The Course aims to lead students to develop (their) skills in spatial prefiguration with mathematical parameters, to master the geometric language and its theoretical foundations, both from the point of view of representation and mathematics, so as to be able to choose the language and tools of representation in respect of expressive purposes; to read and recognize the geometric consistencies of the architectural form; to set the phases of physical/digital modeling to represent and communicate the existing and the project. Therefore, this teaching aims to provide students with the knowledge that they will be able to use in other experiences, academic or not, where physical and digital modeling itself is the result of a complex process of shape synthesis.

Elementary knowledge of Euclidean geometry and its lexicon and the contents of the Drawing and Relief Laboratory. The contents of Mathematical Institutions and, therefore: linear algebra, vectors, lines and planes, differential calculus.

The course is articulated between theoretical contents of both disciplinary scientific fields involved and application contents that will take place in the continuum on the topics suggested during the lessons/exercises. We will produce physical and digital models to develop the awareness to develop the ability to analyze and communicate the architectural heritage using models, intended as declensions of the statutes of Representation, like media whose eidetic and communicative potential becomes significant also in the mathematical field. Therefore, it is important to have a certain mastery of some mathematic elements related to curves and surfaces to make full use of the potential of parametric representation software thanks to a more conscious use of the available functionalities. We will take the fundamentals of analytical geometry in space and deepen the fundamentals of differential geometry of curves and parametric surfaces. THEORETICAL CONTENT_ 3CFU. Reading of the form, built in order to identify the characteristics and significant elements at the basis of parametric culture. Reading of graphic sources for the qualitative/quantitative selection of information useful for physical/digital modeling. foundations of analytical geometry in space: rotating and grooved surfaces, flat sections. foundations of differential geometry of curves and parametric surfaces. APPLICATION CONTENTS_3CFU. The course illustrates different modes of real modeling (Origami, laser-cut, and 3D printing), principles and procedures of some software (GeoGebra and Rhinocheros), with attention to the interpretation of mathematical content, to critically evaluate its effectiveness also communicative.

The course of Geometric Modeling in Architecture is proposed as an multidisciplinary experience, between Representation and Mathematics, and it is strongly applicative. The program is calibrated to be managed remotely, but offers its best effectiveness in a classroom with access to the laboratories of the Politecnico (involved). Each of the disciplinary approaches provides lectures and punctual exercises, the interactions between the disciplines will find space in the creation of physical and digital models. Students are invited to work both individually and in groups and to prepare the examination papers: - physical models of architecture made with different techniques - digital models with Rhinoceros and GeoGebra - tables on course layouts that illustrate the paths between theoretical fundamentals and application problems. These will be carried out in mixed way, in presence and remotely. All the tables and models, both physical and digital, will be subject to a series of revisions in itinere aimed to the progressive refinement of the students' geometric language.

Specific references are provided during the course by the professor.

Lecture notes; Lab exercises; Multimedia materials;

Exam: Compulsory oral exam; Individual graphic design project; Group graphic design project;

Risultati di apprendimento attesi Comprensione degli argomenti trattati e abilità della modellazione fisica e digitale. Capacità di: prefigurazione spaziale, leggere e riconoscere le consistenze geometriche della forma architettonica; impostare le fasi di modellazione fisica/digitale per rappresentare e comunicare l’esistente e il progetto; sviluppo di linguaggi specifici per la prototipazione di artefatti tangibili e non; comunicazione grafica e verbale del processo analitico personale e dei relativi risultati. La valutazione finale del corso tiene conto degli esiti maturati dal singolo studente in ciascuna applicazione e della capacità critica di progettazione e produzione del modello fisico e digitale più idoneo alla descrizione dell’architettura in oggetto. Per essere ammesso alla discussione orale l’allievo deve aver dimostrato una sufficiente conoscenza delle basi teoriche e delle applicazioni ai temi proposti nel corso delle applicazioni in itinere, anche attraverso la produzione di modelli fisici e digitali, individuali e di gruppo e la redazione di tavole illustrative degli approcci interdisciplinari, delle analisi geometriche e dei processi di prototipazione. A tal proposito si segnala che ogni studente dovrà produrre almeno un modello fisico, eventualmente ricorrendo a Fab Lab esterno. Durante l’esame finale lo studente discuterà i propri materiali, prodotti in aula e a casa (non online), inoltre integrerà con possibili sviluppi grafici e considerazioni orali sui contenuti e sulle tematiche del corso. Verrà valutata positivamente la capacità di interagire fattivamente con la docenza, di gestire in autonomia le attività di modellazione, di esporre e comunicare efficacemente il proprio percorso formativo. Il voto finale deriverà da una media ponderata dei risultati ottenuti durante il corso e della loro argomentazione in sede di orale. In particolare, la valutazione si baserà per ⅓ sui contenuti di Matematica, per ⅓ sui contenuti di Disegno e per ⅓ sull’elaborazione di modelli fisici e digitali. La lode sarà assegnata, a discrezione della docenza, agli studenti che avranno dimostrato una consapevolezza critica delle tematiche discusse e una partecipazione proattiva alle attività del corso. Criteria, rules and assessments procedures (only in-presence examinations) Exam modalities: mandatory oral examination, individual graphic elaborations Expected learning outcomes Understanding of the topics discussed during the course; showing good level skills in physical and digital modeling. Ability to: spatial prefiguration, reading and recognizing the geometrical consistencies of the architectural shape; correctly setting the phases of physical and digital modeling to represent and communicate the built and the new design architecture; developing of specific languages for prototyping physical and digital artifacts; graphic and verbal communication of the personal analytical process and of its results. The final evaluation considers the results achieved by the student in each application and the critical ability to design and produce the most suitable physical and digital model describing the analyzed architecture. To participate in the oral discussion, the student must have demonstrated a sufficient knowledge of the theoretical bases and applications proposed during in itinere applications, through the production of physical and digital/ individual and group models, and the production of graphic posters illustrating interdisciplinary approaches, geometrical analysis and prototyping processes. Specifically, each student will have to produce at least one physical model, eventually using an external Fab Lab. During the final exam the student will discuss his/her own materials, developed both in the classroom and at home (not online). It is likely that, during the discussion, the student will have to provide live graphic explanations (schemes/sketches/drawings) and oral considerations on the contents and topics of the course. The teachers will evaluate positively: the ability to effectively interact effectively with the teaching staff, the capability to autonomously manage the physical/digital modeling activities, the autonomy in effectively displaying and communicating the evolution of the student’s personal training path. The final grade will derive from a weighted average of the results obtained during the course and their discussion during the oral session. In particular, the assessment will be based: for ⅓ on the topics of Mathematics, for ⅓ on the topics of Drawing and for ⅓ on the elaboration of physical and digital models. Honors will be awarded, at the discretion of the teacher, to students who have demonstrated a critical awareness of the discussed topics and a proactive participation in the course activities.

In addition to the message sent by the online system, students with disabilities or Specific Learning Disorders (SLD) are invited to directly inform the professor in charge of the course about the special arrangements for the exam that have been agreed with the Special Needs Unit. The professor has to be informed at least one week before the beginning of the examination session in order to provide students with the most suitable arrangements for each specific type of exam.