## 1. Introduction

## 2. Related Works

#### 2.1. Indoor Spaces for Emergency Response

#### 2.2. Generation of Stair Paths

- Step 1:
- Generate the “minimal bounding volume” of the stair flight, as shown in the gray box of Figure 3. Thereafter, extract the top and bottom surfaces of this bounding volume, extract all sides of these surfaces, and then generate the midpoints of each side, as shown by the blue points (top surface) and purple points (bottom surface) in Figure 3;
- Step 2:
- Determine the candidates for the start and end of the stair path (as shown by S′ and E′ in Figure 3) by performing a 3D intersection on the eight midpoints in Step 1 with the stair flight;
- Step 3:
- Create the path end (as shown by E in Figure 3) by searching the nearest landing or slab to Point E′, obtained in Step 2, and adjusting the elevation of Point E′ as high as the selected landing or slab. Point E is the endpoint of the stair flight path;
- Step 4:
- Create the path start (as shown by S in Figure 3) by searching the nearest landing or slab to Point S′ obtained in Step 2 and adjusting the elevation of Point S′ as high as the selected landing or slab. Point S then is the starting point of the stair flight path;
- Step 5:
- Create the waypoint of the run path (as shown by M in Figure 3) by lifting up the elevation of Point S obtained in Step 4 by one step height. Point M then is the waypoint of the stair flight path;
- Step 6:
- Generate the stair flight path by linking up the start point (S), waypoint (M), and endpoint (E) obtained in Step 3–Step 5. The resulting segments are the stair flight path, as shown by the red polyline of Figure 3.

## 3. Requirements and Considerations

#### 3.1. Run Orientation

#### 3.2. Run Structure

#### 3.3. Treads

#### 3.4. Risers

## 4. Implementation

#### 4.1. Overview and Notation

#### 4.2. Algorithm Logic

#### 4.2.1. GetPathStartZValue

#### 4.2.2. GeneratePathStart and GeneratePathWaypoints

_{1}in Figure 13, is the path start. This consideration is for those stair runs without physical risers whose path starts have to be determined by their first step. The method of identifying W

_{1}is first to generate the footprint of the run (as shown by the orange polygon in Figure 13), and lift the elevation of this footprint to the top of the first step, i.e., adding the height of a riser to the Z-value of the path start obtained in Section 4.2.1. The elevated footprint is shown by the cyan polygon in Figure 13. Subsequently, performing the intersection on this footprint with the stair run can yield the bounding area ABCD. Next, the front edge of the first step, i.e., $\overline{AB}$, is then extracted through an appropriate method, which will be addressed later. Then, the middle point of $\overline{AB}$ is the waypoint W

_{1}. Lastly, by lowering the elevation of waypoint W

_{1}to the Z-value of the path start, the resulting point is the path start.

_{1}of the first step. Taking the waypoint of the second step, W

_{2}, as an example, first lift the run footprint to the top of the second step, and perform the intersection on this elevated footprint with the stair run to yield the bounding area. Next, extract all sides of the bounding area and select the two sides with the longest and second longest lengths. At last, select the one that is the closest to the waypoint W

_{1}; the midpoint of that side is the waypoint W

_{2}of the second step. The methods for generating the remaining waypoints can be deduced via this analogy.

#### 4.2.3. GeneratePathEnd

## 5. Verification

#### 5.1. Test Cases

#### 5.2. Test Results

## 6. Conclusions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 2.**Stair-associated paths suggested by i-GIT [1].

**Figure 3.**Illustration of stair flight path generation logic in the 2nd version of the intelligent generation of indoor topology (i-GIT) algorithm [33].

**Figure 12.**Illustration of the method for searching for the connecting slab or stair landing of a stair flight.

**Figure 14.**Illustration of the method for determining the front edge ($\overline{AB}$) of the first step.

**Table 1.**Comparisons of how each algorithm supports different stair run orientations and modeling parameters.

Stair Run Orientation | Stair Modeling Parameters | Value | i-GIT Version 1 | i-GIT Version 2 | This Study |
---|---|---|---|---|---|

Straight | Run structure | Monolithic | v | v | v |

Non-monolithic | v | v | |||

Tread | No tread | v | v | v | |

Treads w/o nosing | v | v | v | ||

Treads w/nosing | v | v | |||

Riser | No riser (upright) | v | v | v | |

No riser (slanted) | v | v | |||

Upright/slanted risers | v | v | |||

Ends w/a riser | v | v | v | ||

Ends w/a tread | v | v | |||

Spiral | Run structure | Monolithic | v | ||

Non-monolithic | v | ||||

Tread | No tread | v | |||

Treads w/o nosing | v | ||||

Treads w/nosing | v | ||||

Riser | No riser (upright) | v | |||

No riser (slanted) | v | ||||

Upright/slanted risers | v | ||||

Ends w/a riser | v | ||||

Ends w/a tread | v | ||||

Winder | Run structure | Monolithic | v | ||

Non-monolithic | v | ||||

Tread | No tread | v | |||

Tread w/o nosing | v | ||||

Treads w/nosing | v | ||||

Riser | No riser (upright) | v | |||

No riser (slanted) | v | ||||

Upright/slanted risers | v | ||||

Ends w/a riser | v | ||||

Ends w/a tread | v |

Test Group No. | Case No. | Run Orientation | Run structure | Tread | Riser | |||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

Monolithic | Non-Monolithic | No Tread | Tread w/o Nosing | Treads w/Nosing | No Riser | No Riser (Upright/Slanted) | Upright/Slanted Risers | Ends w/a Riser | Ends w/a Tread | |||

1 | ABD1 | S | V | P | S | V | ||||||

2 | ABC2 | S | ST | P | U | V | ||||||

3 | ABC3 | S | SM | V | U | V | ||||||

4 | ABD4–7 | S | V | R | U | V | ||||||

5 | ABCD8, AC11–12 | S | V | F | V | V | ||||||

6 | ABCD9–10 | S | V | R | V | V | ||||||

7 | BD11–12 | P | V | F | V | V | ||||||

8 | EF1 | P | V | P | S | V | ||||||

9 | EF2 | P | ST | P | U | V | ||||||

10 | EF3 | P | SM | V | U | V | ||||||

11 | E4 | WL | SM | V | U | V | ||||||

12 | E5 | WU | SM | V | U | V | ||||||

13 | E6 | S | SM | V | U | V |

Case No. | IFC Data Anomaly | Path Start | Waypoints | Path End | Path |
---|---|---|---|---|---|

C1, C4–C7 | IFCSTAIR | not applicable | |||

D2, D3 | Incorrect Attributes | not applicable | |||

D1 | None | correct | incorrect | incorrect | incorrect |

D4–D10 | None | correct | 2 missing | correct | correct |

E6 | None | correct | 3 missing | correct | correct |

Others | None | correct |

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