# Top-Bounded Spaces Formed by the Built Environment for Navigation Systems

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Related Work

## 3. Top-Bounded Spaces Formed by Built Structures

#### 3.1. Definitions

**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.

**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.

#### 3.2. Space UML Model

**TopBoundedSpace**is composed of several types of

**Boundary**, and one

**Boundary**can be shared by one or two spaces.

**Top**,

**Side**, and

**Bottom**are three different kinds of

**Boundary**.

#### 3.2.1. TopBoundedSpace

**TopBoundedSpace**has function and usage attributes. The function attribute normally denotes the intended purpose or usage of the space, such as a balcony for a building, while the usage attribute normally defines its real or actual usage; e.g., a balcony can also be used as a shelter for the lower level.

#### 3.2.2. Boundary

**Boundary**has four attributes: boundary, closure, gradient, and geometry. The attribute boundary defines a physical characteristic (physical or virtual) of a Boundary. Similarly, closure, and gradient are two attributes related to the spatial characteristics, and geometry describes the geometric characteristics.

#### Boundary

#### Closure

#### Gradient

#### Geometry

#### 3.2.3. Top, Side, and Bottom

**Top**,

**Side**, and

**Bottom**are three indispensable elements (Boundary). Generally, structures such as Roof, Shelter, and OuterCeilingSurface (defined in CityGML [46]) can act as the tops, while Wall, Fence, Door, etc., are considered the sides, and Floor and Ground/OuterFloorSurface can be the bottoms. At least one physical Top (with qualified closure) should be included. Surely the Bottom is physical and has qualified closure, while physical Sides are not specifically required, since side structures are not necessary for a top-bounded space, as they can float over or sink into the ground surface (terrain).

#### 3.3. Examples

## 4. Top-Bounded Space Creation Approach

- (a)
- Identify and order construction objects.
- (b)
- Determine top/bottom and generate spaces.
- (c)
- Trim spaces.

#### 4.1. Identification and Ordering of Construction Objects

#### 4.2. Determination of Boundaries and Space Generation

#### 4.3. Space Trimming

## 5. Space Requirements and Space Selection for Specific Agent

#### 5.1. Space Requirements

#### 5.2. Space Selection

#### 5.3. Space Accessibility

## 6. Experiments

#### 6.1. Pedestrian Definition and Size

#### 6.2. Requirements of Top-Bounded Spaces

#### 6.3. Use Case

## 7. Conclusions and Future Work

- (a)
- (b)
- (c)
- Investigating when satisfaction level of users, achieved with proposed approach, would have higher impact of their decisions compared to time- or distance-based routes that are currently in use.
- (d)
- Investigating more top-bounded spaces formed by other objects (e.g., trees) and trying to include them in the navigation system.

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**Examples of top-bounded environments (spaces) formed by built structures. The images in (

**b**,

**f**) come from ArchiExpo (http://trends.archiexpo.com/mmcite-1-as/project-63740-227548.html) and MIT24H (http://mit24h.com/1yDw077_8377cv0/), respectively.

**Figure 3.**Two examples of top-bounded spaces. The photographs of the bus stand and the gazebo come from Kuchingtransit (http://kuchingtransit.blogspot.com/2013/01/l) and Forest (http://www.forestgarden.co.uk/shop_family.asp?category=Features%20and%20Structures&subcategory=Gazebos), respectively.

**Figure 4.**Four different cases of top-bounded space creation based on projecting. For projections of upper and lower polygons, (

**a**) they are equal; (

**b**) the former is a subset of the latter; (

**c**) the latter is a subset of the former; (

**d**) they have overlaps but not exactly the same.

**Figure 5.**Example of trimming spaces: (

**a**) the three building components; (

**b**–

**d**) top-bounded spaces created based on projections; (

**e**) the space trimmed by the other two polygons; and (

**f**) the final three created top-bounded spaces.

**Figure 6.**The dimensions of required space for a pedestrian. ${l}^{\prime},{w}^{\prime},{h}^{\prime}$ describe the size of required space for an agent whose size is $l,w,h$. ${l}_{b}$ is extra space, and ${l}_{c}$ is the comfort distance. For the width, the parameters are ${w}_{b}$ and ${w}_{c}$, but the figures are side views, thus none of them are illustrated. Along the length direction, (

**a**) 0 side case; (

**b**) 1 side case; (

**c**) 2 sides case.

**Figure 7.**Space selection based on the size. (

**a**) the dimension of required space for a pedestrian; Light blue parts are physical boundaries, while olive green areas are virtual in (

**b**).

**Figure 8.**Examples of top-bounded spaces from an accessibility perspective. The top-bounded spaces are occupied by: (

**a**) plants; and (

**b**) a car.

**Figure 9.**Dimensions and space requirements based on body measurements (unit: mm). This figure is made based on the figures in Architects’ Data [47].

**Figure 10.**A 3D building model and creation of top-bounded spaces: (

**a**) the original 3D model; (

**b**–

**d**) the thirteen top-bounded spaces generated by the proposed approach; (

**e**) the unqualified top-bounded spaces, which are marked by red circles; and (

**f**) the qualified top-bounded spaces.

**Table 1.**The created top-bounded spaces selection based on ${r}_{{S}_{i}}$, ${G}_{B}$, and ${h}_{{S}_{i}}$.

No. | ${\mathit{r}}_{{\mathit{S}}_{\mathit{i}}}$ | ${\mathit{G}}_{{\mathit{B}}_{\mathit{i}}}$ (°) | ${\mathit{h}}_{{\mathit{S}}_{\mathit{i}}}$ | Qualified |
---|---|---|---|---|

${S}_{1}$ | 485.30 | 8.34 | 3504.03 | √ |

${S}_{2}$ | 333.08 | 18.17 | 3.594 | × |

${S}_{3}$ | 680.13 | 0 | 6602.51 | √ |

${S}_{4}$ | 638.44 | 18.17 | 862.34 | × |

${S}_{5}$ | 245.51 | 19.39 | 3789.22 | × |

${S}_{6}$ | 705.29 | 0 | 4004.33 | √ |

${S}_{7}$ | 640.08 | 0 | 6433.40 | √ |

${S}_{8}$ | 345.77 | 0 | 7664.48 | × |

${S}_{9}$ | 1911.08 | 0 | 2680.58 | √ |

${S}_{10}$ | 638.40 | 19.39 | 2892.37 | × |

${S}_{11}$ | 337.41 | 0 | 6777.85 | × |

${S}_{12}$ | 640.09 | 0 | 3682.28 | √ |

${S}_{13}$ | 883.89 | 0 | 2607.80 | √ |

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**MDPI and ACS Style**

Yan, J.; Diakité, A.A.; Zlatanova, S.; Aleksandrov, M. Top-Bounded Spaces Formed by the Built Environment for Navigation Systems. *ISPRS Int. J. Geo-Inf.* **2019**, *8*, 224.
https://doi.org/10.3390/ijgi8050224

**AMA Style**

Yan J, Diakité AA, Zlatanova S, Aleksandrov M. Top-Bounded Spaces Formed by the Built Environment for Navigation Systems. *ISPRS International Journal of Geo-Information*. 2019; 8(5):224.
https://doi.org/10.3390/ijgi8050224

**Chicago/Turabian Style**

Yan, Jinjin, Abdoulaye A. Diakité, Sisi Zlatanova, and Mitko Aleksandrov. 2019. "Top-Bounded Spaces Formed by the Built Environment for Navigation Systems" *ISPRS International Journal of Geo-Information* 8, no. 5: 224.
https://doi.org/10.3390/ijgi8050224