This paper presents an innovative procedure to create parametric building information modelling (BIM) objects from point clouds of complex architectural features. BIM technology requires an advanced parametric representation of the geometry involving spatial relationships, constraints and material properties. The aim of the procedure is a BIM-based reconstruction methodology that preserves the level of detail encapsulated in photogrammetric and laser-scanning point clouds, and relies on non-uniform rational basis splines (NURBS) curves. The particular case of architectural objects with irregular shapes is addressed due to the lack of commercial BIM software able to handle such buildings. An actual case study made up of 7.5 billion points is discussed to demonstrate the use of the proposed procedure with huge point-cloud datasets.