculty of Engineering, The University of Tokyo, Dr. Eng. Prof., Dept. of Architecture, Faculty of Engineering, The University of Tokyo, Dr. Eng. 2735
Environment E Isovist at p Vantage Point p Fig.1 isovist Polygon defined Clockwise Polygon defined Counterclockwise Fig.2 2736
4 4 4 P o ds Occluding area S P e Fig.4 Occluding Area Occluding Distance Considered Fig.5 Fig.3 9 M = P e P o ds S I M 2π I(θ) M = I(θ + π) rdrdθ 0 0 dd att d att = log 10 (d + 1) M att 2737
* no attenuation formura (4) formura (5) Fig.6 3 1 1 2 1 2 3 4 Fig.7 list of pair(coordinate, weight). listvertices of P. WHILEDO Find vertex V with largest weight. Aggregate vertices within distance d from V. ( ) Calculate centroid and sum of weight. Append pair(centroid, sum of weight) to result. END WHILE RETURN Result. 2738
1.00 Magnitude of edge 0.80 0.60 0.40 3 0.20 0.00 Edges aside from partition Edges around partition Fig.10 Fig.8 Deviation of Mag. of edge 53 52 51 50 49 48 Edges aside from partition Edges around partition Fig.9 Fig.11 Table 1 - Fig.12 House-MH Fig.13 2739
relatively small edge Fig.14 2740
A METHOD TO DISCRIMINATE OCCLUDING EDGES RELATED TO SPATIAL DIVISION Kaoru YAMAOKA *, Ko NAKAMURA ** and Kengo KUMA *** * Grad. Stud., Dept. of Urban Engineering, Faculty of Engineering, The University of Tokyo, M. Eng. ** Assist. Prof., Dept. of Architecture, Faculty of Engineering, The University of Tokyo, Dr. Eng. *** Prof., Dept. of Architecture, Faculty of Engineering, The University of Tokyo, Dr. Eng. Architectural spaces can be divided into smaller spaces such as, but not limited to living rooms, entrance, corridor. Then, room connectivity graphs can be constructed from architectural spaces based on the division. A Graph-theory-based analysis of architectural space has long history not limited to Space Synta, however the algorithm to construct the room connectivity graph from a shape of architectural space has not been established. Before constructing the room connectivity graph, specifying dividing lines of the architectural space is needed. Jeong and Ban (2011) 6) gives an algorithm for similar purpose, but the algorithm is not robust against the orientation of polygon or adding trivial vertices. Also, the division of architectural spaces is strongly related to the Optical Occlusion and Occluding Edge, which are introduced by Gibson (Fig.3). In this paper, We proposed a method to discriminate occluding edges which are corresponding to the divisions from others such as a tiny relieves or decorations. For that purpose, we dened a magnitude of occluding edge. The magnitude is dened based on the area occluded by the edge and the distance from the edge to the other objects such as walls (Fig.4). Attenuation was also applied according to Weber- Fechner law in order to compensate the effect of a room which is quite large (Fig.6). Then, adjacent occluding edges are clustered. We proposed a greedy algorithm (Fig.7) by taking advantage of the fact that the edges to be clustered eists along single, connected wall. For our case, radius of clustering was set to 0.5 meters. The result is plotted on Fig. 8- and eample of the data is shown in Fig. 10-13. When threshold is set to 0.1, true positive rate of the discrimination was 86%, and true negative rate was 85%. However, it should be noted that the method does not work well paticularly on a small space such as tea room, which is showing the need for a theory that complements this downside. (2015 年 1 月 10 日原稿受理,2015 年 8 月 17 日採用決定 ) 2741