## 2 Methodology to Complete Missing Spatial and Geometrical Attributes  
### General Overview  
The first inventory of object classes present in subsurface volumes of the preliminary study [5] has been further developed to a minimal model. This minimal model integrates necessary attributes to describe position, geometry, indicating the related confidence level, as well as semantics of subsurface objects.  
The model can be presented in several ways, the hierarchic structure of scoped objects (taxonomy) is shown in Appendix A, Figure 11. Figure 2 focuses on the structure of geometrical representation of objects. Objects are classified either as isolated objects (e.g., tree roots), as an aggregation of linear objects (e.g., utility networks) or as volume aggregated objects (e.g., subsurface buildings). This structure has been chosen in the preliminary \"Underground\" study to represent the different legal contexts and their regulating authorities.  
Figure 1: Subsurface global workflow.  
As an example for the detailed description of these subclasses, the representation of linear aggregated objects, mainly used to represent utility networks, can be found in Appendix B, Figure A2.  
Metral [24] (Figure 3) provides interoperability between the minimal model, IFC and CityGML using ontologies like ifcOWL [27] and for CityGML [28].  
Local and national codes (e.g., [29; 30; 31; 32]) are integrated to describe spatial relations among objects. These relations are called \"compliance rules\". They are structured according to a generic rule model presented in [24; 25]. Figure 4 shows the structuring of a rule of the Swiss Gas and Water Industry Association [30; 31; 32], defining the minimal ground cover for a water network: (I) no construction is admitted above the water network, (II) the minimum ground cover for drinkable water is 1.2 m to 1.5 m, (III) a horizontal minimum distance of 0.4 m is necessary.  
Figure 3: Minimal model (subsurface solid geometry) mapped to IFC and CityGML, from Métral [24].  
Figure 2: Minimal model focused on simplified geometric representation.  
Strategies to complete missing geometrical attributes of subsurface objects are called \"completion rules\" and apply the generic rule model as well.  
All rule types are stored together with subsurface objects in a triple store database (RDF). The triple store is structured according to the ontology, integrating minimal model, ifcOWL, CityGML and the generic rule model. The ontology provides objects with necessary geometrical and functional attributes as well as with information about the completeness and precision of geographical and geometrical data.  
Objects are visualized through a twofold volume representation:  
* A primary object: to describe a geometrically simplified version of the real object, integrating data completion strategies.
* A secondary object: to consider a virtual bounding box assigned to a confidence metric aimed at measuring the probability that the full primary object is inside it.  
The level of information present in the SITG [23] database is extensive, as shown in Table 1. Priority is given to spatial and geometrical attributes needed for object representation. Additional attributes can be added to the model if required.