Università Roma Tre

Contents
THROUGH THE EXPERIENCES OF SIGNIFICANT CASES, THE COURSE WILL ADDRESS, IN ARCHEOLOGICAL AND ARCHITECTURAL SITES, THE DIFFERENT METHODS OF 3D INTEGRATED SURVEY (DIRECT, PHOTOGRAMMETRY, LASER SCANNING). WILL BE INTRODUCED METHODOLOGIES FOR CRITICAL SURVEY AND STRATIGRAPHIC ANALYSIS, APPLIED TO THE CASE STUDY.
IN THE MODULE OF GIS SYSTEMS FOR THE RESTORATION, SUCH ANALYZES WILL BE SYSTEMATIZED IN A GEOGRAPHIC INFORMATION SYSTEM.

Bertocci S., Bini M., Manuale di rilievo architettonico e urbano, Città studi edizioni, Novara 2012
M. Docci D. Maestri, Manuale del rilevamento architettonico e urbano, n.e. Laterza Editore, Bari 2009

The course is divided into two parts: theory and applications.
Topics:
• Geographic Information System, Information System and cultural heritage;
• Cartography, georeferencing and Reference System
• Raster and Vectorial elements in GIS
• Geographic Information System for cultural heritage, examples: Constantine; Castrovirreyna, Izalco, Rome;
• Information System for cultural heritage and archeology.

Box, P. (1999). GIS and cultural resource management: A manual for heritage managers. Bangkok, Thailand: UNESCO.

Plane curves. Equation of a plane. Point-Plane distance. Plane sections. Parametric Curves in R². Arc length and curvature. Examples using Mathematica software: plot, symbolic and numerical commands. Modeling a curve profile of an image. Polar coordinates. Rigid transformations: translations, rotations and reflexions. Rotation and reflexion matrices. Curves defined by their curvature.
Space curves. Parametric Curves in R³. Curvature and torsion. Frenet frame: tangent, normal and binormal vectors. Rigid transformations in R³. Rotation and reflexion matrices. Curves on surfaces. Cylindrical and spherical coordinates.
Surfaces. Parametric surfaces in R³. Jacobian matrix. The gradient. Two variable function plot. Surface intersections. Domes and vaults. Tubes, conic and cylindric surfaces. 
Modeling a surface from an architectural example. Point cloud-Surface distance.

Alfred Gray, E. Abbena, S. Salamon Modern Differential Geometry of Curves and Surfaces with Mathematica, Third Edition Chapman & Hall/CRC (2006))

M. Abate, F. Tovena, Curves and Surfaces, Springer (2006)

Canciani M., Falcolini C., Saccone, M., Spadafora G.: From point clouds to architectural models: algorithms for shape reconstruction, 2013.