## 21002094-3 - MATEMATICA - CURVE E SUPERFICI

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

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

Alfred Gray, E. Abbena, S. Salamon Modern Differential Geometry of Curves and Surfaces with Mathematica, Third Edition Chapman & Hall/CRC (2006)
Lecture notes with examples on the use of the software Mathematica are at the link of the course http://www.formulas.it/sito/corsi/matematica-curve-e-superfici-falcolini/

Type of delivery of the course

Lessons are, if possible, in the Department lecture rooms with the possibility of listening on-line lessons using the Teams platform. The lessons are given as lectures or laboratory for all students using the software Mathematica, to elaborate and analyze the mathematical models, and Metashape for the photogrammetric survey and the construction of "Point clouds". In case of an extension of the health emergency from COVID-19, all the provisions that regulate the methods of carrying out the teaching activities and student assessment will be implemented.

Attendance

Attendance at the course is mandatory for 75%

Type of evaluation

Oral exam consists of a presentation of works on the three moduli: in particular the subject will be a mathematical model of a surface from a 3D architectural example; the model is optimized with respect to its distance from the "Point cloud" of the survey obtained from their own pictures by a photogrammetric software.In case of an extension of the health emergency from COVID-19, all the provisions that regulate the methods of carrying out the teaching activities and student assessment will be implemented.