## 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)
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/

M. Abate, F. Tovena, Curve e Superfici, Springer (2006)

Type of delivery of the course

The on-line lessons are given at the beginning on Moodle platform and for the rest of the course on Teams platform. The lessons are given as lectures or laboratory for all students in a on-line mode 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

Students must have attended at least 75% of the classes to be eligible for the exam

Type of evaluation

ORAL EXHAM: presentation of a composition, on 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. Before the oral exham a common test will be taken and used as a starting base for the oral part. 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.