# Building Geometry Simplification for Improving Mesh Quality of Numerical Analysis Model
## 2 Literature Review  
To achieve the automatic simplification of three-dimensional (3D) geometry, the simplification of a surface mesh is commonly used, such as a mesh decimation algorithm. Surface mesh simplification involves partially deleting the vertices constituting the mesh [12], and was developed for models that include several millions of faces and vertices, such as human body geometry. In research studies on the application of numerical analysis in construction, surface mesh simplification has been used primarily to simplify the computer-simulated person (CSP) geometry in indoor environment analysis models [13; 14]. However, building geometries consist mainly of planes that are perpendicular or parallel to each other [15]. Therefore, they are expressed as simple surface meshes with hundreds of vertices. If vertices are deleted using the surface mesh simplification algorithm, the geometry may be excessively deformed. Most studies on the simplification of the 3D geometries of buildings have been conducted for the computational optimization of buildings and map visualization. [PERSON] [16] proposed a method for generating a new polyhedron from the major surfaces of the sidewall of a building geometry, and excluded negligible surfaces with small areas. Thereafter, the detailed geometry of the roof was reproduced as post-processing. [PERSON] et al. [17] varied the complexity of a horizontal cross-section of a building, and formed a prism geometry by sweeping the cross-section in the vertical direction to simplify the building model. Similarly, [PERSON] et al. [18] integrated buildings with similar heights, and simplified them into a prism geometry with a flat roof in order to simplify a set of adjacent buildings. In most cases, the building geometry is composed of walls that are perpendicular or parallel to each other, with little change in the vertical direction. The abovementioned studies presented simplification methods that consider these geometric features of buildings. However, for visualization of the 3D map, only the exterior geometry of the buildings was targeted, and its applicability to indoor models was not evaluated. Owing to the increased usage of file formats such as building information modeling (BIM) and geography markup language (GML) formats, such as CityGML, simplification studies that use the information of individual components of buildings have been conducted for visualization. [PERSON] et al. [19] integrated building components using morphological operations to perform a simplification. The hierarchical connection information between components was analyzed to determine the components to be integrated. [PERSON] et al. [20] classified the level of detail of a building according to the steps (section and height, roof and slab, door and window) required for extracting building components from the BIM model. As these methods use the semantic information of buildings, they are dependent on the data format of the building model. Most of these building simplification methods for visualization purposes apply different simplification criteria to the sidewall and roof surfaces, and they determine mainly the exterior properties of the building. As a consistency and objective criterion of geometric design is required for the analysis of physical phenomena, these methods are not suitable as preprocessing approaches for numerical analyses. Generally, simplification in FVM analysis is performed at the discretion of the researcher, and there have been a limited number of studies regarding the application of an automatic geometry simplification based on consistent criteria. [PERSON] et al. [21] approximated the sloping roof of an atrium model for a fire safety analysis, and it was in the form of a staircase-shaped polyhedron. The roof was simplified in four levels depending on the scale of the stairs. From a comparison of the simulation results, the temperature error of the simplified model was analyzed, and was found to be less than 10%.