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Computational models for measuring spatial quality of interior design in virtual environment
Building and Environment 49 (2012) 67e85
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Building and Environment journal homepage: www.elsevier.com/locate/buildenv
Computational models for measuring spatial quality of interior design in virtual environment Aswin Indraprasthaa, *, Michihiko Shinozakib,1 a b
Department of Engineering and Design, Shibaura Institute of Technology, Shibaura 3-9-14, Minato-ku, Tokyo 108-8548, Japan Shibaura 3-9-14, Minato-ku, Tokyo 108-8548, Japan
a r t i c l e i n f o
a b s t r a c t
Article history: Received 20 April 2011 Received in revised form 9 September 2011 Accepted 15 September 2011
This paper presents a computational model designed to analyze and to assess quality of architectural space. The model consists of two parts: first part is a model of subdivided enclosed spaces, which is an approximation of spatial layout regarding the enclosure and the circulation path. Second part is a model of spatial quality assessment using three spatial parameters and two distinct approaches. The first approach of this assessment is visual distance and the second approach is viewing angle. The assessment valued by these approaches then combined to obtain spatial quality ranking of each of the subdivided enclosed space. Previous studies on spatial assessment showed the relationship between visual distance and spatial quality can be modeled through mathematical approaches. Our work proposes an improvement on the method of spatial mapping model and spatial quality assessment. Experiments have been conducted on interior design and we developed spatial evaluation using three parameters: visual openness, privacy and physical accessibility. Furthermore, we conducted a comparison study of privacy assessment on design variances. Finding shows some distinctive results on the assessment approaches that can lead to more elaborative spatial quality evaluation. The outcome on spatial quality assessment can facilitate spatial quality evaluation of interior design in early stages of design development. 2011 Elsevier Ltd. All rights reserved.
Keywords: Computational model Interior space Spatial qualities rankings Virtual environment
1. Introduction This study focused on the architectural space of interior design as a result of the arrangement of architectural elements. An architectural space is defined as the void between physical boundaries of the enclosures where its existence is independent of the user’s presence. As an architectural space composed by its physical setting, we developed a model using superimpose technique to map this space into what we named as subdivided enclosed space. The mapping procedure follows the basic relationships between design elements and circulation paths using territorial lines approach as studied by Koile [1]. The benefit of this model is it offers a more elaborative object of assessments specifically relates with spatial quality parameters. In previous study of spatial quality evaluation [2,3], a single proxy usually used to represent object of evaluation (i.e. center of the room or any arbitrary point in the room). Some of earlier models have focus on spatial mapping
mechanism and procedures [4] with less emphasize on the development of spatial quality evaluation. Our spatial mapping model results in an array of points in an interior plan where each point has different spatial quality ranking that related with their relative position to the architectural elements. This model proposes a better analytic tool for spatial quality evaluation. The comparison of our model with previous works is presented in Table 1. The spatial quality parameters used in this study are determined and intended to improve previous achievements. For example, Fischer-Gewirtzman and Wagner [5] and Pinsly et al. [6] analyzed spatial openness and visual exposure. Both parameters related with visual openness, which is bound for metric-based evaluation. Demirkan et al. [7] used distance measurement to analyze privacy in an interior space. We determine three spatial parameters for this study: visual openness, privacy and physical accessibility. 2. Architectural spatial quality
* Corresponding author. Tel.: þ81 3 6722 2732; fax: þ81 3 5859 9249. E-mail addresses: [email protected] (A. Indraprastha), sinozaki@sic. shibaura-it.ac.jp (M. Shinozaki). 1 Tel.: þ81 3 6722 2732; fax: þ81 3 5859 9249. 0360-1323/$ e see front matter 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.buildenv.2011.09.017
Architecture is experienced not just by attributes of its boundaries. The variability in the interior (enclosed space) and exterior (enclosure) comprise the essence of architecture. Several architects [8e10] as well as psychologists [11] have found that the
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Table 1 Comparison of models and methods. Gross method (1977)
Koile method (2001)
Sora method (2008)
Our method (2010)
Goal
Classification of enclosed space by its boundaries
Quality of space by viewpoint and geometric elements
Limitation
Only physical boundary forms a subdivided enclosed space, failed to accommodate center space, and no hierarchical attributes related to the space Enclosed space classification based on its boundary
Design representation by hierarchical territorial space Limit to the territorial spaces as a result of element, edge, and circulation model Abstraction model of design representation
Only to measure quality at arbitrary viewpoint position relative to the boundary element Spatial quality measurement based on viewpoint
Spatial map that represents relationship of boundary elements and circulation space Experimented on rectangular-based plan
Numerical values that represents rank of enclosed space
Graphic representation of model
Numerical result of measurement
State of the art
Result/Output
experiences in the same space can vary with the changes in architectural design elements such as colors and transparency. Another aspect of architectural space is that architects always compose space according to the boundaries and inter-relationships between the architectural elements and its planned activities. March and Steadman [3] used network graph to denote topological relationships between rooms e which room gives access to another, which room is adjacent to another. Péna [4] suggested that the matrix relationship of activities should be constructed to model adjacency of spaces regarding designated activities. Both studies had used basic mathematical model of spatial configuration in order to understand relationship between spatial design and activities. Our model of enclosed spaces is the elaboration from previous study with the advancement of having a map configuration of what we named as subdivided enclosed space inside a set of interior space. We advice each area of subdivided enclosed space expresses distinct spatial quality that is significant for spatial quality analysis and further conceptual design elaboration. 3. Mapping the interior by virtual agent The concept of spatial quality mapping by previous works referred to the preposition that on an enclosed space or interior space, the hierarchy of the space can be mapped by the strength of influence of its boundary elements [12e15]. A study of spatial mapping has been conducted by using number of solid boundaries to classify enclosed spaces [13], combining concept of territory space to map strength influence of boundary elements into enclosed space [1] and recently, used distance model to classify hierarchy of enclosed space [14]. Our model began with the classification of enclosed space [15] where there are six defined architectural spaces: by linear elements (column), by single vertical plane (i.e. wall), L-shaped space, parallel space, U-shaped space and four planes to define full closure of space. The basic enclosed space category we used for this research is L-shaped space (Fig. 1).
a
b
Spatial map based on hierarchical relationship of boundary elements and circulation space Layout of spatial mapping resulting in determination of subdivided enclosed space
Following the basic classification of enclosed space, our model of spatial mapping is based on the visual perception and position of the virtual agent. Therefore, the rules for generating spatial mapping are taking account the detected objects by virtual agent. Our method of enclosed space detection is based on the hierarchical structure of the space as previously been studied. On this model, the hierarchy of enclosed space is as follows: 1. L-shaped space; defined by two non-collinear solid boundaries. 2. Circulation space; defined where it has territorial space of circulation gate (i.e. door). 3. Attractor space; defined where it has territorial space of other architectural elements at the boundary such as openings. 4. Subdivided space; defined as result of the rules of spatial mapping. As result of this concept, we determined an interior space as a unit analysis. An interior space is a space that comprises of enclosures, enclosed space and circulation path. We named this area as bounded area (Fig. 2). A bounded area comprises of rectangular-type arrangement of enclosed spaces that depend on the configuration of architectural elements at its enclosure. We employed procedural rules by considering relationship between bounded area and its circulation path. The bounded area may enclosed by opaque boundaries (walls), openings (windows or doors) and other architectural elements. A circulation path is a circulation connector inside the bounded areas. Circulation gates such as door and path form a circulation space inside the bounded area.
Architectural plan
Interior space(s)
Enclosed space
Enclosure Circulation path
Bounded area for computational analysis Fig. 1. Diagrammatic model of enclosed space, a) L-shaped space; b) U-shaped space.
Fig. 2. Unit of analysis.
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a
69
Variant of gate position
Ed Md
b
Enclosed space by center point
c
Enclosed space subdivided by rules 1
1
1
1
2
2
2
1
1
2 3
3
2
3 2
3
1
2 1
1
1
2
1
1
1
1
1
Fig. 3. Subdivided enclosed space having a path terminated in the space.
a Variant of gates position
b Enclosed space by center point
c Enclosed space subdivided by rules 1
1
1
1
2 3 2 1
2 2
3
3 2 1
1
2
3
2 1
3 2
1 2
1
3
1
3 2
1
2 1
1
1
Fig. 4. Subdivided enclosed space having a linear path passing through space.
2 3
1
1
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a
For determining subdivided enclosed space, our computational method works by analyzing set of points detected by agent as he loosk around his surroundings. This analysis comprises of procedural rules based on spatial hierarchy of bounded area.
Variant of gates position
3.1. Model of circulation path in a bounded area
b
Enclosed space by center point
c
Enclosed space subdivided by rules
As previously mentioned, procedural rules for creating a map of spatial configuration is based on the relationship between bounded area and its circulation path. The computation for dividing enclosed space is conducted under the rules of circulation path inside the bounded area. Here, the pathespace relationship is defined as the connection between bounded areas and circulation paths. In architecture, a circulation path is the connection in which people traverse from one node to another [1,4]. In narrower scope, a circulation path is the connection between a circulation gate (door) and the space within the enclosure. There are two ways considered as the relationship between the paths and space [15]: terminate in space and pass through space. 3.1.1. Terminate in space If a room has only one door, then the circulation path is terminated inside the room. The model of subdivided enclosed space by circulation path is then the result of the relationship between the enclosed space and circulation area. Fig. 3 illustrates procedural steps of dividing enclosed space having a circulation path terminated in the bounded area. The rules to subdivide enclosed space are as follows:
d
Final result 3
1
2
2 2 3
1
2 1
2 1 1
2
2 1
2 2
2
3 2 1
2
2
3
3 1
1
3
3 2
3
2
1
2 1
Fig. 5. Subdivided enclosed space having angular path passing through space.
Determine L-shaped enclosed space (number 1 in Fig. 3c) by the center point of each boundary (Fig. 3b); Determine remaining space (number 2 in Fig. 3c) with respect to the circulation gate and center point; Determine the axial line along the center point and perpendicular to the path direction; Make parallel lines from the gate to the axial line (Fig. 3c) to obtain circulation space (number 3 in Fig. 3c). Following these rules, we established configuration of enclosed space having a circulation space that terminates in the center of the interior space.
Fig. 6. Set of points based on x-axial line and y-axial line.
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Fig. 7. Illustration on determination of subdivided enclosed space according to x-axial line and y-axial line.
3.1.2. Pass through space If there is more than one circulation gate in a room, the relationship between the paths and space known as pass through space. We developed two models: cut axially and cut obliquely. In both models, the circulation paths may have linear or non-linear positions.
3.1.2.1. Linear path. The circulation path is defined as linear if two gates are connected by a straight line. The rules to determine subdivided enclosed space are the same as the previous rules. Fig. 4 illustrates procedural steps of dividing an enclosed space having a linear circulation path passing through a bounded area. The rules of this relationship are extensions of the first set of rules.
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c b a
a
b
c
Area of windows=0.64 (m2) Area of wall=26.125 (m2) Ratio=0.02
Area of windows=1.16 (m2) Area of wall=26.125 (m2) Ratio=0.04
Area of windows=3.72 (m2) Area of wall=26.125 (m2) Ratio=0.142
Fig. 8. Determination of center point of each subdivided enclosed space based on quadrant position.
3.1.2.2. Angular path. The path is defined as angular if two gates are connected by angular line. In this situation, we hypothesized that the center point is a significant factor to determine subdivided enclosed spaces and circulation spaces. By considering this, when two paths encounter a space, their connection must pass through a center point or an axial line as defined by the previous rules.
Fig. 10. The size of window relative to their attached wall determines value of transparency.
Fig. 5 illustrates procedural steps of subdividing an enclosed space having angular circulation path passing through a bounded area.
Fig. 9. Graphical example of computation of subdivided enclosed space, a) Initial plan; b) determination of L-shaped enclosed space; c) circulation area using axial line; d) determination area of opening territory by extending its edges perpendicular to axial line; e) determination of extended area by extending L-shaped edges perpendicular to the nearest lines; f) center points of the subdivided enclosed spaces.
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Table 2 Two approaches to measure visual openness. By distance
By viewing angle
Average distance Average distance from q to from p to window 1 and window 2 ¼ X1 window 1 and window 2 ¼ X2 X1 < X2 Visual openness at p is lower than visual openness at q
Ratio of viewing angle and Ratio of viewing angle and maximum angle at p ¼ Y1 maximum angle at q ¼ Y2 Y1 < Y2 Visual openness at p is lower than visual openness at q
The rules to subdivide enclosed space are as follows: Define L-shaped enclosed space by the center point of each boundary (number 1 in Fig. 5c); Evaluate remaining space with respect to the circulation gate and center point (number 2 in Fig. 5c); Determine the minimum convex area; Divide the area by its center point; Determine axial lines along the center point and perpendicular to the path direction; Determine parallel lines from each gate to the axial line (number 3 in Fig. 5c). 3.2. Algorithm and procedural rules The followings are rules that are executed sequentially over set of points. These rules are applied following results of object detection and inner point computation over the inner coordinates of boundary objects relative to the position of agent. The general procedures are as follows: 1. Determine the center point of the polygon c ¼ (xc,yc) by finding out the minimum and maximum point of the vertices. 2. Determine the horizontal axial line and the vertical axial line. From the previous step, y ¼ yc ¼ horizontal axial line; x ¼ xc ¼ vertical axial line. 3. Define a set of points based on the two axial lines. This is done by sorting the points along the horizontal axial line, followed by sorting the points along the vertical axial line. 3.1. Sorting the points along the horizontal axial line is done by dividing the points into two sets: those that are located above the line (ypi> yc), and those that are located below
the line (ypi < yc). They are defined as xþpi ¼ set of points above the x-axial line and xpi ¼ set of points below the xaxial line: xþ pi ¼ (xþxpi,ypi) where ypi > yc; xpi ¼ (xxpi,ypi) where ypi < yc. 3.2. Accordingly, sorting the points along the vertical axial line is done by dividing the points into two sets: those that are located on the right side of the line (xpi > xc), and those that are located on the left side of the line (xpi < xc). They are defined as yþpi ¼ set of points on the right side of the yaxial line and ypi ¼ set of points on the left side of the yaxial line (Fig. 6) yþ pi ¼ (xpi,yþypi) where xpi > xc; ypi ¼ (yxpi,ypi) where xpi < xc. 4. Determine the intersected points at the horizontal and vertical axes. As of now, we have four sets of points: {xþpi}, {xpi}, {yþpi}, {ypi}. Each of these set members must be mapped into the designated axis, so that we have intersected point sets. 5. Determine the midpoint of two sequential points from each intersected point set. 6. Determine the center point of the result of Step 5. Fig. 7 illustrates the overall procedure as explained above. The procedure for combining intersected points on both the axial lines results in generating divided enclosed spaces. The next stage is to generate the center points of these spaces by running procedural rules on each point. We determined these center points based on the evaluation of the intersected points of each line by their quadrant. As previously explained, we separated each detected point according to their quadrant with respect to the axial lines, therefore we obtained four sets of points: {xþ}, {x}, {yþ}, and {y}. The center point of the subdivided enclosed space is given by means of
Fig. 11. Cases to determine maximum viewing angle at p.
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a
b
window 1
4 6
door
3
2 5
7
8
9
10
14
15
11
door
12
13
16
17 door
18 19 20
21
22
26
27
23
24 25 window 0.5
1. 0
Fig. 12. Result of visual openness measurement on room 1 of Kaufmann house.
their position in the quadrant, which is determined as the relationship of these sets: {xþ, y}, {xþ, yþ}, {x, y}, {x, yþ}. Fig. 8 below illustrates this concept: This approach maintains the origin of the intersected points at the axial lines and results in a better calculation for determining center point of each subdivided enclosed space.
3.2.1. Determine axial lines The determination of axial lines is significant in our model as a guideline for subsequent procedures. The axial lines are determined by determining the area of a polygon based on the set of its boundary points and computing its center points at the x-axis and at the y-axis. The necessary equations are:
Fig. 13. Kaufmann House by Frank Lloyd Wright.
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Fig. 14. Rachofsky house by Richard Meier.
i1 1X Area of boundaryðAÞ ¼ ðx y xiþ1 yi Þ 2 i ¼ 0 i iþ1 i1 1 X Center at X ¼ ðx y xiþ1 yi Þðxi þ xiþ1 Þ 6A i ¼ 0 i iþ1
(1)
(2)
Center at Y ¼
i1 1 X ðx y xiþ1 yi Þðyi þ yiþ1 Þ 6A i ¼ 0 i iþ1
(3)
3.2.2. Intersected points at axial lines Define the axial lines as: y ¼ yc and x ¼ xc, and (xc,yc) is the center point. At this stage, we evaluate the points of each quadrant with the axial lines (refer to Fig. 5):
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Table 3 Procedures of measurement for spatial quality level.
Procedures for measurements
1
2
VO: visual openness
PR: privacy
Calculate average distance Pn vo i ¼ 1 dWi Dp ¼ n
Dip ¼
Pk pr
i¼1
k
2
p
Dp Dp
PRp ¼ Exp
i¼1
pr
dWip
n
pr 2 p pr Dp
Calculate level using distance method by factor of transparency index VOD ¼ VOD ðtrÞ PRD ¼ PRD ðtrÞ p p
Pn
ac
Dp ¼
i¼1
dDac ip
n
p
ACp ¼ Exp
ac 2 p
D
ac Dp
ACD ¼ ACD ðtrÞ p
p
Calculate ratio of covered angle
uvo p ¼ 5
þ
D
p
4
Pk
pr
dWip
Calculate strength of influence VOD ¼ Exp
3
AC: physical accessibility
qp 100
uac p ¼
qp 100
upr p ¼
qp 100
Calculate strength of influence VOup ¼ Exp
u2p up
PRup ¼ Exp
upr 2p
upr p
6
Normalize value of (3) and (5)
7
Combine both result and obtain arithmetic average 1 1 VOp ¼ ðVOD þ VOup Þ PRp ¼ ðPRD þ PRup Þ p p 2 2
Quadrant 1 ¼ {(xpi,ypi)} where xpi < xc and ypi > yc; intersected points at y; yc ¼ {(xpi,yc)}; intersected points at x; xc ¼ {(xc,ypi)}. Set points in quadrant 1 ¼ {q1(xpi,yc) and q1(xc,ypi)}. Quadrant 2 ¼ {(xpi,ypi)} where xpi > xc and ypi > yc; intersected points at y; yc ¼ {(xpi,yc)}; intersected points at x; xc ¼ {(xc,ypi)}. Set points in quadrant 2 ¼ {q2(xpi,yc) and q2(xc,ypi)}. Quadrant 3 ¼ {(xpi,ypi)} where xpi < xc and ypi < yc; intersected points at y; yc ¼ {(xpi,yc)}; intersected points at x; xc ¼ {(xc,ypi)}. Set points in quadrant 3 ¼ {q3(xpi,yc) and q3(xc,ypi)}. Quadrant 4 ¼ {(xpi,ypi)} where xpi > xc and ypi < yc; intersected points at y; yc ¼ {(xpi,yc)}; intersected points at x; xc ¼ {(xc,ypi)}. Set points in quadrant 4 ¼ {q4(xpi,yc) and q4(xc,ypi)}. 3.2.3. Midpoints at each set in the quadrant For each set, the program computes the midpoints on two sequential points of the sorted set. The definition and rule is as follows. Definition and rule: {qn(xpi,yc)} and {qn(xc,ypi)}; n ¼ (1,.,4); set of points at quadrant n by horizontal and vertical axes. 0 0 {qn (xpi,yc) and qn (xc,ypi)}; n ¼ (1,.,4); set of sorted points at quadrant n by horizontal and vertical axes.
ACp ¼ Exp
ACp ¼
ac 2 p
D
ac Dp
1 ðACD þ ACup Þ p 2
{Mid_qn(x)(xpi,yc)} ¼ midpoint set at quadrant n by horizontal axis. {Mid-qn(y)(xc,ypi)} ¼ midpoint set at quadrant n by vertical axis. 0 {Mid-qn(x)(xpi,yc)} ¼ {qn (((xpi þ xpiþ1)/2),yc)} Mid-qn(y) qn0 (xc,ypi)} ¼ { (xc,((ypi þ ypiþ1)/2))} {
3.2.4. Center points at each set in the quadrant The center points of each quadrant are determined by combining the midpoints at the vertical and horizontal lines. The definition and rule is as follows: Definition and rule: {Mid_qn(x)(xpi,yc)} ¼ midpoint set at quadrant n by horizontal axis. {Mid-qn(y)(xc,ypi)} ¼ midpoint set at quadrant n by vertical axis. {Cen_qn(pi)} ¼ center points set at quadrant n. {Cen_qn(pi)} ¼ {Mid_qn(x)xpi,Mid-qn(y)ypi}. All computational process conducted in Virtools. The result of this process is the configuration of subdivided enclosed spaces as illustrated in Fig. 9:
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Table 4 Visual openness index measurement on house plans. Kaufmann house plan
Two windows
Rachofsky house plan
One window
One window
4. Model of spatial quality parameters In an architectural spatial quality model, we proposed factors that influenced enclosed space quality which are visual openness, privacy and physical accessibility. These basic parameters could have effect on how we regard particular interior space or enclosed space based on the configuration of architectural elements of enclosure. The previous work showed an empirical finding that the viewing distance and viewing angle yielded significant influence toward spatial evaluation and orientation [16]. Therefore, we develop our method of measurement based on the distance of architectural element to the point of measurement and the covering viewing angle from point of measurement to particular architectural element.
One window
One window
The result of this model is numerical level attached to each of the subdivided enclosed space that gives ranking on the particular spatial parameter. The followings are explanation of each parameter: 4.1. Visual openness parameter In modeling visual openness, we considered window as the source of its influence. This visual openness influence is received by each of subdivided enclosed space in a different level regarding their layout in a bounded area. The significance of this index is that it can express the visual openness influence upon enclosed space with such qualitative and quantitative attribute attached such as privacy, natural light and air.
Table 5 Privacy index measurement on house plans. Kaufmann house plan
Two windows, three doors
Rachofsky house plan
One window, two doors
One window, one door
One window, two doors
Two doors
One window, three doors
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Table 6 Physical accessibility index measurement on house plans. Kaufmann house plan
Three doors
Rachofsky house plan
Two doors
One door
The term visual openness index refers to the level of visual influence at a center point of a subdivided enclosed space. We defined three variables to compute visual openness: 1. Visual distance; refers to the distance from a reference point p to the openings (i.e. windows); 2. Transparency ratio; refers to the ratio of opening area and its adjacent wall area; 3. Viewing area; refers to the ratio of viewing area from point p having all windows and maximum viewing area defined as 100 . We defined transparency level here is a value drawn by fraction of the dimension between opening and remaining solid surface where the opening is located. Fig. 10 illustrates this concept: The procedure to compute visual openness is by taking average value of visual openness by visual distance and transparency ratio and visual openness by viewing area. Table 2 shows our approach to combine measurements of visual openness: 4.2. Privacy parameter Privacy parameter or visual privacy parameter refers to the visual penetration of a point p in bounded area as a result of being viewed from external spaces [6,7]. In our model, level of privacy depends on two factors: openings (i.e. window) and circulation gate (i.e. door). Aside of the function to circulate light and fresh air; window is an architectural element that provides visual exchange by its level of transparency. We used same approach to determine transparency ratio as with the visual openness parameter. The procedure to compute privacy is by taking average value of privacy by distance and privacy by viewing area. By distance method, the greater distance from window and/or door, the greater privacy level. Accordingly, greater angle to cover all windows and/ or doors is resulting in lower privacy level. 4.3. Physical accessibility parameter In our model, physical accessibility parameter refers to the value of average distance from point p at the center of a particular subdivided enclosed space, to the doors in that bounded area. The
Two doors
Two doors
Three doors
physical accessibility index represents ease of accessibility of a subdivided enclosed space in an interior space. The procedure to compute accessibility is similar with the previous where using two approaches, except for computing accessibility index, the object of measurement is circulation gate (i.e. door). 4.4. Procedures of measurement Each of spatial quality parameter has distinctive characteristic regarding the influential strength of its source, for example: 1. Visual openness parameter at p in space; the greater average distance to the windows means the lower visual openness index and the greater fraction of viewing angle means the greater visual openness index. 2. Privacy parameter at p in space; the greater average distance to the windows and the doors means the higher privacy index and the greater fraction of viewing angle means the lower privacy index. 3. Accessibility index at p in space; the greater average distance to the doors means the lower accessibility index and the greater fraction of viewing angle means the greater accessibility index. The illustrative diagram of method of measurement for visual openness, privacy and accessibility index is presented in Table 3. 4.5. Definition and equation The procedure for computation takes some abbreviations and definitions as follows: dWp ¼ distance from p to center point of window; dDp ¼ distance from p to center point of door; aWi ¼ area of window i; aWLi ¼ area of adjacent wall of window i; aDi ¼ area of door i; aWDi ¼ area of adjacent wall of door i; n ¼ number of window; k ¼ number of doors; trwi ¼ (aWi/aWLi)¼ transparency index of window i; trdi ¼ (aDi/ aWDi)¼transparency index of door i; qvo ¼ visual angle at p having all window covered; uvo ¼ visual openness ratio of covered angle;
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Fig. 15. Spatial qualities level on Kaufmann house.
qpr ¼ visual angle at p having all windows and doors covered; upr ¼ privacy ratio of covered angle; qac ¼ visual angle at p having all doors covered; uac ¼ physical accessibility ratio of covered angle.
4.6. The viewing angle method In addition to the distance method, we propose the viewing angle method for measuring influence of spatial parameters relative to the position of the point of reference.
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Fig. 16. Spatial qualities level on Rachofsky house.
The viewing angle of measurement is obtained as a fraction of angle u to cover outer edge of object of measurement to the maximum model of viewing angle. We determined the model of a maximum horizontal viewing angle as 100 . The variable u centered at the point p and its direction vector depends on the position and layout of the object of measurement. The principle of this approach is to obtain maximum angle to cover
outer edges of object of measurement from p. This concept is illustrated in Fig. 11: 4.7. Normalization There are two numerical values as the results from two distinct methods. To obtain average value at each point p, we made normalization on each result as follows:
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Fig. 17. Summary of spatial qualities evaluation on case studies.
Definition: 1. SP as spatial parameter, SP ¼ {VO, PR, AC}; 2. SP dðpÞ as spatial quality index by distance at p; SP sðpÞ as spatial quality index by viewing angle at p; 3. nSP dðpÞ as normalization by distance at p; nSP sðpÞ as normalization by viewing angle at p; 4. MaxSP d as maximum value of spatial quality index by distance of all points p in space; MinSP d as minimum value of spatial quality index by distance of all points p in space; 5. MaxSP s as maximum value of spatial quality index by viewing angle of all points p in space; MinSP s as minimum value of spatial quality index by viewing angle of all points p in space.
nSP dðpÞ ¼
ðSPdðpÞ MinSP d Þ
ðMaxSP d MinSP d Þ
;
nSP d˛½0; 1
(4)
at a particular point of reference. By this case, it is appropriate to combine both results to give an average weight of spatial qualities on each point of reference. We use arithmetic mean of these both values to represent average value obtained by objective and subjective variable. 5. Experiments and result The input for the experiments is CAD polygon. We used the architectural plans of Kaufmann House [17] (Falling Water house) by Frank Lloyd Wright (Fig. 13) and Rachofsky house by Richard Meier [18] (Fig. 14). The experiments on six different layouts are explained as follows (Tables 4e6). Each table below illustrates detailed layout of the rooms, position of center point of subdivided enclosed spaces and architectural elements characteristic (i.e. number and dimension of wall, window and door).
and
nSP sðpÞ ¼
ðSP sðpÞ MinSP s Þ ; ðMaxSP s MinSP s Þ
5.1. Result
nSP s˛½0; 1
(5)
4.8. Combined value On one example of visual openness measurement (Fig. 12), it is showed that there are different results of visual openness level that relates to the position of the point of reference to the window. By their definitions, the distance and visual angle method has characteristic that may lead to how we quantify visual openness objectively. By distance method, the visual openness level depends on the average distance to all windows. However, as suggested by Henry [16], visual distance also influenced by viewing area that may lead to subjective evaluation
Fig. 18. Comparison result.
The results of spatial quality measurements on six rooms are presented as follows; first is the spatial qualities measurement on Kaufmann house and Rachofsky house (Figs 15 and 16). Second is comparison on the result of both case studies. We presented the spatial quality level of each reference point as the combined result by distance method and by viewing angle method. Based on this evaluation, spatial quality evaluation depends on the layout configuration of the openings that made up the spatial mapping as we developed. In such, the openings affect the result of spatial quality ranking. The rooms of Kaufmann house serve as bedrooms while room 1 and room 3 of Rachofsky house serve as multipurpose rooms. Fig. 17 (a and b) presents the results of spatial qualities of three parameters: visual openness, privacy and physical accessibility considering the area of each room. Fig. 17(a) presents a result that can be used for quantitative spatial quality over the same function. In this case study, room 3 of Kaufmann house has the highest level of visual openness, privacy and physical accessibility. This result shows the relationships of the subdivided enclosed space as reference of measurement, the layout of the openings and spatial qualities. Although it needs more empirical finding, it is interesting to note that this method gives a possibility of more elaborate and objective analysis over spatial qualities parameters. The diagram (Fig. 18) shows that the physical accessibility and privacy levels of three plans of Rachofsky house are lower than the Kaufmann house. The shapes of the plan and configuration of the openings contribute to this result. On the case of visual openness evaluation, the dimension of the windows in Rachofsky house contributes for increasing its level compared with the Kaufmann house.
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A. Indraprastha, M. Shinozaki / Building and Environment 49 (2012) 67e85 Table 7 Spatial qualities measurement on design alternatives. Design variance
Spatial qualities level
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Table 7 (continued ) Design variance
Spatial qualities level
Fig. 19. Spatial qualities optimization.
6. Application for design alternatives analysis In this section, we demonstrated practicability of spatial qualities evaluation using previously explained methods. As a tool to improve design process, this demonstration showed analytical examination over series of design alternatives. On the case of visual
window 1
2
6
7
door
3 4
5
9
10
11
14
15
openness (VO), privacy (PR) and physical accessibility (AC) parameters respectively, this analysis can help to improve spatial quality of a bedroom design. Regardless the unlimited possibility to create design alternatives, these cases demonstrated rational iteration of design improvements by transformation (rotate, translate) of design elements from original design. Here, each of design alternatives has its final layout by transformation of windows and doors with their dimensions remain intact. On each alternative, the layout is developed intuitively and thus, independent from the intention or specific purpose for spatial qualities parameters. Since the results of these efforts are to be compared with the original design, all measurements results are valued relative to original design. The spatial qualities levels over design alternatives are presented as follows (Table 7): By comparing each design alternatives with original design on spatial quality parameters, improvements on spatial qualities can be shown as following diagrams (Fig. 19): All design variances have higher privacy level than the original. However, alternative 5 has highest level of spatial qualities. In this regards, with the variables of measurement are the position of openings and circulation gate, we can optimize design plans based on three spatial qualities parameters.
door
1
2
4
3
8
door
12
13
16
17 door
5
8
7
6
18 19 20
21
22
26
27
23
24 25
window
window 0 .5
0 .5
1. 0
Room 1
1. 0
R oom 3 Fig. 20. Visual openness level of the rooms in Kaufmann house.
9
10
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Table 8 Visualization of original design and best design alternative.
Original design
3D view 1
3D view 2
Best improvement
3D view 1
3D view 2
7. Summary and discussion
7.2. On spatial qualities evaluation
7.1. On mapping interior space
The model of spatial qualities evaluation using three spatial parameters has been experimented. Furthermore, this evaluation using distance and viewing angle methods revealed the results that had not been reviewed in previous studies. In our model, by combining distance and viewing angle methods, we can manage to compute influential strength of an architectural element as it is received at a particular point in space. The decay function has been employed to give distinctive result over relative small variants given the context of interior plan. This result as well revealed the relationship between layouts of the interior design and measurement variables that had some interesting result (Table 8). In this context, in addition to give visual cues, numerical values of spatial qualities levels represent influential strength of the parameter on the area of subdivided enclosed space. This model of spatial mapping gives opportunity for deeper spatial analysis over the configuration of architectural space. Based on the boundary elements and the relationship between space and circulation path, this model can be developed further to analyse design preferences of an architect by his spatial designs.
We presented a methodology for mapping architectural space by developing a semi-automatic method to generate subdivided enclosed spaces over CAD-type data. Our finding revealed the improvement of spatial qualities analysis using subdivided enclosed spaces as area of references. Moreover, generating map of interior space facilitates a visual cue to help designer develop better spatial configuration of his plan. This is based on the proposition that our method uses the relationship between architectural elements and circulation space that made up the subdivided enclosed spaces. In example, the analysis of visual openness on a series of design plan with the same function will facilitate understanding on organizing architectural space in the process of design as depicted in Fig. 20: In Fig. 20 colors gradient indicates level of visual openness and circle radius represents model of influential area of the visual openness level (For interpretation of the references to color in this paragraph, the reader is referred to the web version of this article.). Another possibility for the implementation of this method is to analyze the spatial signature of particular architects or styles in addition to the typological study based on architectural elements of the enclosure. On its limitation, this work remains focuses on rectangularbased interior plan with only use three physical setting variables: wall, window and door. We are aware that for future improvement there are some significant factors need to be addressed such as considering more architectural elements including height of the ceiling.
References [1] Koile Kimberle. The architect’s collaborator: toward intelligence design tools for conceptual design. PhD Dissertation. MIT; 2001. [2] Alexander Christopher, Ishikawa Sara, Silverstein Murray. A pattern language: Towns, Buildings, Construction. New York: Oxford University Press; 1977. [3] March Lionel, Steadman Philip. The geometry of environment. Cambridge: The MIT Press; 1971.
A. Indraprastha, M. Shinozaki / Building and Environment 49 (2012) 67e85 [4] Pena William. Problem seeking: an architectural programming primer. 4th ed. Wiley; 2001. [5] Fischer-Gewirtzman Dafna, Wagner Israel A. Spatial openness as a practical metric for evaluating built-up environments. Environ Plann B Plann Des 2003; 30:37e49. [6] Pinsly Dalit Shach, Fisher-Gewirtzman Dafna, Burt Michael. ‘Visual Exposure’ analysis model: a comparative evaluation of three case studies. Urban Des Int 2007;12:155e68. Palgrave Macmillan. [7] Demirkan H, Osman Demirbas O. Privacy dimension: a case study in the interior architecture design studio. J Environ Psychol 2000;20:53e64. [8] McGlynn Sue, Smith Graham, Alcock Alan, Murrain Paul. Responsive environment. In: Ian Bentley, editor. Oxford: Architectural Press; 1985. [9] Rasmussen Steen Eiler. Experiencing architecture. Cambridge: MIT Press; 1959. [10] Lawson Bryan. The language of space. 5th ed. Architectural Press; 2007. [11] Tversky Barbara. Three dimensions of spatial cognition. In: Theories of memory, vol. II. Psychology Press; 1998.
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[12] Leupen Bernard, Grafe Christoph, Korning Nicola, Lampe Marc, Dezeeuw Peter. Design and analysis. New York: Van Nostrand Reinhold; 1997. [13] Do Ellen Yi-Luen, Gross MD. Tools for visual and spatial analysis of CAD models. In: Computer assisted architectural design futures ’97. Kluwer Academic Publisher; 1997. pp. 189e202. [14] Key Sora, Gross Mark D, Do Ellen Yi-Luen. Computing spatial qualities for architecture. In: Proceeding of ACADIA 2008; 2008. p. 472e7. [15] Ching Francis DK. Architecture: form, space and order. 3rd ed.. New Jersey: John Wiley and Sons; 2007. [16] Henry Daniel. Spatial perception in virtual environment: evaluating an architectural application. In: Virtual reality annual international symposium, IEEE Xplore; 1993. p. 33e40. [17] Hoesly Bernhard. Frank Lloyd Wright: Fallingwater, AþU 118; July 1980. p.155e66. [18] Meier Richard, Futagawa Yukio, Futagawa Yoshio. Richard Meier, GA document, vol. 8; 2008.
Contents lists available at SciVerse ScienceDirect
Building and Environment journal homepage: www.elsevier.com/locate/buildenv
Computational models for measuring spatial quality of interior design in virtual environment Aswin Indraprasthaa, *, Michihiko Shinozakib,1 a b
Department of Engineering and Design, Shibaura Institute of Technology, Shibaura 3-9-14, Minato-ku, Tokyo 108-8548, Japan Shibaura 3-9-14, Minato-ku, Tokyo 108-8548, Japan
a r t i c l e i n f o
a b s t r a c t
Article history: Received 20 April 2011 Received in revised form 9 September 2011 Accepted 15 September 2011
This paper presents a computational model designed to analyze and to assess quality of architectural space. The model consists of two parts: first part is a model of subdivided enclosed spaces, which is an approximation of spatial layout regarding the enclosure and the circulation path. Second part is a model of spatial quality assessment using three spatial parameters and two distinct approaches. The first approach of this assessment is visual distance and the second approach is viewing angle. The assessment valued by these approaches then combined to obtain spatial quality ranking of each of the subdivided enclosed space. Previous studies on spatial assessment showed the relationship between visual distance and spatial quality can be modeled through mathematical approaches. Our work proposes an improvement on the method of spatial mapping model and spatial quality assessment. Experiments have been conducted on interior design and we developed spatial evaluation using three parameters: visual openness, privacy and physical accessibility. Furthermore, we conducted a comparison study of privacy assessment on design variances. Finding shows some distinctive results on the assessment approaches that can lead to more elaborative spatial quality evaluation. The outcome on spatial quality assessment can facilitate spatial quality evaluation of interior design in early stages of design development. 2011 Elsevier Ltd. All rights reserved.
Keywords: Computational model Interior space Spatial qualities rankings Virtual environment
1. Introduction This study focused on the architectural space of interior design as a result of the arrangement of architectural elements. An architectural space is defined as the void between physical boundaries of the enclosures where its existence is independent of the user’s presence. As an architectural space composed by its physical setting, we developed a model using superimpose technique to map this space into what we named as subdivided enclosed space. The mapping procedure follows the basic relationships between design elements and circulation paths using territorial lines approach as studied by Koile [1]. The benefit of this model is it offers a more elaborative object of assessments specifically relates with spatial quality parameters. In previous study of spatial quality evaluation [2,3], a single proxy usually used to represent object of evaluation (i.e. center of the room or any arbitrary point in the room). Some of earlier models have focus on spatial mapping
mechanism and procedures [4] with less emphasize on the development of spatial quality evaluation. Our spatial mapping model results in an array of points in an interior plan where each point has different spatial quality ranking that related with their relative position to the architectural elements. This model proposes a better analytic tool for spatial quality evaluation. The comparison of our model with previous works is presented in Table 1. The spatial quality parameters used in this study are determined and intended to improve previous achievements. For example, Fischer-Gewirtzman and Wagner [5] and Pinsly et al. [6] analyzed spatial openness and visual exposure. Both parameters related with visual openness, which is bound for metric-based evaluation. Demirkan et al. [7] used distance measurement to analyze privacy in an interior space. We determine three spatial parameters for this study: visual openness, privacy and physical accessibility. 2. Architectural spatial quality
* Corresponding author. Tel.: þ81 3 6722 2732; fax: þ81 3 5859 9249. E-mail addresses: [email protected] (A. Indraprastha), sinozaki@sic. shibaura-it.ac.jp (M. Shinozaki). 1 Tel.: þ81 3 6722 2732; fax: þ81 3 5859 9249. 0360-1323/$ e see front matter 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.buildenv.2011.09.017
Architecture is experienced not just by attributes of its boundaries. The variability in the interior (enclosed space) and exterior (enclosure) comprise the essence of architecture. Several architects [8e10] as well as psychologists [11] have found that the
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Table 1 Comparison of models and methods. Gross method (1977)
Koile method (2001)
Sora method (2008)
Our method (2010)
Goal
Classification of enclosed space by its boundaries
Quality of space by viewpoint and geometric elements
Limitation
Only physical boundary forms a subdivided enclosed space, failed to accommodate center space, and no hierarchical attributes related to the space Enclosed space classification based on its boundary
Design representation by hierarchical territorial space Limit to the territorial spaces as a result of element, edge, and circulation model Abstraction model of design representation
Only to measure quality at arbitrary viewpoint position relative to the boundary element Spatial quality measurement based on viewpoint
Spatial map that represents relationship of boundary elements and circulation space Experimented on rectangular-based plan
Numerical values that represents rank of enclosed space
Graphic representation of model
Numerical result of measurement
State of the art
Result/Output
experiences in the same space can vary with the changes in architectural design elements such as colors and transparency. Another aspect of architectural space is that architects always compose space according to the boundaries and inter-relationships between the architectural elements and its planned activities. March and Steadman [3] used network graph to denote topological relationships between rooms e which room gives access to another, which room is adjacent to another. Péna [4] suggested that the matrix relationship of activities should be constructed to model adjacency of spaces regarding designated activities. Both studies had used basic mathematical model of spatial configuration in order to understand relationship between spatial design and activities. Our model of enclosed spaces is the elaboration from previous study with the advancement of having a map configuration of what we named as subdivided enclosed space inside a set of interior space. We advice each area of subdivided enclosed space expresses distinct spatial quality that is significant for spatial quality analysis and further conceptual design elaboration. 3. Mapping the interior by virtual agent The concept of spatial quality mapping by previous works referred to the preposition that on an enclosed space or interior space, the hierarchy of the space can be mapped by the strength of influence of its boundary elements [12e15]. A study of spatial mapping has been conducted by using number of solid boundaries to classify enclosed spaces [13], combining concept of territory space to map strength influence of boundary elements into enclosed space [1] and recently, used distance model to classify hierarchy of enclosed space [14]. Our model began with the classification of enclosed space [15] where there are six defined architectural spaces: by linear elements (column), by single vertical plane (i.e. wall), L-shaped space, parallel space, U-shaped space and four planes to define full closure of space. The basic enclosed space category we used for this research is L-shaped space (Fig. 1).
a
b
Spatial map based on hierarchical relationship of boundary elements and circulation space Layout of spatial mapping resulting in determination of subdivided enclosed space
Following the basic classification of enclosed space, our model of spatial mapping is based on the visual perception and position of the virtual agent. Therefore, the rules for generating spatial mapping are taking account the detected objects by virtual agent. Our method of enclosed space detection is based on the hierarchical structure of the space as previously been studied. On this model, the hierarchy of enclosed space is as follows: 1. L-shaped space; defined by two non-collinear solid boundaries. 2. Circulation space; defined where it has territorial space of circulation gate (i.e. door). 3. Attractor space; defined where it has territorial space of other architectural elements at the boundary such as openings. 4. Subdivided space; defined as result of the rules of spatial mapping. As result of this concept, we determined an interior space as a unit analysis. An interior space is a space that comprises of enclosures, enclosed space and circulation path. We named this area as bounded area (Fig. 2). A bounded area comprises of rectangular-type arrangement of enclosed spaces that depend on the configuration of architectural elements at its enclosure. We employed procedural rules by considering relationship between bounded area and its circulation path. The bounded area may enclosed by opaque boundaries (walls), openings (windows or doors) and other architectural elements. A circulation path is a circulation connector inside the bounded areas. Circulation gates such as door and path form a circulation space inside the bounded area.
Architectural plan
Interior space(s)
Enclosed space
Enclosure Circulation path
Bounded area for computational analysis Fig. 1. Diagrammatic model of enclosed space, a) L-shaped space; b) U-shaped space.
Fig. 2. Unit of analysis.
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a
69
Variant of gate position
Ed Md
b
Enclosed space by center point
c
Enclosed space subdivided by rules 1
1
1
1
2
2
2
1
1
2 3
3
2
3 2
3
1
2 1
1
1
2
1
1
1
1
1
Fig. 3. Subdivided enclosed space having a path terminated in the space.
a Variant of gates position
b Enclosed space by center point
c Enclosed space subdivided by rules 1
1
1
1
2 3 2 1
2 2
3
3 2 1
1
2
3
2 1
3 2
1 2
1
3
1
3 2
1
2 1
1
1
Fig. 4. Subdivided enclosed space having a linear path passing through space.
2 3
1
1
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a
For determining subdivided enclosed space, our computational method works by analyzing set of points detected by agent as he loosk around his surroundings. This analysis comprises of procedural rules based on spatial hierarchy of bounded area.
Variant of gates position
3.1. Model of circulation path in a bounded area
b
Enclosed space by center point
c
Enclosed space subdivided by rules
As previously mentioned, procedural rules for creating a map of spatial configuration is based on the relationship between bounded area and its circulation path. The computation for dividing enclosed space is conducted under the rules of circulation path inside the bounded area. Here, the pathespace relationship is defined as the connection between bounded areas and circulation paths. In architecture, a circulation path is the connection in which people traverse from one node to another [1,4]. In narrower scope, a circulation path is the connection between a circulation gate (door) and the space within the enclosure. There are two ways considered as the relationship between the paths and space [15]: terminate in space and pass through space. 3.1.1. Terminate in space If a room has only one door, then the circulation path is terminated inside the room. The model of subdivided enclosed space by circulation path is then the result of the relationship between the enclosed space and circulation area. Fig. 3 illustrates procedural steps of dividing enclosed space having a circulation path terminated in the bounded area. The rules to subdivide enclosed space are as follows:
d
Final result 3
1
2
2 2 3
1
2 1
2 1 1
2
2 1
2 2
2
3 2 1
2
2
3
3 1
1
3
3 2
3
2
1
2 1
Fig. 5. Subdivided enclosed space having angular path passing through space.
Determine L-shaped enclosed space (number 1 in Fig. 3c) by the center point of each boundary (Fig. 3b); Determine remaining space (number 2 in Fig. 3c) with respect to the circulation gate and center point; Determine the axial line along the center point and perpendicular to the path direction; Make parallel lines from the gate to the axial line (Fig. 3c) to obtain circulation space (number 3 in Fig. 3c). Following these rules, we established configuration of enclosed space having a circulation space that terminates in the center of the interior space.
Fig. 6. Set of points based on x-axial line and y-axial line.
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Fig. 7. Illustration on determination of subdivided enclosed space according to x-axial line and y-axial line.
3.1.2. Pass through space If there is more than one circulation gate in a room, the relationship between the paths and space known as pass through space. We developed two models: cut axially and cut obliquely. In both models, the circulation paths may have linear or non-linear positions.
3.1.2.1. Linear path. The circulation path is defined as linear if two gates are connected by a straight line. The rules to determine subdivided enclosed space are the same as the previous rules. Fig. 4 illustrates procedural steps of dividing an enclosed space having a linear circulation path passing through a bounded area. The rules of this relationship are extensions of the first set of rules.
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c b a
a
b
c
Area of windows=0.64 (m2) Area of wall=26.125 (m2) Ratio=0.02
Area of windows=1.16 (m2) Area of wall=26.125 (m2) Ratio=0.04
Area of windows=3.72 (m2) Area of wall=26.125 (m2) Ratio=0.142
Fig. 8. Determination of center point of each subdivided enclosed space based on quadrant position.
3.1.2.2. Angular path. The path is defined as angular if two gates are connected by angular line. In this situation, we hypothesized that the center point is a significant factor to determine subdivided enclosed spaces and circulation spaces. By considering this, when two paths encounter a space, their connection must pass through a center point or an axial line as defined by the previous rules.
Fig. 10. The size of window relative to their attached wall determines value of transparency.
Fig. 5 illustrates procedural steps of subdividing an enclosed space having angular circulation path passing through a bounded area.
Fig. 9. Graphical example of computation of subdivided enclosed space, a) Initial plan; b) determination of L-shaped enclosed space; c) circulation area using axial line; d) determination area of opening territory by extending its edges perpendicular to axial line; e) determination of extended area by extending L-shaped edges perpendicular to the nearest lines; f) center points of the subdivided enclosed spaces.
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Table 2 Two approaches to measure visual openness. By distance
By viewing angle
Average distance Average distance from q to from p to window 1 and window 2 ¼ X1 window 1 and window 2 ¼ X2 X1 < X2 Visual openness at p is lower than visual openness at q
Ratio of viewing angle and Ratio of viewing angle and maximum angle at p ¼ Y1 maximum angle at q ¼ Y2 Y1 < Y2 Visual openness at p is lower than visual openness at q
The rules to subdivide enclosed space are as follows: Define L-shaped enclosed space by the center point of each boundary (number 1 in Fig. 5c); Evaluate remaining space with respect to the circulation gate and center point (number 2 in Fig. 5c); Determine the minimum convex area; Divide the area by its center point; Determine axial lines along the center point and perpendicular to the path direction; Determine parallel lines from each gate to the axial line (number 3 in Fig. 5c). 3.2. Algorithm and procedural rules The followings are rules that are executed sequentially over set of points. These rules are applied following results of object detection and inner point computation over the inner coordinates of boundary objects relative to the position of agent. The general procedures are as follows: 1. Determine the center point of the polygon c ¼ (xc,yc) by finding out the minimum and maximum point of the vertices. 2. Determine the horizontal axial line and the vertical axial line. From the previous step, y ¼ yc ¼ horizontal axial line; x ¼ xc ¼ vertical axial line. 3. Define a set of points based on the two axial lines. This is done by sorting the points along the horizontal axial line, followed by sorting the points along the vertical axial line. 3.1. Sorting the points along the horizontal axial line is done by dividing the points into two sets: those that are located above the line (ypi> yc), and those that are located below
the line (ypi < yc). They are defined as xþpi ¼ set of points above the x-axial line and xpi ¼ set of points below the xaxial line: xþ pi ¼ (xþxpi,ypi) where ypi > yc; xpi ¼ (xxpi,ypi) where ypi < yc. 3.2. Accordingly, sorting the points along the vertical axial line is done by dividing the points into two sets: those that are located on the right side of the line (xpi > xc), and those that are located on the left side of the line (xpi < xc). They are defined as yþpi ¼ set of points on the right side of the yaxial line and ypi ¼ set of points on the left side of the yaxial line (Fig. 6) yþ pi ¼ (xpi,yþypi) where xpi > xc; ypi ¼ (yxpi,ypi) where xpi < xc. 4. Determine the intersected points at the horizontal and vertical axes. As of now, we have four sets of points: {xþpi}, {xpi}, {yþpi}, {ypi}. Each of these set members must be mapped into the designated axis, so that we have intersected point sets. 5. Determine the midpoint of two sequential points from each intersected point set. 6. Determine the center point of the result of Step 5. Fig. 7 illustrates the overall procedure as explained above. The procedure for combining intersected points on both the axial lines results in generating divided enclosed spaces. The next stage is to generate the center points of these spaces by running procedural rules on each point. We determined these center points based on the evaluation of the intersected points of each line by their quadrant. As previously explained, we separated each detected point according to their quadrant with respect to the axial lines, therefore we obtained four sets of points: {xþ}, {x}, {yþ}, and {y}. The center point of the subdivided enclosed space is given by means of
Fig. 11. Cases to determine maximum viewing angle at p.
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a
b
window 1
4 6
door
3
2 5
7
8
9
10
14
15
11
door
12
13
16
17 door
18 19 20
21
22
26
27
23
24 25 window 0.5
1. 0
Fig. 12. Result of visual openness measurement on room 1 of Kaufmann house.
their position in the quadrant, which is determined as the relationship of these sets: {xþ, y}, {xþ, yþ}, {x, y}, {x, yþ}. Fig. 8 below illustrates this concept: This approach maintains the origin of the intersected points at the axial lines and results in a better calculation for determining center point of each subdivided enclosed space.
3.2.1. Determine axial lines The determination of axial lines is significant in our model as a guideline for subsequent procedures. The axial lines are determined by determining the area of a polygon based on the set of its boundary points and computing its center points at the x-axis and at the y-axis. The necessary equations are:
Fig. 13. Kaufmann House by Frank Lloyd Wright.
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Fig. 14. Rachofsky house by Richard Meier.
i1 1X Area of boundaryðAÞ ¼ ðx y xiþ1 yi Þ 2 i ¼ 0 i iþ1 i1 1 X Center at X ¼ ðx y xiþ1 yi Þðxi þ xiþ1 Þ 6A i ¼ 0 i iþ1
(1)
(2)
Center at Y ¼
i1 1 X ðx y xiþ1 yi Þðyi þ yiþ1 Þ 6A i ¼ 0 i iþ1
(3)
3.2.2. Intersected points at axial lines Define the axial lines as: y ¼ yc and x ¼ xc, and (xc,yc) is the center point. At this stage, we evaluate the points of each quadrant with the axial lines (refer to Fig. 5):
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Table 3 Procedures of measurement for spatial quality level.
Procedures for measurements
1
2
VO: visual openness
PR: privacy
Calculate average distance Pn vo i ¼ 1 dWi Dp ¼ n
Dip ¼
Pk pr
i¼1
k
2
p
Dp Dp
PRp ¼ Exp
i¼1
pr
dWip
n
pr 2 p pr Dp
Calculate level using distance method by factor of transparency index VOD ¼ VOD ðtrÞ PRD ¼ PRD ðtrÞ p p
Pn
ac
Dp ¼
i¼1
dDac ip
n
p
ACp ¼ Exp
ac 2 p
D
ac Dp
ACD ¼ ACD ðtrÞ p
p
Calculate ratio of covered angle
uvo p ¼ 5
þ
D
p
4
Pk
pr
dWip
Calculate strength of influence VOD ¼ Exp
3
AC: physical accessibility
qp 100
uac p ¼
qp 100
upr p ¼
qp 100
Calculate strength of influence VOup ¼ Exp
u2p up
PRup ¼ Exp
upr 2p
upr p
6
Normalize value of (3) and (5)
7
Combine both result and obtain arithmetic average 1 1 VOp ¼ ðVOD þ VOup Þ PRp ¼ ðPRD þ PRup Þ p p 2 2
Quadrant 1 ¼ {(xpi,ypi)} where xpi < xc and ypi > yc; intersected points at y; yc ¼ {(xpi,yc)}; intersected points at x; xc ¼ {(xc,ypi)}. Set points in quadrant 1 ¼ {q1(xpi,yc) and q1(xc,ypi)}. Quadrant 2 ¼ {(xpi,ypi)} where xpi > xc and ypi > yc; intersected points at y; yc ¼ {(xpi,yc)}; intersected points at x; xc ¼ {(xc,ypi)}. Set points in quadrant 2 ¼ {q2(xpi,yc) and q2(xc,ypi)}. Quadrant 3 ¼ {(xpi,ypi)} where xpi < xc and ypi < yc; intersected points at y; yc ¼ {(xpi,yc)}; intersected points at x; xc ¼ {(xc,ypi)}. Set points in quadrant 3 ¼ {q3(xpi,yc) and q3(xc,ypi)}. Quadrant 4 ¼ {(xpi,ypi)} where xpi > xc and ypi < yc; intersected points at y; yc ¼ {(xpi,yc)}; intersected points at x; xc ¼ {(xc,ypi)}. Set points in quadrant 4 ¼ {q4(xpi,yc) and q4(xc,ypi)}. 3.2.3. Midpoints at each set in the quadrant For each set, the program computes the midpoints on two sequential points of the sorted set. The definition and rule is as follows. Definition and rule: {qn(xpi,yc)} and {qn(xc,ypi)}; n ¼ (1,.,4); set of points at quadrant n by horizontal and vertical axes. 0 0 {qn (xpi,yc) and qn (xc,ypi)}; n ¼ (1,.,4); set of sorted points at quadrant n by horizontal and vertical axes.
ACp ¼ Exp
ACp ¼
ac 2 p
D
ac Dp
1 ðACD þ ACup Þ p 2
{Mid_qn(x)(xpi,yc)} ¼ midpoint set at quadrant n by horizontal axis. {Mid-qn(y)(xc,ypi)} ¼ midpoint set at quadrant n by vertical axis. 0 {Mid-qn(x)(xpi,yc)} ¼ {qn (((xpi þ xpiþ1)/2),yc)} Mid-qn(y) qn0 (xc,ypi)} ¼ { (xc,((ypi þ ypiþ1)/2))} {
3.2.4. Center points at each set in the quadrant The center points of each quadrant are determined by combining the midpoints at the vertical and horizontal lines. The definition and rule is as follows: Definition and rule: {Mid_qn(x)(xpi,yc)} ¼ midpoint set at quadrant n by horizontal axis. {Mid-qn(y)(xc,ypi)} ¼ midpoint set at quadrant n by vertical axis. {Cen_qn(pi)} ¼ center points set at quadrant n. {Cen_qn(pi)} ¼ {Mid_qn(x)xpi,Mid-qn(y)ypi}. All computational process conducted in Virtools. The result of this process is the configuration of subdivided enclosed spaces as illustrated in Fig. 9:
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Table 4 Visual openness index measurement on house plans. Kaufmann house plan
Two windows
Rachofsky house plan
One window
One window
4. Model of spatial quality parameters In an architectural spatial quality model, we proposed factors that influenced enclosed space quality which are visual openness, privacy and physical accessibility. These basic parameters could have effect on how we regard particular interior space or enclosed space based on the configuration of architectural elements of enclosure. The previous work showed an empirical finding that the viewing distance and viewing angle yielded significant influence toward spatial evaluation and orientation [16]. Therefore, we develop our method of measurement based on the distance of architectural element to the point of measurement and the covering viewing angle from point of measurement to particular architectural element.
One window
One window
The result of this model is numerical level attached to each of the subdivided enclosed space that gives ranking on the particular spatial parameter. The followings are explanation of each parameter: 4.1. Visual openness parameter In modeling visual openness, we considered window as the source of its influence. This visual openness influence is received by each of subdivided enclosed space in a different level regarding their layout in a bounded area. The significance of this index is that it can express the visual openness influence upon enclosed space with such qualitative and quantitative attribute attached such as privacy, natural light and air.
Table 5 Privacy index measurement on house plans. Kaufmann house plan
Two windows, three doors
Rachofsky house plan
One window, two doors
One window, one door
One window, two doors
Two doors
One window, three doors
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Table 6 Physical accessibility index measurement on house plans. Kaufmann house plan
Three doors
Rachofsky house plan
Two doors
One door
The term visual openness index refers to the level of visual influence at a center point of a subdivided enclosed space. We defined three variables to compute visual openness: 1. Visual distance; refers to the distance from a reference point p to the openings (i.e. windows); 2. Transparency ratio; refers to the ratio of opening area and its adjacent wall area; 3. Viewing area; refers to the ratio of viewing area from point p having all windows and maximum viewing area defined as 100 . We defined transparency level here is a value drawn by fraction of the dimension between opening and remaining solid surface where the opening is located. Fig. 10 illustrates this concept: The procedure to compute visual openness is by taking average value of visual openness by visual distance and transparency ratio and visual openness by viewing area. Table 2 shows our approach to combine measurements of visual openness: 4.2. Privacy parameter Privacy parameter or visual privacy parameter refers to the visual penetration of a point p in bounded area as a result of being viewed from external spaces [6,7]. In our model, level of privacy depends on two factors: openings (i.e. window) and circulation gate (i.e. door). Aside of the function to circulate light and fresh air; window is an architectural element that provides visual exchange by its level of transparency. We used same approach to determine transparency ratio as with the visual openness parameter. The procedure to compute privacy is by taking average value of privacy by distance and privacy by viewing area. By distance method, the greater distance from window and/or door, the greater privacy level. Accordingly, greater angle to cover all windows and/ or doors is resulting in lower privacy level. 4.3. Physical accessibility parameter In our model, physical accessibility parameter refers to the value of average distance from point p at the center of a particular subdivided enclosed space, to the doors in that bounded area. The
Two doors
Two doors
Three doors
physical accessibility index represents ease of accessibility of a subdivided enclosed space in an interior space. The procedure to compute accessibility is similar with the previous where using two approaches, except for computing accessibility index, the object of measurement is circulation gate (i.e. door). 4.4. Procedures of measurement Each of spatial quality parameter has distinctive characteristic regarding the influential strength of its source, for example: 1. Visual openness parameter at p in space; the greater average distance to the windows means the lower visual openness index and the greater fraction of viewing angle means the greater visual openness index. 2. Privacy parameter at p in space; the greater average distance to the windows and the doors means the higher privacy index and the greater fraction of viewing angle means the lower privacy index. 3. Accessibility index at p in space; the greater average distance to the doors means the lower accessibility index and the greater fraction of viewing angle means the greater accessibility index. The illustrative diagram of method of measurement for visual openness, privacy and accessibility index is presented in Table 3. 4.5. Definition and equation The procedure for computation takes some abbreviations and definitions as follows: dWp ¼ distance from p to center point of window; dDp ¼ distance from p to center point of door; aWi ¼ area of window i; aWLi ¼ area of adjacent wall of window i; aDi ¼ area of door i; aWDi ¼ area of adjacent wall of door i; n ¼ number of window; k ¼ number of doors; trwi ¼ (aWi/aWLi)¼ transparency index of window i; trdi ¼ (aDi/ aWDi)¼transparency index of door i; qvo ¼ visual angle at p having all window covered; uvo ¼ visual openness ratio of covered angle;
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Fig. 15. Spatial qualities level on Kaufmann house.
qpr ¼ visual angle at p having all windows and doors covered; upr ¼ privacy ratio of covered angle; qac ¼ visual angle at p having all doors covered; uac ¼ physical accessibility ratio of covered angle.
4.6. The viewing angle method In addition to the distance method, we propose the viewing angle method for measuring influence of spatial parameters relative to the position of the point of reference.
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Fig. 16. Spatial qualities level on Rachofsky house.
The viewing angle of measurement is obtained as a fraction of angle u to cover outer edge of object of measurement to the maximum model of viewing angle. We determined the model of a maximum horizontal viewing angle as 100 . The variable u centered at the point p and its direction vector depends on the position and layout of the object of measurement. The principle of this approach is to obtain maximum angle to cover
outer edges of object of measurement from p. This concept is illustrated in Fig. 11: 4.7. Normalization There are two numerical values as the results from two distinct methods. To obtain average value at each point p, we made normalization on each result as follows:
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Fig. 17. Summary of spatial qualities evaluation on case studies.
Definition: 1. SP as spatial parameter, SP ¼ {VO, PR, AC}; 2. SP dðpÞ as spatial quality index by distance at p; SP sðpÞ as spatial quality index by viewing angle at p; 3. nSP dðpÞ as normalization by distance at p; nSP sðpÞ as normalization by viewing angle at p; 4. MaxSP d as maximum value of spatial quality index by distance of all points p in space; MinSP d as minimum value of spatial quality index by distance of all points p in space; 5. MaxSP s as maximum value of spatial quality index by viewing angle of all points p in space; MinSP s as minimum value of spatial quality index by viewing angle of all points p in space.
nSP dðpÞ ¼
ðSPdðpÞ MinSP d Þ
ðMaxSP d MinSP d Þ
;
nSP d˛½0; 1
(4)
at a particular point of reference. By this case, it is appropriate to combine both results to give an average weight of spatial qualities on each point of reference. We use arithmetic mean of these both values to represent average value obtained by objective and subjective variable. 5. Experiments and result The input for the experiments is CAD polygon. We used the architectural plans of Kaufmann House [17] (Falling Water house) by Frank Lloyd Wright (Fig. 13) and Rachofsky house by Richard Meier [18] (Fig. 14). The experiments on six different layouts are explained as follows (Tables 4e6). Each table below illustrates detailed layout of the rooms, position of center point of subdivided enclosed spaces and architectural elements characteristic (i.e. number and dimension of wall, window and door).
and
nSP sðpÞ ¼
ðSP sðpÞ MinSP s Þ ; ðMaxSP s MinSP s Þ
5.1. Result
nSP s˛½0; 1
(5)
4.8. Combined value On one example of visual openness measurement (Fig. 12), it is showed that there are different results of visual openness level that relates to the position of the point of reference to the window. By their definitions, the distance and visual angle method has characteristic that may lead to how we quantify visual openness objectively. By distance method, the visual openness level depends on the average distance to all windows. However, as suggested by Henry [16], visual distance also influenced by viewing area that may lead to subjective evaluation
Fig. 18. Comparison result.
The results of spatial quality measurements on six rooms are presented as follows; first is the spatial qualities measurement on Kaufmann house and Rachofsky house (Figs 15 and 16). Second is comparison on the result of both case studies. We presented the spatial quality level of each reference point as the combined result by distance method and by viewing angle method. Based on this evaluation, spatial quality evaluation depends on the layout configuration of the openings that made up the spatial mapping as we developed. In such, the openings affect the result of spatial quality ranking. The rooms of Kaufmann house serve as bedrooms while room 1 and room 3 of Rachofsky house serve as multipurpose rooms. Fig. 17 (a and b) presents the results of spatial qualities of three parameters: visual openness, privacy and physical accessibility considering the area of each room. Fig. 17(a) presents a result that can be used for quantitative spatial quality over the same function. In this case study, room 3 of Kaufmann house has the highest level of visual openness, privacy and physical accessibility. This result shows the relationships of the subdivided enclosed space as reference of measurement, the layout of the openings and spatial qualities. Although it needs more empirical finding, it is interesting to note that this method gives a possibility of more elaborate and objective analysis over spatial qualities parameters. The diagram (Fig. 18) shows that the physical accessibility and privacy levels of three plans of Rachofsky house are lower than the Kaufmann house. The shapes of the plan and configuration of the openings contribute to this result. On the case of visual openness evaluation, the dimension of the windows in Rachofsky house contributes for increasing its level compared with the Kaufmann house.
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A. Indraprastha, M. Shinozaki / Building and Environment 49 (2012) 67e85 Table 7 Spatial qualities measurement on design alternatives. Design variance
Spatial qualities level
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Table 7 (continued ) Design variance
Spatial qualities level
Fig. 19. Spatial qualities optimization.
6. Application for design alternatives analysis In this section, we demonstrated practicability of spatial qualities evaluation using previously explained methods. As a tool to improve design process, this demonstration showed analytical examination over series of design alternatives. On the case of visual
window 1
2
6
7
door
3 4
5
9
10
11
14
15
openness (VO), privacy (PR) and physical accessibility (AC) parameters respectively, this analysis can help to improve spatial quality of a bedroom design. Regardless the unlimited possibility to create design alternatives, these cases demonstrated rational iteration of design improvements by transformation (rotate, translate) of design elements from original design. Here, each of design alternatives has its final layout by transformation of windows and doors with their dimensions remain intact. On each alternative, the layout is developed intuitively and thus, independent from the intention or specific purpose for spatial qualities parameters. Since the results of these efforts are to be compared with the original design, all measurements results are valued relative to original design. The spatial qualities levels over design alternatives are presented as follows (Table 7): By comparing each design alternatives with original design on spatial quality parameters, improvements on spatial qualities can be shown as following diagrams (Fig. 19): All design variances have higher privacy level than the original. However, alternative 5 has highest level of spatial qualities. In this regards, with the variables of measurement are the position of openings and circulation gate, we can optimize design plans based on three spatial qualities parameters.
door
1
2
4
3
8
door
12
13
16
17 door
5
8
7
6
18 19 20
21
22
26
27
23
24 25
window
window 0 .5
0 .5
1. 0
Room 1
1. 0
R oom 3 Fig. 20. Visual openness level of the rooms in Kaufmann house.
9
10
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Table 8 Visualization of original design and best design alternative.
Original design
3D view 1
3D view 2
Best improvement
3D view 1
3D view 2
7. Summary and discussion
7.2. On spatial qualities evaluation
7.1. On mapping interior space
The model of spatial qualities evaluation using three spatial parameters has been experimented. Furthermore, this evaluation using distance and viewing angle methods revealed the results that had not been reviewed in previous studies. In our model, by combining distance and viewing angle methods, we can manage to compute influential strength of an architectural element as it is received at a particular point in space. The decay function has been employed to give distinctive result over relative small variants given the context of interior plan. This result as well revealed the relationship between layouts of the interior design and measurement variables that had some interesting result (Table 8). In this context, in addition to give visual cues, numerical values of spatial qualities levels represent influential strength of the parameter on the area of subdivided enclosed space. This model of spatial mapping gives opportunity for deeper spatial analysis over the configuration of architectural space. Based on the boundary elements and the relationship between space and circulation path, this model can be developed further to analyse design preferences of an architect by his spatial designs.
We presented a methodology for mapping architectural space by developing a semi-automatic method to generate subdivided enclosed spaces over CAD-type data. Our finding revealed the improvement of spatial qualities analysis using subdivided enclosed spaces as area of references. Moreover, generating map of interior space facilitates a visual cue to help designer develop better spatial configuration of his plan. This is based on the proposition that our method uses the relationship between architectural elements and circulation space that made up the subdivided enclosed spaces. In example, the analysis of visual openness on a series of design plan with the same function will facilitate understanding on organizing architectural space in the process of design as depicted in Fig. 20: In Fig. 20 colors gradient indicates level of visual openness and circle radius represents model of influential area of the visual openness level (For interpretation of the references to color in this paragraph, the reader is referred to the web version of this article.). Another possibility for the implementation of this method is to analyze the spatial signature of particular architects or styles in addition to the typological study based on architectural elements of the enclosure. On its limitation, this work remains focuses on rectangularbased interior plan with only use three physical setting variables: wall, window and door. We are aware that for future improvement there are some significant factors need to be addressed such as considering more architectural elements including height of the ceiling.
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