In this paper, more details are presented: (i) we supply complementary clear definitions of the Top, and Side, rather than defining them by examples; (ii) a new element Bottom is added; and (iii) the structure of top-bounded space is quantitatively provided by using a unified modelling language (UML) model.
Spaces formed by built structures are the hollow (unoccupied) parts where people can pursue activities. Although spaces may also be defined as boundless structures, providing their boundaries in a spatial model is necessary to account for local specificities. We therefore define the discussed spaces (environments) on the basis of their identified boundaries, i.e., spaces are virtual (non-existing) elements used to represent the closed volumes bounded by (virtual or physical) boundaries.
Top, Side, and Bottom are three generalised notions to represent a top (e.g., roof or shelter), side (e.g., wall), and bottom (e.g., ground or floor) structures. These concepts allow considering more complex boundary configurations. For example, a roof is always a top while the opposite is not true. The same holds for the relationship between a side and a wall. All three elements are boundaries of top-bounded space, so they are sub-classes of the class Boundary. Their definitions are as follows:
Top: A top is a structure above the ground, which can cover a space under it, and provides a physical or virtual upper boundary to such a space. A physical top can stand as: (i) a protection from weather conditions (e.g., rain, wind, cold, or heat); or (ii) a limitation to estimate clearance (e.g., for flying or carrying large items). The top can be an artificial or a natural structure/object (e.g., wood, stone, or tree).
Side: A side is a structure that encloses a space from around directions and stands as a physical or virtual lateral boundary of a given space. A physical side can act as: (i) a protection from weather conditions (e.g., wind); or (ii) a limitation to estimate entrance possibilities (e.g., finding a door or flying above). To a certain extent, a physical side is more similar to a fence, although it may have functions similar to those of a wall, such as carrying a load (e.g., load-bearing pillars). For example, a side can be used to delimit or prevent people from entering or exiting. Similar to a top, a side can be an artificial (e.g., wall or fence) or a natural structure/object (e.g., tree or river).
Bottom: A bottom is a structure that encloses a space from the lower direction and offers a platform where agents can stand by physical contact. Similar to the two former structures, a bottom can be an artificial (e.g., floor or slab) or a natural structure/object (e.g., ground). In this work, the ground/floor is assumed to be the default bottom structure.
Thus, the detailed definition of a top-bounded space based on the three essential elements is:
Top-bounded space (environment): Such a space is semi-open to the outdoors, physically enclosed by top(s) in the top direction, and may have side(s) but is not physically enclosed completely (i.e., indoors). The bottom is assumed to be present by default. This kind of space can be consistently classified as neither indoors nor outdoors, and it shares properties with both categories.
a,b shows two top-bounded spaces, but the former has sides, and the latter does not. A variety of structures can act as the source of top(s), e.g., indoor environment (Figure 1
c), bridge (Figure 1
d), or shelter (Figure 1
e). Furthermore, the function of top(s) can be different; some of them can help agents escape from rain or strong sun (Figure 1
a–e), but others cannot (Figure 1
The bus stand and gazebo in Figure 3
are two suitable illustrations of the models of top-bounded spaces. The bus stand has five physical boundaries on the same plane: a quadrilateral top (A
), three sides (B
, and E
), and a bottom (D
). To make it an enclosed volume, two more missing lateral sides (
) are needed. Therefore, the boundaries A
, and E
are physical, while the boundaries
are virtual. The gazebo has eight physical boundaries (A
, and D
are four physical tilted triangular tops; E
, and G
are three physical sides; and H
is the physical bottom. Thus, in this example, four virtual boundaries (
, and I
) are needed to make an enclosed space. Comparing the bus stand and the gazebo, we can observe that the shapes of boundaries are not limited to quadrilaterals and that they can be tilted.