Università Roma Tre

The course will address, through experiences on significant cases, in the archaeological and architectural field, the different methodologies of 3D survey(direct, photogrammetric, laser scanning) integrated with each other. Critical methodologies and stratigraphic analysis, applied to the case studies, will be introduced.
In the gis system module for restoration, these analyses will be systematised in a geographic information system.

ALAGNA, A., Stratigrafia per il restauro architettonico, il metodo dell’analisi stratigrafica delle superfici murarie per la conoscenza e la conservazione del costruito storico, Roma 2008.
A. BOATO, L'archeologia in architettura : misurazioni, stratigrafie, datazioni, restauro, introduzione di B. Paolo Torsello. - Venezia : Marsilio, 2008
BROGIOLO, G.P., CAGNANA, A., a cura di, Archeologia dell’architettura metodi e interpretazioni, Firenze 2012.
BRUSAPORCI, S. CENTOFANTI, M. , Sistemi Informativi Architettonici per la gestione, tutela e fruizione dell'edilizia storica, 2012.
DOGLIONI, F., Stratigrafia e restauro, tra conoscenza e conservazione dell’architettura, Trieste 1997.
FRANCOVICH, R., PARENTI, R., a cura di, Archeologia e restauro dei monumenti, I Ciclo di Lezioni sulla Ricerca Applicata all’Archeologia, Certosa di Pontignano (Siena), 28 Settembre – 10 Ottobre 1987, Firenze 1988.
HARRIS, E.C., Principles of Archaeological stratigraphy, London 1979, (trad. Ital.. D. Manacorda, Principi di stratigrafia archeologica, Roma 1983.
L. MARINO, Il rilievo per il restauro : ricognizioni, misurazioni, accertamenti, restituzioni, elaborazioni. - Milano : Hoepli, 1990

This course is an introduction to GIS. The aim is to provide basic knowledge on the use of
software to manage Information Systems in the project of restoration of cultural heritage.
Below the main topics discussed:
• GIS, Information Systems and Restoration;
• Cartography, Georeferencing;
• Vector and Raster Graphics Elements;
• Gis for urban restoration, examples of Constantine, Castrovirreyna, Izalco, Rione Monti;
• Information systems for restoration and archeology, archiving and management.

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)
Dispense con esempi di utilizzo del software Mathematica sono presenti nel sito del corso http://www.formulas.it/sito/corsi/matematica-curve-e-superfici-falcolini/