# From 9-IM Topological Operators to Qualitative Spatial Relations using 3D Selective Nef Complexes and Logic Rules for Bodies

### Helmi Ben Hmida, Christophe Cruz, Frank Boochs, Christophe Nicolle

#### Abstract

This paper presents a method to compute automatically topological relations using SWRL rules. The calculation of these rules is based on the definition of a Selective Nef Complexes Nef Polyhedra structure generated from standard Polyhedron. The Selective Nef Complexes is a data model providing a set of binary Boolean operators such as Union, Difference, Intersection and Symmetric difference, and unary operators such as Interior, Closure and Boundary. In this work, these operators are used to compute topological relations between objects defined by the constraints of the 9 Intersection Model (9-IM) from Egenhofer. With the help of these constraints, we defined a procedure to compute the topological relations on Nef polyhedra. These topological relationships are Disjoint, Meets, Contains, Inside, Covers, CoveredBy, Equals and Overlaps, and defined in a top-level ontology with a specific semantic definition on relation such as Transitive, Symmetric, Asymmetric, Functional, Reflexive, and Irreflexive. The results of the computation of topological relationships are stored in an OWL-DL ontology allowing after what to infer on these new relationships between objects. In addition, logic rules based on the Semantic Web Rule Language allows the definition of logic programs that define which topological relationships have to be computed on which kind of objects with specific attributes. For instance, a “Building” that overlaps a “Railway” is a “RailStation”.

#### References

- Abdul-Rahman, A., Pilouk, M., 2007. Spatial data modelling for 3D GIS. Springer Publishing Company.
- Antoniou, G., Harmelen, F., 2009. Web ontology language: OWL. Handbook on ontologies, pp. 91-- 110.
- Boley, H., Tabet, S., Wagner, G., 2001. Design rationale of RuleML: A markup language for semantic web rules, pp. 381--402.
- Borrmann, A., Schraufstetter, S., Rank, E., 2009. Implementing metric operators of a spatial query language for 3D building models: octree and B-Rep approaches. Journal of Computing in Civil Engineering, Volume 23, p. 34.
- Calvanese, D., De Giacomo, G., Lenzerini, M., Nardi, D., 2001. Reasoning in expressive description logics. Handbook of Automated Reasoning, Volume 2, pp. 1581--1634.
- Consortium, O. G., 2012. OGC Reference Model (ORM). [Online], Available at: http://www.opengeospatial.org/ standards/orm [Accessed 14 04 2012].
- Egenhofer, M. J., 2010. Qualitative Spatial-Relation Reasoning for Design, NSF International Workshop on Studying Visual and Spatial Reasoning for Design Creativity, Aixen-Provence.
- Egenhofer, M. J., Herring, J., 1990. A mathematical framework for the definition of topological relationships. In: Fourth International Symposium on Spatial Data Handling. pp. 803--813.
- Ellul, C., Haklay, M. M., 2009. Using a B-rep structure to query 9-intersection topological relationships in 3D GIS--reviewing the approach and improving performance. 3D Geo-information Sciences, pp. 127-- 151.
- Galton, A., 2009. Spatial and temporal knowledge representation. Earth Science Informatics, Volume 2, pp. 169--187.
- Granados, M., Hachenberger, P., Hert, S., Kettner, L., Mehlhorn, K., Seel, M., 2003. Boolean operations on 3D selective Nef complexes: Data structure, algorithms, and implementation. Algorithms-ESA 2003, pp. 654--666.
- Gruber, T. R., 1993. A translation approach to portable ontology specifications. Knowledge acquisition, Volume 5, pp. 199--220.
- Horrocks, I. et al., 2004. SWRL: A semantic web rule language combining OWL and RuleML. W3C Member submission, Volume 21, p. 79.
- Karmacharya, A., Cruz, C., Boochs, F. & Marzani, F., 2011. Integration of Spatial processing and knowledge Processing through the Semantic Web Stack. GeoSpatial Semantics, pp. 200--216.
- Lienhardt, P., 1991. Topological models for boundary representation: a comparison with n-dimensional generalized maps. Computer-Aided Design, Volume 23, pp. 59--82.
- Meagher, D., 1982. Geometric modeling using octree encoding. Computer Graphics and Image Processing, Volume 19, pp. 129--147.
- Nef, W., 1978. Beitrage zur Theorie der Polyeder: mit Anwendungen in der Computergraphik. Lang.
- Perry, M. & Herring, J., 2010. GeoSPARQL--A geographic query language for RDF data. A proposal for an OGC Draft Candidate Standard. Open Geospatial Consortium, Volume 27.
- Randell, D. A., Cui, Z., Cohn, A. G., 1992. A spatial logic based on regions and connection. KR, Volume 92, pp. 165--176.
- Sterling, L., Shapiro, E., Eytan, M., 1986. The art of Prolog. Wiley Online Library.
- Stocker, M., Sirin, E., 2009. Pelletspatial: A hybrid rcc-8 and rdf/owl reasoning and query engine. Proc. 6th International Workshop OWL: Experiences and Directions (OWLED), Volume 529.

#### Paper Citation

#### in Harvard Style

Ben Hmida H., Cruz C., Boochs F. and Nicolle C. (2012). **From 9-IM Topological Operators to Qualitative Spatial Relations using 3D Selective Nef Complexes and Logic Rules for Bodies** . In *Proceedings of the International Conference on Knowledge Engineering and Ontology Development - Volume 1: KEOD, (IC3K 2012)* ISBN 978-989-8565-30-3, pages 208-213. DOI: 10.5220/0004135702080213

#### in Bibtex Style

@conference{keod12,

author={Helmi Ben Hmida and Christophe Cruz and Frank Boochs and Christophe Nicolle},

title={From 9-IM Topological Operators to Qualitative Spatial Relations using 3D Selective Nef Complexes and Logic Rules for Bodies},

booktitle={Proceedings of the International Conference on Knowledge Engineering and Ontology Development - Volume 1: KEOD, (IC3K 2012)},

year={2012},

pages={208-213},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0004135702080213},

isbn={978-989-8565-30-3},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the International Conference on Knowledge Engineering and Ontology Development - Volume 1: KEOD, (IC3K 2012)

TI - From 9-IM Topological Operators to Qualitative Spatial Relations using 3D Selective Nef Complexes and Logic Rules for Bodies

SN - 978-989-8565-30-3

AU - Ben Hmida H.

AU - Cruz C.

AU - Boochs F.

AU - Nicolle C.

PY - 2012

SP - 208

EP - 213

DO - 10.5220/0004135702080213