Spaces Between

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SPACES BETWEEN Measuring enclosedness between buildings

SPACES BETWEEN Measuring enclosedness between buildings Anne Herndon


How can we measure the degree of enclosedness of urban spaces?

ABSTRACT As architects, we acknowledge the roles our buildings play in shaping the negative spaces between them, the zones in which urban life occurs. However, our assessments can be subjective and not as useful as they might be. This project seeks to define a mathematical and universally-applicable method for describing qualitative aspects of the spaces between buildings using quantitative measures. It focuses on a quality this study will call “enclosedness:” how enclosed an exterior space feels to its occupants. The study results in a Grasshopper script that generates a “heat-map”-style visual representation of the enclosedness ratings of different parts of the space based on a mathematical formula.

KEYWORDS Enclosedness, Urban Space, Urban Morphology, Urbanism, Grasshopper, Rhino, Negative Space, Isovist

INTRODUCTION When researching enclosedness it is necessary to understand which physical attributes of a space, specifically regarding the forms and arrangements of the buildings surrounding a space, contribute to an occupant’s perception of enclosedness. Which factors, for example, cause the space shown in the photo to the right (top) to feel less enclosed than the space in the photo below it? In the first, the building is perceived as an object within a field. The viewer is standing outside an enclosed building and in a space that feels open (more so in person when one can see the streets extending out in all four directions from the intersection). On the other hand, the buildings’ role in the second scene is quite different. Rather than appearing to enclose rooms within the buildings, they act as walls of an exterior room in which the occupant is located. The difference is easy to intuit by looking at the photos, but how do we measure such a quality in a way that can be applied uniformly to a range of spaces, regardless of how cleanly they fall into one category or the other?

Pearl Brewery development, San Antonio, USA Example of a low level of enclosedness Image credit: Lake|Flato Architects

IT’S ALL IN YOUR POINT OF VIEW We must start by recognizing that a single value of enclosedness cannot possibly be applied to an entire “space.” In other words, given a particular public park or plaza, the enclosedness can vary dramatically depending on the exact position of the viewer. This is due to the changing relationship of three-dimensional objects as seen from a single point. 4

Pearl Brewery development, San Antonio, USA Example of a high level of enclosedness Image credit: Casey Dunn

Hemisfair Park, San Antonio, TX

Hemisfair Park in San Antonio provides an example of this. In the images above, a 360-degree viewshed is shown in orange from three different points within the park. The volume of space indcluded in that viewshed is known as an “isovist.” In the first, there are several buildings near the point, and their arrangement is such that the viewer has few opportunities to see beyond them. This has the effect of creating an enclosed exterior “room,” similar to the second photo on the previous page. The second image of Hemisfair shows the opposite. From this viewpoint, the so-called room is much larger, and buildings within view are more likely to appear as objects in a field than as walls to an outdoor room in which the viewer is standing. The third image shows something in between the first two, an intimate outdoor room interrupted by deep view corridors, wider than those in the first image.

The experience of enclosedness varies dramatically depending on the point of view. Any method for evaluating the enclosedness of a given area must, therefore, produce a unique value for each unique point within the area of study.

BUT WHAT TO MEASURE? After establishing the importance of creating an equation that yields unique enclosedness ratings for each occupiable point within a space, the question remained which variables to include in such an equation. After considering the example of Hemisfair Park (among others), consulting a number of colleagues, and spending time in a diversity of urban spaces, I assembled the


following list of variables believed to affect the feeling of enclosedness from a given point within a space: 1. Distances from the viewpoint to elements forming the perimeter of the “room” visible from that point 2. Heights of elements visible from the viewpoint 3. Perceived continuity of the perimeter formed by the elements that surrounds the viewpoint (see images to the right) To address these three variables, the study proposes two different methods of calculating enclosedness ratings: one that takes into account the first two variables, and another that takes into account the third. method #1 we will call “average line length” and method #2 “peripheral continuity.” It is important to note that any metric for enclosedness necessarily contains a degree of arbitrariness given that it measures a qualitative characteristic of which there is no universallyaccepted definition. This cannot be avoided. However, the primary importance of this study is not the creation not of a non-arbitrary metric, but of a metric that may be derived through a mathematical procedure and therefore applied systematically to any space. The universality of the metric allows comparison of enclosedness between different spaces and between points within a single space.

Example of a space whose perimeter has a high level of continuity Town Square Telc, Czechoslovakia image credit: Jan Gehl 1980 (Life Between Buildings)

Example of a space whose perimeters tend to have a low level of continuity, depending on the point of view Hemisfair Park San Antonio, USA




The tool we will employ in both the average line length method and the peripheral continuity method is the isovist. The term came into use in the seventies as a description of the part of a space visible from a given point. The isovist functions by sending an infinite number of rays out in all directions from a given point. These rays are terminated when they encounter an obstacle. The resulting shape describes the area visible from the viewpoint.

Employing the isovist in two-dimensional space, as it has most often been often used, provides the means of evaluating the first variable thought to affect enclosedness: the distances between the viewpoint and the elements surrounding it. Sending out an infinite number of rays is of course impossible, but any number of rays can be used as long as they are evenly distributed radially. The example below uses 160 rays. A maximum distance is given for each ray, based on the theory that beyond a certain distance from the given point, elements no longer impact the viewers’ experience of enclosedness.

The following calculations are performed using a Grasshopper script which has an isovist component at its core. The model used to test the script contains the buildings in downtown San Antonio that surround Travis Park, the space chosen for this trial.

This maximum distance was determined arbitrarily but in consultation with several members of the R&D Core

Isovist shown for a point within Travis Park, San Antonio, USA 7

Team to be 400 feet. Were a maximum line length not to be employed, a line continuing thousands of feet in space would dramatically affect the subsequent calculation while representing minimal or no experiential difference in enclosedness from a line of sight measuring 400 feet. The lengths of the rays are then calculated and averaged to supply the mean distance from the viewpoint to the surrounding objects. This has addressed the first of the three variables identified - distance between viewer and surrounding objects - but the calculation is not yet complete. If we take the isovist one step further into the third dimension, we can use a similar procedure to address the second variable identified: the heights of buildings. Now rays are not only sent out in the xy plane as shown in the previous diagram, but are lofted at a series of different angles (see below). The number of sets of lofted rays is,

Threedimensional use of isovist: rays are lofted at a variety of angles note: this image does not show the lines being cut at their maximum lengths of 400’ 8

again, arbitrary. For this study seven sets were used. The same procedure is then followed of terminating the rays once each one either encounters an obstacle or reaches the maximum 400 feet in length. The lengths of lofted lines in each of these lofted sets are determined and an average length calculated for each set. Now we have seven values for average line lengths - one for each angle of loft. There is an important caveat in considering the heights of surrounding elements: the change in height appears to become less meaningful in the experience of enclosedness the taller the elements become. For example, a two-story building feels more different from a one-story building than a ten-story building does from a nine-story building. The perception of change seems to be negatively and exponentially related to building height. To account for this, the average distance of each collection of lofted lines does not factor equally into the overall rating of enclosedness. Instead, the individual averages are weighted so that the

higher the angle of loft, the less the value affects the overall rating. Additionally, the angles chosen for loft increase exponentially so that the higher the loft, the less data are collected. The angles used are 0, 2, 4, 8, 16, 32 and 64 degrees from horizontal.

This method has accounted for the first two variables: distance between the viewer and surrounding objects, and heights of surrounding objects. It de-emphasizes the difference between object heights the taller the objects become.

Finally, the weighted average is calculated for the seven individual averages, using the formula shown below, where x represents the average line length at a given angle of loft and the subscript represents the angle of loft.


7(X0) + 6(X2) + 5(X4) + 4(X8) + 3(X16) + 2(X32) + 1(X64) 28 The single resulting value represents the first of the two ways to evaluate enclosedness for a particular viewpoint.1 1

This number is then adjusted using a multiplier that causes the final value to fall between 0 and 1, which will become important in a later stage when we map these values onto a plan of the space.

0° loft

PC0: 100%

16° loft PC16: 51%

2° loft

PC2: 96%

32° loft PC32: 5%

The second enclosedness calculation, which accounts for the third variable of peripheral continuity, uses the same lines created in the previous calculation. This time, rather than measuring their lengths and averaging those numbers, we instead evaluate simply the percentage of lines that encounter an obstacle. Rays that were previously terminated at 400 feet are now considered as not encountering an obstacle (shown in orange in the images below). Percentages of lines encountering obstacles are first calculated for each loft angle, and then averaged using the same weighted formula shown above. The resulting

4° loft

64° loft

PC4: 85%

PC64: 0%

8° loft

PC8: 66%

Plan views showing which lines encounter obstacles at loft angles indicated; blue lines encounter obstacles within the given maximum distance and orange lines do not 9

value describes how continuous the perimeter of the outdoor “room” is from the perspective of the given point.

FROM POINT TO GRID So far we’ve outlined two methods for assigning a value of enclosedness to a single point: one that considers average line length of the isovists, and the other that assesses peripheral continuity using the same isovists. The next step runs the same calculations for an entire space. In theory, an infinite number of points could be assessed. In practice, we test only a grid of points, the density of which will determine the resolution of our final heat map. The two values for enclosedness are then calculated for


Grasshopper script that calculates two sets of enclosedness ratings for a collection of points in a digital Rhino model 11

Enclosedness values calculated by Grasshopper script using method #1: Average Line Length 12


583 0.88 701 0.61 745 0.54 754 0.53 827 0.44 863 0.40 860 0.41 818 0.45 619 0.78 597 0.84 708 0.60 757 0.52 817 0.45 890 0.38 904 0.37 887 0.38 852 0.41 697 0.62 597 0.84 720 0.58 776 0.50 845 0.42 918 0.36 939 0.34 910 0.36 868 0.40 744 0.54


27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53




631 0.75 681 0.65 610 0.81 610 0.81 617 0.79 613 0.80 641 0.73 786 0.49 768 0.51 598 0.84 705 0.60 721 0.58 698 0.62 716 0.59 728 0.57 782 0.49 794 0.48 695 0.62 567 0.93 700 0.61 736 0.55 720 0.58 760 0.52 777 0.50 803 0.46 778 0.50 613 0.80




GRIDPOINT 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26

54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80

590 0.86 735 0.56 824 0.44 887 0.38 939 0.34 968 0.32 942 0.34 903 0.37 810 0.46 574 0.91 762 0.52 827 0.44 904 0.37 940 0.34 966 0.32 964 0.32 947 0.33 916 0.36 574 0.91 661 0.69 783 0.49 860 0.41 932 0.35 959 0.33 973 0.32 993 0.30 1004 0.30

each point of the grid using a single Grasshopper script, whose structure is shown in the image on the preceding spread. Running the script for each gripoint generates two sets of numerical data, one for average line length and one for peripheral continuity. Each set of numbers is adjusted to fall between 0 and 1.

The script then assigns a color to each square of the grid based on this number, with 0 corresponding to white and 1 corresponding to a saturated color. The more saturated the color, the higher the value of enclosedness for that square of the grid.

Colored graph showing values of enclosedness for Travis Park based on method #: Average Line Length 13








0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26

83% 81% 83% 83% 83% 84% 84% 78% 79% 84% 81% 80% 82% 81% 81% 79% 79% 81% 85% 81% 80% 81% 80% 80% 78% 79% 83%

27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53

85% 81% 81% 81% 78% 76% 76% 77% 83% 85% 81% 81% 79% 76% 75% 75% 76% 81% 85% 82% 80% 78% 75% 74% 75% 76% 80%

54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80

86% 81% 78% 76% 74% 73% 74% 75% 78% 86% 80% 78% 75% 75% 74% 74% 75% 75% 86% 84% 79% 77% 75% 74% 74% 73% 73%

Enclosedness values calculated by Grasshopper script using method #2: Peripheral Continuity (% of radial lines of isovists that encounter an obstacle)

Colored graph showing values of enclosedness for Travis Park based on method #2: Peripheral Continuity 15

DISCUSSION OF RESULTS As evident in a comparison of the two colored grids, the results of each method of calculation are similar but not identical. However, if we examine the results against some basic information such as building height, each method seems to be working. The building with the label “10” is the 10-story St. Anthony hotel, the tallest building bordering Travis Park, and the feeling one has of walking along the sidewalk immediately in front of the hotel is (anecdotally) one of relatively high enclosedness. This area of the diagrams is accordingly highly saturated for both methods. On the other hand, the northeast corner of the park feels relatively unenclosed due to the parking lots located on both the northeast corner of the intersection and the block to the east of the park. This portion of the graph is accordingly pale in color, representing low enclosedness values.

2 2

3 4


7 1




N values of enclosedness based on method #1: average line length; the numbers represent the number of stories of each building

Since method #1 is based on heights and plan distances, its measurements relate to the volume of the conceptual outdoor “room” created by surrounding buildings. Method #2, on the other hand, disregards metric distances entirely, and instead relates to the porosity of the space’s perimeter.

2 2

3 4


7 1




N 16

values of enclosedness based on method #2: peripheral enclosure; the numbers represent the number of stories of each building

FUTURE WORK The primary challenge of this process was obtaining a usable digital model. Because most building height data was publicly unavailable, the model used was created with the help of an app which estimates distances by analyzing photos. This is inaccurate and time-consuming. Furthermore, the model included only building information, but buildings are just one part of the urban environment affecting an occupant’s experience. Trees, site walls, bus stops, furniture, and even groups of parked cars are among the objects that can dramatically influence the feeling of enclosedness in a space. Obtaining a model representing all these items is important. For unbuilt projects in the design phase, these elements are typically available as part of the modeling process. For modeling existing sites, laser scanning and point cloud reconstruction should be explored in more depth and revisited as time goes on and these technologies advance.

REFERENCES Benedikt, M. L. (1979). To take hold of space: Isovists and isovist fields. Environment and Planning B: Planning and Design, 6, 47-65. Gehl, J. (1987). Life Between Buildings: Using public space. New York: Van Nostrand Reinhold. Hayward, S., & Franklin, S.S. (1974). Perceived openness-enclosure of architectural space. Environment and Behavior, 6(1), 37-52. Stamps, A. E., (2005). Enclosure and Safety in Urbanscapes. Environment and Behavior, 37(1), 102-133.


Lake|Flato Architects 311 Third Street, San Antonio, Texas 78205 210.227.3335 18

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