We present a passive computer vision method that exploits existing mapping and navigation databases in order to automatically create 3D building models. Our method defines a grammar for representing changes in building geometry that approximately follow the Manhattan-world assumption which states there is a predominance of three mutually orthogonal directions in the scene. By using multiple calibrated aerial images, we extend previous Manhattan-world methods to robustly produce a single, coherent, complete geometric model of a building with partial textures. Our method uses an optimization to discover a 3D building geometry that produces the same set of façade orientation changes observed in the captured images. We have applied our method to several real-world buildings and have analyzed our approach using synthetic buildings.