Clingo2DSR - A clingo-based software system for declarative spatial reasoning

Figures & data

Figure 1. Two acceptable layouts where the bathroom object is shielded from the vision limit line, adapted from (Department of Building and Housing, 2011).

Figure 2. Class diagram of spatial theory solving via Clingo’s python API.

Figure 3. An alternative interpretation of the privacy code based on visibility space, regions from which an object is visible (Bhatt et al., 2012).

Figure 4. Cascading spatial evaluations.

Figure 5. Class attributes and methods for the geometry database.

Figure 6. Topological relation partial overlap between two regions as defined in $\mathcal{R}\mathcal{C}\mathcal{C}$ −5, and incidence relation inside between points and regions.

Table 1. Spatial functions in Clingo2DSR

Spatial Functions	Description	ASP theory atoms
$\mathrm{extent}:$ $\mathrm{Region}\to \mathbb{R}$	Area for 2D regions or volume for 3D regions.	&extent{Region} = real
$\mathrm{centre}:$ $\mathrm{Region}\to \mathrm{Point}$	Centre point of region.	&centre{Region} = point
$\mathrm{aabb}:$ $\mathrm{Region}\to \mathrm{Box}$	Minimum axis-aligned bounding box of region.	&aabb{Region} = box
$\mathrm{distance}:$ $\mathrm{Region}\times \mathrm{Region}\to \mathbb{R}$	Minimum distance between two regions.	&distance{Region, Region} = real
$\mathrm{shift}:$ $\mathrm{Region}\times \mathrm{Point}\to \mathrm{Region}$	Translates region by the given vector point.	&shift{Region + Point} = region
$\mathrm{scale}:$ $\mathrm{Region}\times \mathrm{Point}\to \mathrm{Region}$	Scales region by the given vector point w.r.t its centre.	&scale{Region * Point} = region
$\mathrm{rotate}:$ $\mathrm{Region}\times \mathbb{R}\to \mathrm{Region}$	Rotates region by the given angle w.r.t. its centre.	&rotate{Region, Angle} = region
$\mathrm{flip}:$ $\mathrm{Region}\times \mathrm{Segment}\to \mathrm{Region}$	Flips region w.r.t the given line segment	&flip{Region\Segment} = region
$\mathrm{offset}:$ $\mathrm{Region}\times \mathbb{R}\to \mathrm{Region}$	Inflates or deflates region by the given distance	&offset{Region, Distance} = region
$\mathrm{union}:$ $\mathrm{Regio}{\mathrm{n}}^{\mathrm{N}}\to \mathrm{Region}$	Union of a set of regions.	&union{Region;} = region
$\mathrm{intersect}:$ $\mathrm{Regio}{\mathrm{n}}^{\mathrm{N}}\to \mathrm{Region}$	Intersection of a set of regions.	&intersect{Region;} = region
$\mathrm{difference}:$ $\mathrm{Region}\times \mathrm{Region}\to \mathrm{Region}$	Difference of two regions.	&diff{Region - Region} = region
Spatial Relations	Description	ASP theory atoms
$\mathrm{size}($ $\mathrm{Relation},\mathrm{Region},\mathrm{Region})$	Size relations between regions: smaller, equisize, larger.	&size{Region, Region}
$\mathrm{topology}($ $\mathrm{Relation},\mathrm{Region},\mathrm{Region})$	Contact relations between regions: discrete (dr), partial_overlap (po), proper_part (pp), proper_part_inverse (ppi), equal (eq).	&incidence{Point, Region}
$\mathrm{incidence}($ $\mathrm{Relation},\mathrm{Point},\mathrm{Region})$	Incidence relations between points and regions: interior, on_boundary, exterior.	&topology{Region, Region}

Figure 7. 2D footprints of functional spaces of common bathroom objects. Taken from (Neufert et al., 2000).

Table

Algorithm 1 Compute spatial functions.

Figure 8. Deducing topological relations disconnected between two regions a and B by comparing their bounding box coordinates.

Table

Algorithm 2 Determine (incidence) spatial relations.

Table

Algorithm 3 Parse and Transform (PAT)

Table

Algorithm 4 Spatial Propagator (SP)

Figure 9. Shape of the $\mathit{i}$th input polygon in the empirical experiments, for $1\le \mathit{i}\le \mathit{n}$.

Table 2. Runtime (seconds) of four stages for $\mathit{m}=200$ and $\mathit{m}=3000$ in experiment 1.

m	Loading GDB	Grounding	Solving (total)	Spatial computations during solving
200	0.0231	0.0013	0.0801	0.0773
3000	0.0171	0.0001	18.4616	18.4317

Figure 10. Plot of experiment 1 comparing input size $\mathit{m}$ (teeth per polygon) with computational runtime of spatial computation, for fixed number of polygons, $\mathit{n}=10$.

Table 3. Results of experiment 2 comparing number of polygons ($\mathit{n}$) given as input to the experiment 2 ASP program with the solving and spatial runtimes, and the number of spatial function applications, with and without the GDB feature of storing and retrieving spatial computation results.

		n
Store		5	10	15	20	25	30
No	Total solving time (sec)	0.02	0.42	3.10	14.32	49.33	137.18
	Spatial computing time (sec)	0.02	0.27	1.44	4.80	12.13	25.58
	Spatial operation count	792	16192	88192	288793	719992	1513793
Yes	Total solving time (sec)	0.01	0.17	1.76	9.76	38.04	112.80
	Spatial computing time (sec)	0.00	0.02	0.11	0.39	1.07	2.29
	Spatial operation count	20	90	210	380	600	870

Figure 11. Minimum clearance requirements between successive doors on access routes. Taken directly from (Department of Building and Housing, 2011).

Figure 12. Operational spaces of doors (green regions) and access routes (compliant as gray regions and non-compliant as orange regions) in four distinct scenarios alternating the swing direction and the hinge side.

Figure 13. Privacy violations in the NZ building. Functional spaces, visibility spaces, and access routes are, respectively, denoted as yellow, purple and gray regions.

Table 4. Model statistics and runtime performance of Clingo2DSR for checking code compliance on real-world buildings.

Code provisions	Model statistics	Runtime	Reference documents
There shall be no direct line of sight between an access route or accessible route and a WC,urinal, bath, shower, or bidet.	Two-storey building in New Zealand with 8304 BIM objects	1.6 seconds	NZBC-G1-6.1.1
Where doors open into a lobby, the clear space between open doors shall comply with Figure 27.	12.5cmTwo-storey building in New Zealand with 6796 BIM objects	8.4 seconds	NZBC-D1/AS1–7.0.1
The clear width of an accessibleroute shall be no less than 1200 mm.		0.3 seconds	NZBC-D1/AS1–2.2.1
Access route shall have a heightclearance of minimum 2100 mm		0.2 seconds	NZBC-D1/AS1–1.4.1

Figure 14. 1) a person working from heights, taken directly from (der Bauwirtschaft (BG BAU), 2021). 2) movement spaces, fall spaces, and hazard spaces in a building under construction.

Figure 15. 1) The 13-storey building at timepoint 73 (The second slab quadrant on the second floor is about to be constructed). 2) The generated SVG outputs showing hazard spaces as red regions at time point 73 (a) and at timepoint 75 (b) when the fourth slab quadrant is placed.

Table 5. Model statistics and runtime performance of Clingo2DSR for construction safety analysis on real-world buildings.

Code provision	Model statistics	Runtimes	Reference document
Each worker constructing a leadingedge 6 feet or more above a lower level must be protected by guardrailsystems, safety net systems, or personal fall arrest systems.	9-storey building in Germany with 5415 BIM objects	0.59 seconds	42cmOSHA 29 CFR 1926.501(b)(2)*
	Four-storey building in Denmark with 707 BIM objects	0.24 seconds
	Two-storey fire station in Germany with 1273 BIM objects	0.2 seconds
	Thirteen-storey building in Denmark with 259 objects	2.28 seconds for 122 timepoints

Department of Building and Housing. (2011, October, 20). Compliance document for New Zealand building code clause G1 personal hygiene (2nd ed). https://www.building.govt.nz/assets/Uploads/building-code-compliance/g-services-and-facilities/g1-personal-hygiene/asvm/G1-personal-hygiene-2nd-edition-amendment-6.pdf

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Neufert, E., Neufert, P., Baiche, B., & Walliman, N. (2000). Architects’ data. Blackwell Science.

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der Bauwirtschaft (BG BAU), B. (2021, November, 9). B100 Absturzsicherungen auf Baustellen Seitenschutz/Absperrungen (Fall protection on construction sites). https://www.bgbau.de/fileadmin/Medien-Objekte/Medien/Bausteine/b_100/b_100.pdf

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