A purposive sample

Example 1: Visual-openness is quantitative-valued and measures the portion of a territory visible from another territory.⁴ It produces a value between 0 and 1.0. In the Gale house, for example, the visual-openness of the Living territory from the Dining territory is 0.78. Figure 3.5 shows the visible portion of the Living territory. Figure 3.6 shows the view from the Living territory toward the Dining territory.

Figure 3.5: Shaded region of Gale Living territory is visible from Dining territory;

visual-openness value of Living from Dining is 0.78.

Each * represents a viewpoint used by the visibility calculation.

4. The visual openness routine works from the 2D territory model: it tiles a territory, figures out which tiles are visible from specified viewpoints, then calculates the ratio of visible tiles to total number of tiles. Tile size and viewpoint place-ment are user-controlled parameters. Defaults: 6” square tiles; viewpoints at territory center and along relevant openings, 2.0 feet inside the territory and 1.5 feet apart.

Figure 3.6: Living territory of Gale house; view to Dining territory.

Example 2: Visually-open is boolean-valued and defined in terms of visual-openness by putting a threshold on visual-openness: A territory is considered visually-open from another territory if at least 0.6 of its area is visible from the other territory. The Living territory in the Gale house is considered visually-open from the Dining territory because its visual-openness

value is 0.78.

Example 3: Privacy is vector-valued, with components for visual-openness and physi-cal-accessibility. Visual-openness is described above. Physical-accessibility is vector-valued, with components for distance between two design objects and change in direction along the shortest path between two design objects⁵. Each of these components is quantitative-valued. The distance is calculated from the locations of the two design objects, the change in direction is calculated from a path derived from the physical form. (See Figure 3.7 for an exam-ple.) The design characteristic ^privacy thus has components for visual openness, distance between two design objects, and change in direction along a path between two design objects. We could define a boolean-valued design characteristic called ^private by putting thresholds on some or all of these. Notice, however, that the components for ^privacy are incommensurate, and it’s not necessarily meaningful, nor obvious how to combine them into a single boolean-valued design

characteristic representing the concept of being private. We’ll see later that even without defining boolean-valued characteristics for valued characteristics, TAC can rank values for vector-valued characteristics and reason about how to increase or decrease them by using a partial order.

Figure 3.7: Path for calculating change in direction from Gale Front door to Living territory.

Change in direction is 207.0 degrees; path was found using the circulation model.

Example 4: Perceived-main-entryness is vector-valued and gives a measure of the percep-tion of an exterior door as a main entry. Characteristics that influence a visitor’s choice of door when approaching a house are components of perceived-main-entryness. These include whether the door is visible from the street, whether there is a path that leads to the door from the street and how straight that path is, how far the door is from the street, and how formal the door is.

We define a door as formal if it is of solid wood instead of glass and/or is hinged rather than sliding.

Example 5: The design characteristic perceived-main-entry is defined in terms of

perceived-main-entryness. Its value is the exterior door that is most likely to be perceived as the main entry, i.e. the exterior door with the largest perceived-main-entryness value. TAC constructs a partial order that ranks exterior doors by their perceived-main-entryness values,

L iving Front d oo r

and returns the top of the partial order as the value of perceived-main-entry. (TAC’s construc-tion and use of a partial order is discussed in more detail later.)

How are design characteristics defined?

As the above examples have illustrated, design characteristics are related to physical form and often to other design characteristics. A characteristic is directly related to physical form by means of an opaque evaluation function that operates on one or several of the models representing a design. The characteristic visual-openness, for example, is calculated via a computational geometry routine that operates on a design’s territory model. As noted earlier, characteristics directly related to physical form are at the bottom of a decomposition hierarchy, with characteris-tics derived from them higher up. The decomposition hierarchy is implemented via three kinds of dependencies each of which is illustrated below.

Example 1: The design characteristic visually-open is related to visual-openness by providing it with an evaluation function body that checks whether a visual-openness value is greater than 0.6: (gt (visual-openness x from y) 0.6). The function body is written using a Lisp-like functional language which we’ve called the design characteristic definition language.

The language’s terms are the names of design characteristics and TAC-functions, variable names, and constants. The names of design characteristics or TAC-functions occupy the first (functional) position of expressions.⁶ (See Appendix B for a list of design characteristics and TAC functions, and Appendix C for lists of language terms.)

Example 2: The design characteristic ^privacy has two components, visual-openness and

physical-accessibility. The design characteristic physical-accessibility, in turn, has two components, distance-btw and change-in-direction-btw. Each of these components has an opaque evaluation function. The evaluation function for ^privacy collects all components into a vector of design characteristic expressions: ((visual-openness x from y) (distance-btw x and y) (change-in-direction-(distance-btw x and y)). It evaluates each of those expressions with respect to supplied arguments, examining design element, edge, territory, and circulation models in the process, and returns a vector consisting of the visual openness between the two arguments, distance between the two arguments, and change in direction between the two argu-ments.

Example 3: A design characteristic may have necessary conditions, which turn the body of the characteristic’s evaluation function into an if statement:

if necessary conditions are true

then compute a value

else return the symbol no-value.

The design characteristic perceived-main-entryness, for example, has components representing physical accessibility and formality of a door. The characteristic also has two neces-sary conditions: for an exterior door to be perceived as a main entry, the door must be visible from and have a path from the usual approach point.⁷ The defined domain of a design characteristic provides an additional implicit necessary condition: only exterior doors have perceived-main-entryness values. The components and necessary conditions for perceived-main-entryness

are represented using expressions in TAC’s design characteristic definition language:

perceived-main-entryness (x)

• necessary conditions ((built-exterior-paths to x from usual-approach) (visible-from x usual-approach))

• components ((physical-accessibility of x from usual-approach) (formality-of-entry x))

The design characteristics in the above definition are as follows: built-exterior-paths

returns a set of exterior paths between two objects; visible-from determines whether one object is visible from a second; physical-accessibility, discussed earlier, returns values for distance between and change in direction along a path between two objects; formality-of-entry returns a vector containing values for door solidity, which represents the portion of a door that is wood, and degree-of-hinge, which represents door hinge type. The design characteristic, degree-of-hinge, is an example of a qualitative-valued design characteristic whose range is an ordered set of values. A hinged door has a higher degree-of-hinge value than a sliding door, for example.

Relating door hinge type to formality, we say that a hinged door is more formal than a sliding door.⁸

The value returned for the design characteristic perceived-main-entryness is thus either the vector of values ((distance-btw x and usual-approach)(change-in-direction-btw x and usual-approach)(solidity of x)(degree-of-hinge of x)) or the symbol no-value.

7. The usual approach point represents the primary location from which someone would approach a building. A building may have several approach points; one of them may be deemed the usual one.

8. Calling this design characteristic “degree-of-hinge” is a bit awkward; the important point is that its values can be ranked.

As noted above, design characteristics form a decomposition hierarchy. This hierarchy is established via dependencies derived from evaluation function bodies, components, and necessary conditions. Shown below are dependencies for the above examples. Characteristics at the bottom of the hierarchy, i.e. with no characteristics below them, are computed directly from design objects.

Figure 3.8: Dependency links for example design characteristics.