The goal of the course is to provide students with methods, tools and useful procedures to the knowledge and analysis of historic buildings, their physical characteristics, construction and conservation. Particular attention will be given to learning the methods of integrated survey, using traditional techniques of direct survey coordinated with 3D relief (image based and range based).
teacher profile teaching materials
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.
(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
Fruizione: 21002037 MATEMATICA - CURVE E SUPERFICI in Architettura - Progettazione architettonica LM-4 N0 FALCOLINI CORRADO
Programme
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.
Core Documentation
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
Type of delivery of the course
The lessons are given as lectures or laboratory for all students. In the second part of the course the laboratory is organized in groups of 2 students to prepare a final composition. The laboratory uses the software Mathematica, to elaborate and analyze the mathematical models, and Photoscan for the photogrammetric survey and the construction of "Point clouds".Attendance
The frequency is mandatory for 75% of the lessons.Type of evaluation
written and oral exams