3-D Cadastral Boundary Relationship Classification Algorithms using Conformal Geometric Algebra

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As urban centers continue to grow and develop, there is an increasing need for institutions to be able to digitally model and perform relationship analysis on 3-D cadastral boundary data. 3-D boundary analysis can be performed through visual inspection of survey plan drawings, but this often requires professional expertise such as a land surveyor or lawyer. This study examined the development, testing, and application of methodological processes and algorithms that were designed to classify various geometrical and topological relationships between the boundary components of two 3-D cadastral units to solve cadastral boundary problems. It applied established mathematical theory using Conformal Geometric Algebra objects and operational techniques, in combination with various 3-D point-point distance evaluations and geometric concepts to the classification of relationships between 3-D cadastral boundaries. A literature search suggests that the theory and methodology as it was applied in this study have not been used to classify topological relationships between 3-D cadastral boundaries elsewhere. Six sets of data flow processing algorithms were developed to determine the relationship classifications between boundary component pair sets that exist between two 3-D cadastral units. The classification processes were first validated using seven simulated experimental testing datasets, each consisting of two cube-like units. The classification processes were then applied to a cadastral dataset that was derived from a condominium survey plan registered in Alberta, Canada. This showed how the methods developed here can be applied to solving a practical 3-D cadastral boundary problem example in the land surveying field, specifically towards validating a shared boundary between two adjacent condominium units as is intended on the plan before survey plan registration. Results from the experimental datasets support the methods that were proposed to classify 53 distinct types of topological relationships between 3-D boundary component pair sets. While this type of boundary relationship analysis can be done through visual inspection of survey plans, the methods developed here are more mathematically rigorous. These processes could be leveraged by land surveyors and land administration professionals when analyzing 3-D survey plan boundaries.
3-D Cadastre, Conformal Geometric Algebra, Digital Cadastre, Land Management, Topology
Pullano, D. (2021). 3-D Cadastral Boundary Relationship Classification Algorithms using Conformal Geometric Algebra (Master's thesis, University of Calgary, Calgary, Canada). Retrieved from https://prism.ucalgary.ca.