Geometric algorithms are usually designed based on the assumption of using arbitraryprecision representations. However, in modern computer systems floating-point arithmetic and finite-precision approximation are often used as implementing exact computations would require large computational resources and would be rather slow in the applications. Snap rounding (SR) is a widely used technique to transform representations of infinite precision into fixed-precision formats. It slightly modifies the original geometry of the input in order to obtain a better organized geometric object arrangement and avoid the issues caused by applying floating-point arithmetic in geometric algorithms. The existing implementations of SR primarily focus on processing sets of line segments, while in practice polygons are of great significance as well yet has not received adequate attention so far. In this thesis, a new method is proposed to perform SR on 2-dimensional polygons. Firstly the input polygons are embedded into a triangulation. Subsequently, the triangulation is tagged with the ID information of polygons and the polygon boundaries are extracted and stored in a container. The boundaries and the triangulation are then dynamically processed according to the identification of close polygonal vertices and close vertex and boundaries (under a predefined tolerance). After having snapped all the close elements the rounded polygons will be reconstructed from the processed boundaries. The testing results show the proposed method is capable of eliminating small gaps between elements (i.e. vertices and boundaries) and is adaptable to various inputs. The topological and geometrical properties of polygons are preserved as much as possible. Finally, an overview of the limitations is provided, along with potential directions for future research.

Currently more than 4 billion people live in urban areas around the globe, a trend that is expected to be increased in the upcoming years. While urbanisation provides the space for innovation and new opportunities, in the meantime physical, technical and social challenges are rising and the cities’ vulnerability is increasing. A tool to tackle these issues are Computational Fluid Dynamics (CFD) simulations, which can provide insight in various topics. CFD simulations are valuable for modelling complex urban phenomena such as wind flow, microclimates and thermal comfort. A CFD requires as an input a 3D geometric dataset that represents objects in the urban environment which are most commonly buildings and then according to this input the air flow is simulated around it. When creating geometries automatically for CFD simulations, several clean up tasks must be completed for them to be usable without any issues. One of the problems arising is related to the redundant faces shared between adjacent buildings, which have no purpose for outdoor flow simulations and cause complications when creating the mesh that is needed for the CFD. This synthesis project focuses on addressing the aforementioned issue by removing the shared faces. The ultimate goal of this project was to create an open-source product that can efficiently and in an automated way remove the adjacent faces between buildings. The benefits will be imminent during the meshing process, as we strive to reduce the time that consultancies spend fixing the input geometries before running a CFD simulation, along with an overall improved user experience. This report is organised in four main sections. The first section is the general introduction of the issue that needs to resolved. The second section defines more in depth the problem and sets the research questions, in accordance to that, in the third section the research methodology is developed. In the fourth section the results of both methods are presented. The fifth sectionfocuses on a reflection of the project, while the sixth section presents the final conclusions. Finally, the seventh section contains the specifics of the project management itself. The project was carried out in cooperation with Dassault Syst`emes and is developed in the context of the GEO1101 course in MSc Geomatics TU Delft. In addition to this report we have created a GitHub repository (https://github.com/Fabisser/facesBgone) that contains the source code of the two methods.