From Point Clouds to Architectural Models: Algorithms for Shape Reconstruction

The use of terrestrial laser scanners in architectural survey applications has become more and more common. Row data complexity, as given by scanner restitution, leads to several problems about design and 3D-modelling starting from Point Clouds. In this context we present a study on architectural sections and mathematical algorithms for their shape reconstruction, according to known or definite geometrical rules, focusing on shapes of different complexity. Each step of the semi-automatic algorithm has been developed using Mathematica software and CAD, integrating both programs in order to reconstruct a geometrical CAD model of the object. Our study is motivated by the fact that, for architectural survey, most of three dimensional modelling procedures concerning point clouds produce superabundant, but often unnecessary, information and are also very expensive in terms of cpu time using more and more sophisticated hardware and software. On the contrary, it's important to simplify/decimate the point cloud in order to recognize a particular form out of some definite geometric/architectonic shapes. Such a process consists of several steps: first the definition of plane sections and characterization of their architecture; secondly the construction of a continuous plane curve depending on some parameters. In the third step we allow the selection on the curve of some nodal points with given specific characteristics (symmetry, tangency conditions, shadowing exclusion, corners, ... ). The fourth and last step is the construction of a best shape defined by the comparison with an abacus of known geometrical elements, such as moulding profiles, leading to a precise architectonical section. The algorithms have been developed and tested in very different situations and are presented in a case study of complex geometries such as some mouldings profiles in the Church of San Carlo alle Quattro Fontane.