Reconstruction of edges in digital building models

Traditionally, the geometry of building components or rooms is either described by their boundary or it is defined by constructive solid models. Modeling tools are available which are based on the principle of constructing building components and of composing a building by adding building components step by step. However, topological relations are relevant besides the shape of components and rooms. These topological relationships are not necessarily explicit information in boundary representation or constructive solid models. As a consequence, they must be computed. At present time, there exists to the best knowledge of the author only a single approach in this subject area that is able to reconstruct topological relations including their geometry. The objects which need to be considered are building components, built-in components and rooms. The challenge is to calculate the three relevant aspects of geometry in digital building models completely and in an efficient way. These three relevant aspects are clashes, voids and contact faces. The existing approach to calculate these aspects is based on space partitioning concepts. Space partitioning concepts store neighboring relations explicitly. The approach presented in this paper is also based on space partitioning. One basic and novel consideration of the approach presented in this paper is to execute the reconstruction procedure in a mesh. The mesh itself is not refined anymore at a certain point during the calculations to avoid uncontrollable refinements. The second basic and novel consideration is the way of avoiding topological inconsistencies. Integer values are chosen for coordinates, and a specific algorithm is presented that guarantees that topological inconsistencies cannot occur. The research presented in this paper addresses the first step on the way to compute clashes, voids and contact faces. This is the reconstruction of edges. This paper presents the theory and a pilot implementation for the reconstruction of straight edges. Examples show the benefits of the approach presented. Open questions are discussed.