Described herein is a process and system for constructing three-dimensional (3D) representations of buildings. The 3D representations of buildings are semantic models that include roof nodes, roof edges, as well as roof faces with associated properties (e.g., pitch, azimuth). The system receives a 2D representation such as a roof outline including nodes connected by edges and associated data such as a height value, a pitch value, an independent structure, or a dependent structure. The system determines height values where a building structure changes. The system propagates a wavefront representing a cross-section of the building to the height values to generate 3D model edges. The 3D representation is generated based on the 3D model edges. The system can create 3D representations of buildings including roof structures of arbitrary complexity and can create representations of dependent roof structures such as dormers.