## 1 Introduction  
The building information modeling (BIM) and the geographic information system (GIS) emerge from different areas as follows: GIS starts as a mapping tool and is currently a comprehensive geospatial data management and analysis platform used in the geospatial industry [1] and BIM is widely used in the architecture, engineering, and construction (AEC) domain [2] and is a platform for building information creation, management, and sharing [3; 4]. The integrated application of BIM and GIS has been applied in various fields and has benefited both areas. In the AEC domain, BIM and GIS have been jointly used in various stages of the building life cycle, such as planning, construction, operation, and maintenance. They have been applied to disassemble offshore platforms [5], build retrofit [6], green building design [7], construction site layout optimization [8], and construction supply chain management [9]. For the geospatial industry, they have been used to assess building-level flood damage [10] and room-level traffic noise [11], as well as improve indoor navigation [12; 13]. The main challenge with BIM and GIS integration comes from the conversion of geometric information between BIM and GIS [14; 15]. On the BIM side, the representative Industry Foundation Classes (IFC) standard uses multiple methods to represent three-dimensional (3D) objects, including boundary representation (B-Rep), swept solid, constructive solid geometry (CSG), clipping, mapped representation, and, in some cases, surface model [16]. Among them, B-Rep, CSG, and swept solid are classic methods for solid modeling [17], and clipping is considered to be a special type of CSG, as only the Boolean difference operation is involved. As a matter of fact, several studies simply referred to clipping as CSG [18; 19]. However, IFC explicitly differentiates them from each other, as two distinctive classes have been defined, i.e., _IfcBooleanClippingResult_ and _IfcCsgSolid_. A mapped representation is a representation that uses any of CSG, B-Rep, and swept solid representations of other entities, usually after coordinate transformation. Swept solid, clipping, and CSG representations are implicit models defined by certain parameters, the exact shapes are only calculated when needed, for example, for display, whereas B-Rep representations are explicit models [17]. Figure 1 represents examples of B-Rep, swept solid, CSG, and clipping. In contrast, on the GIS side, City Geography Markup Language (CityGML) mainly uses B-Rep and surface model. B-Rep is used to represent room and building spaces, whereas surface models are used to represent internal or external walls, ceilings, windows, doors, and roofs. Another frequently used data format on the GIS side is the shapefile format. Multipatch is one of its shape types that uses B-Rep to represent 3D objects [20]. Automated conversion of BIM datasets to GIS datasets is of great significance, given the fact that a great number of building models are needed for the construction of virtual city models that can be used in studies regarding smart city, etc., and because manual creation of such a large quantity of building models is time-consuming, cumbersome, and of low efficiency [18]. The automatic conversion has been realized for IFC B-Rep and swept solid [22], but not for IFC clipping. A clipping is the result of the Boolean difference between a swept solid and a half space solid, or between the result of the Boolean difference and a half space solid [23]. Clippings is classified into either one-clipping or multi-clipping depending on the number of half spaces involved. The primary challenge in automating IFC clipping conversion is the unbounded half space used by multi-clipping, because it is impossible to use bounded B-Rep to exactly represent boundless spaces. As a result, the conversion of clipping representations  
Figure 1: Basic representation methods used in IFC. (**a**) Boundary representation (B-Rep); (**b**) swept Solid; (**c**) constructive solid geometry (CSG) [21]; and (**d**) clipping.