## 21002094-3 - MATEMATICA - CURVE E SUPERFICI

The course is aimed at studying and analysis of curves and surfaces in plane and in space as mathematical models of architectural elements. To learn, applying to different case studies, the differential properties of parametric curves and surfaces and their composition in a virtual model. By modelling you it is possible to process a thorough analysis of the architectural structure functional to several interventions in the field of restoration.
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/

Type of delivery of the course

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".

Attendance

The frequency is mandatory for 75% of the lessons.

Type of evaluation

Written exam: on problems related to analytic properties of a curve in space and on graphic and algebraic description of curves and surfaces. Oral exam: 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.