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18-20 August VALIDATION AND INFERENCE OF GEOMETRICAL RELATIONSHIPS IN IFC 3B.5 Thomas Krijnen, Delft University of Technology, NL Francesca Noardo, Ken Arroyo Ohori, Hugo Ledoux, and Jantien Stoter

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18-20 August Inference, or from a dense graph to bag of elements for processing and manipulation 2 transactional update extract valid subgraphs

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18-20 August The complete BIM as a set of aspect models in a federated work environment 3

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18-20 August How to export relationships (e.g space boundaries) when the elements are in disjoint models? 4 Application 1 Application 2 ?

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18-20 August 5 Implementation https://github.com/tudelft3d/IfcOpenShell/blob/cgal/src/ifcconvert/validate_wall_connectivity.cpp IfcOpenShell the open source ifc toolkit and geometry engine

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18-20 August 6 Boundary Representation (BRep) u (periodic) ⟶ v ⟶ 0 2π

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18-20 August CGAL Nef Polyhedra 7 https://doc.cgal.org/latest/Nef_3/index.html

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18-20 August 8 Boundary Representation matches IFC geometry model curved surfaces and semantics (like radii) CGAL Nef Polyhedra arbitrarily precise number types lazy exact evaluation: propagating rounding errors to interval | fallback to exact when uncertain closed under all binary set operations

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18-20 August Relationships in IFC 9

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18-20 August Egenhofer spatial predicates 10 EGENHOFER & FRANZOSA (1991) Point-set topological spatial relations, International Journal of Geographical Information System, 5:2, 161-174, DOI: 10.1080/02693799108927841

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18-20 August Minkowski sum 11 https://www8.cs.umu.se/kurser/TDBAfl/VT06/algorithms/BOOK/BOOK5/NODE199.HTM

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18-20 August Methodology (e.g wall connectivity) 12 wall axis (for qualifying start/end) wall body wall boundary volume (computed) boundary intersection (computed) legend

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18-20 August Validation of three public building models 13 Duplex1, Fzk2, and Smiley3; 1 IFC2X3; Autodesk Revit Architecture 2011; U.S Army, Corps of Engineers 2 IFC2X_FINAL; Autodesk Architectural Desktop; Automation and Applied Informatics (IAI) / Karlsruhe Institute of Technology (KIT) 3 IFC4; Archicad 20; IAI / KIT

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18-20 August Results spatial containment two elements contained in wrong storey 14

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18-20 August Results wall connectivity 15 Duplex Fzk Smiley missing relation 2 2 0 invalid relation: wrong connection type 4 6 0 invalid relation: walls not touching 8 0 0

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18-20 August Results wall connectivity (Duplex) 16 wrong connection type is supplied | no connectivity information | not touching but for which connection information

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18-20 August Results space boundaries (Duplex) 17

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18-20 August Results space boundaries (Smiley) 18

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18-20 August Performance (Duplex) 19 Task Time (s) a. IFC parsing (tokenization and storage) 0.7174 b. Geometry mapping 0.0364 c. Geometry creation 0.5732 d. Conversion to Nef polyhedron 1.4116 e. Minkowski sum with small cube 7.0064 f. 3D Box intersection pairs 0.0006 g. Boolean intersection on Nef 16.5032 h. Conversion of result back to polyhedron 1.5342

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18-20 August Conclusion 20 Infered connections to enable distributed and transactional working Geometrical validation shows all assessed models contain flaws Calculate predicates and quantities to comply to local norms Exact CGAL Nef Polyhedra are robust, but the Minkowski sum is slow on concave inputs.