Geomatics and Environmental Engineering, vol. 16, no. 2

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Vol. 16 No. 2 (2022): Geomatics and Environmental Engineering

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Submitted
Sep 29, 2021
Accepted
Feb 7, 2022
Published
Mar 3, 2022
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This work is licensed under a Creative Commons Attribution 4.0 International License.

Representing 3D Topological Adjacencies between Volumes Using a 36-Intersection Model

https://doi.org/10.7494/geom.2022.16.2.127
Syahiirah Salleh
Universiti Teknologi Malaysia, Faculty of Built Environment and Surveying, Johor, Malaysia
https://orcid.org/0000-0002-4694-6622
Uznir Ujang
Universiti Teknologi Malaysia, Faculty of Built Environment and Surveying, Johor, Malaysia
https://orcid.org/0000-0001-5281-8478
Suhaibah Azri
Universiti Teknologi Malaysia, Faculty of Built Environment and Surveying, Johor, Malaysia
https://orcid.org/0000-0001-7926-9608

Corresponding Author(s) : Syahiirah Salleh

syahiirahsalleh78@gmail.com

Geomatics and Environmental Engineering, Vol. 16 No. 2 (2022): Geomatics and Environmental Engineering

Abstract

Topological properties of objects should be maintained and preserved to concisely represent objects. However, the implementation of 2D topological rules requires the decomposition of 3D objects into lower dimensions to determine topological relationships. This results in 2D topological relationships although the connected objects are in 3D. Hence, accurate representation of 3D connectivity in 3D models is limited. 3D topological rules can be implemented to include topological connectivity in 3D space. This paper implemented an extension of the 27-Intersection Model (27-IM) called the 36-Intersection Model (36-IM) to represent 3D topological adjacencies of two objects in 3D space. This resulted in a 12 × 3 intersection matrix or 36-IM that represented the intersections in terms of dimension and number of separations. Six cases were tested, consisting of "œmeets", "œdisjoint" "œintersects at a line", "œintersects at a point", "œcontains", and "œoverlaps". The resulting 36-IM matrices provided an accurate representation of how the objects in 3D space were related and their dimension of intersections. The formalisms of the 36-IM matrices were also interoperable which allowed the interpretation of 36-IM using the 9IM and DE-9IM to determine general topological relationships. By examining the intersection of interiors, boundaries and exteriors of 3D objects without object decomposition, 3D topological relationships can be determined as well as the dimension and manner of intersection.

Keywords

topological relation topological rules 36-IM topology GIS 3D modelling
Salleh, S., Ujang, U., & Azri, S. (2022). Representing 3D Topological Adjacencies between Volumes Using a 36-Intersection Model. Geomatics and Environmental Engineering, 16(2), 127–155. https://doi.org/10.7494/geom.2022.16.2.127
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