Università Roma Tre

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.

R. Caddeo, A. Gray Lezioni di geometria differenziale. Curve e Superfici. vol. 1 Cooperativa Universitaria Editrice Cagliaritana (2001)
(oppure nuova versione in inglese dallo stesso testo 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, Curve e Superfici, Springer (2006)

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

Falcolini C., Talamanca V. Modelli geometrici applicati a nuvole di punti. In: "Mathematica Italia UGM 2015 - Atti del Convegno".
ISBN: 978-88-96810-04-0, Napoli, 22 - 24 maggio 2015