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Risorse bibliografiche
Risorsa bibliografica obbligatoria
Risorsa bibliografica facoltativa
Scheda Riassuntiva
Anno Accademico 2021/2022
Scuola Scuola di Architettura Urbanistica Ingegneria delle Costruzioni
Insegnamento 055826 - APPLIED MATHEMATICS FOR PARAMETRIC ARCHITECTURE
Docente Vianello Maurizio Stefano
Cfu 6.00 Tipo insegnamento Monodisciplinare

Corso di Studi Codice Piano di Studio preventivamente approvato Da (compreso) A (escluso) Nome Sezione Insegnamento
Arc - Urb - Cost (1 liv.)(ord. 270) - MI (1094) PROGETTAZIONE DELL'ARCHITETTURA***AZZZZ055826 - APPLIED MATHEMATICS FOR PARAMETRIC ARCHITECTURE
Arc - Urb - Cost (1 liv.)(ord. 270) - MI (497) INGEGNERIA EDILE E DELLE COSTRUZIONIIE1AZZZZ055826 - APPLIED MATHEMATICS FOR PARAMETRIC ARCHITECTURE
Arc - Urb - Cost (Mag.)(ord. 270) - MI (1017) ARCHITETTURA - ARCHITETTURA DELLE COSTRUZIONI***AZZZZ055826 - APPLIED MATHEMATICS FOR PARAMETRIC ARCHITECTURE
Arc - Urb - Cost (Mag.)(ord. 270) - MI (1195) ARCHITETTURA - AMBIENTE COSTRUITO - INTERNI - ARCHITECTURE - BUILT ENVIRONMENT - INTERIORS***AZZZZ055826 - APPLIED MATHEMATICS FOR PARAMETRIC ARCHITECTURE
Arc - Urb - Cost (Mag.)(ord. 270) - MI (1217) ARCHITETTURA E DISEGNO URBANO - ARCHITECTURE AND URBAN DESIGN***AZZZZ055826 - APPLIED MATHEMATICS FOR PARAMETRIC ARCHITECTURE

Obiettivi dell'insegnamento

The goal of the course is to provide students who have an interest in applications of mathematical ideas to Architecture with a compact overview of the tools and technique which are used or are of inspiration in some areas, such as computational design. Knowledge and understanding of mathematical concepts which go beyond what is traditionally taught in basic courses of Architectural Schools are now needed for some sophisticated applications, and this course aims to help students to be aware of and acquire such knowledge, according to their interests


Risultati di apprendimento attesi

Students are expected to become aware of some key mathematical ideas which

are behind techniques used in contemporary architecture.

Students are expected to be able to apply such ideas in an investigation of a topic of their interest.


Argomenti trattati

Mathematical tools for descriptive and computational modelling of surfaces will be introduced: n-order Bezier curves and Bezier surfaces, NURBS, Coon patches. Problem of continuity for joinings of curves or surfaces.

Curvature and basic notions about geometry of curves and surfaces.

Application to the derivation of the Euler model for an elastic rod.

Properties of minimal surfaces and their use in some contemporary architectural projects will be investigated, together with some connections to the mechanical properties of membranes.

Tasseletions of the plane will be introduced, with some of their applications in arts and architecture, and their classification into 17 classes through the notion of "symmetry group".

Basic introduction to "fractality" and some connections with Architectural theory, together with "L-systems", for some contemporary applications. Self-similarity, compass and box-counting dimensions and their use in Architecture.

Deformations and Algorithmic manipulation of curves and surfaces. Examples and applications of the modelling software "Grasshopper".

Students will be invited to provide ideas and proposals of topics of their interest where some connections bewteen Architecture and Mathematics are relevant.

The approach of the course will not be strictly mathematical and, in view of this, some software tools typical of modern Architectural Design. In specific recitation sections students will be receive a basic introduction to Grasshopper.

A basic knowledge of Calculus and Linear Algebra is required. Some ideas about curves and surfaces will be useful.

 

 


Prerequisiti
 

Modalità di valutazione

A two step evaluation method will be followed:

(1) a short preliminary written or oral part concerning the main topics discussed in the course.

(2) evaluation of a project about mathematics applied to Computational Design and Architecture, chosen according to the students' interests, among the topics suggested by the teacher during the Course. Students will also have the possibility of suggesting fields or themes of their own choice, taken from their previous experience.

 


Bibliografia
Risorsa bibliografica facoltativaA LINK to a short and partial video-introduction to last year's course...... https://youtu.be/jJhvIT5_B-Y
Note:

This is just to give an idea...

Risorsa bibliografica facoltativaPottmann, Asperl, Hofer, Kilian, Architectural Geometry, Editore: Editore: Bentley Institute Press, Anno edizione: 2017
Risorsa bibliografica facoltativaEssential Mathematics for Design https://developer.rhino3d.com/guides/general/essential-mathematics/
Risorsa bibliografica facoltativaNathan Carter, Introduction to the Mathematics of Computer Graphics, Editore: AMS/MAA Press, Anno edizione: 2016, ISBN: 978-1-61444-122-9
Risorsa bibliografica facoltativaMichael J. Ostwald, Josephine Vaughan, The Fractal Dimension of Architecture, Editore: Birkhäuser, Anno edizione: 2016, ISBN: 978-3-319-32424-1
Risorsa bibliografica facoltativaMore material provided by the teacher

Software utilizzato
Nessun software richiesto

Forme didattiche
Tipo Forma Didattica Ore di attività svolte in aula
(hh:mm)
Ore di studio autonome
(hh:mm)
Lezione
33:00
49:30
Esercitazione
27:00
40:30
Laboratorio Informatico
0:00
0:00
Laboratorio Sperimentale
0:00
0:00
Laboratorio Di Progetto
0:00
0:00
Totale 60:00 90:00

Informazioni in lingua inglese a supporto dell'internazionalizzazione
Insegnamento erogato in lingua Inglese
Disponibilità di materiale didattico/slides in lingua inglese
Disponibilità di libri di testo/bibliografia in lingua inglese
Possibilità di sostenere l'esame in lingua inglese
Disponibilità di supporto didattico in lingua inglese

Note Docente
schedaincarico v. 1.6.9 / 1.6.9
Area Servizi ICT
30/11/2021