Programme

Introductory topics: drawing tools and materials; graphic conventions and symbols. Fundamental geometric entities. Improper geometric elements. Projection and sectional drawing techniques. Principles of perspective and homological relationships.
For each graphical representation method (orthographic projection, axonometric projection, central projection — perspective, oblique projection, and shadow theory), the spatial construction, reference systems, and representation of fundamental geometric entities will be examined. The course will then address conditions of incidence, parallelism, and perpendicularity, along with the resolution of graphical problems — including determining the true shape and size of planar figures — as well as problems involving sectioning, intersection, and measurement.

Core Documentation

In addition to the texts listed in the bibliography, students will find further readings available on the course’s Teams channel.

G. SPADAFORA, FONDAMENTI E APPLICAZIONI DI GEOMETRIA DESCRITTIVA. LE PROIEZIONI PARALLELE. PRINCIPI TEORICI E APPLICAZIONI. FRANCO ANGELI EDITORE, MILANO 2019
M. DOCCI, M. GAIANI, D. MAESTRI, SCIENZA DEL DISEGNO, CITTÀ STUDI EDIZIONI,TORINO, 2011, 2A ED.
M. CANCIANI, IL DISEGNO IN PROSPETTIVA, KAPPA, ROMA, 2005.

Reference Bibliography

G. SPADAFORA, FONDAMENTI E APPLICAZIONI DI GEOMETRIA DESCRITTIVA. LE PROIEZIONI PARALLELE. PRINCIPI TEORICI E APPLICAZIONI. FRANCO ANGELI EDITORE, MILANO 2019 M. DOCCI, M. GAIANI, D. MAESTRI, SCIENZA DEL DISEGNO, CITTÀ STUDI EDIZIONI,TORINO, 2011, 2A ED. R. MIGLIARI, GEOMETRIA DESCRITTIVA, CITTÀ STUDI EDIZIONI, NOVARA, 2009, VOLL. I E 2. M. CANCIANI, I DISEGNI DI PROGETTO, CITTÀ STUDI EDIZIONI, NOVARA, 2009. M. CANCIANI, IL DISEGNO IN PROSPETTIVA, KAPPA, ROMA, 2005. U. SACCARDI, ELEMENTI DI PROIETTIVA E APPLICAZIONI DELLA GEOMETRIA DESCRITTIVA, LEF LIBRERIA EDITRICE FIORENTINA, FIRENZE, 2004. A. SGROSSO, LA RAPPRESENTAZIONE GEOMETRICA DELL’ARCHITETTURA, TORINO, 1996. M. BERARDI, D. MAESTRI, ASSONOMETRIA, ROMA, 1980.

Type of delivery of the course

The course lasts 100 hours and it’s organized into two days a week, four hours each. Lesson includes lectures and guided exercises which consist in the execution, with teacher support, of a series of exercises regarding exposed concepts. Classes provide the execution of drawings on the blackboard and the projection of navigable three-dimensional models that show the spatial relationships between the geometric entities. Guided exercises or to-be-solved ones for each method of representation exposed are available on the website course (fagd.altervista.org).

Attendance

The attendance is obligatory in at least 75% of the course. Attendance is recorded through the signing of an attendance sheet.

Type of evaluation

Verification of the knowledges takes place through a graphic exam and the discussion of three final drawings, 50X70 cm size. Drawings regarde one of the architectural themes chosen with teacher supervision and are drawn by pencil on cardboard. The goal is to verify that the students have fully understood the subjects exposed during classes and their competence to apply them not only on solids and figures, but also in the representation of architecture. Any exercises assigned during the course and corrected during the reviews, also constitute examination scripts. In detail: - A binder with transparent sleeves (A4 format) containing: the study of the agreed architectural topic, developed freehand, along with technical drawings (using ruler and set square) of plans, elevations, sections, and volumetric studies, possibly also on A3 sheets. - Three preliminary 50x70 cm freehand boards, serving as drafts for the final presentation boards on the selected architectural theme. - Three final 50x70 cm boards on cardboard, executed with ruler and set square. - In-class exercises, redrawn where necessary based on review feedback. - A notebook containing lecture notes. - Any additional assignments given during the semester (such as drawings and physical models based on representation methods). The graphic exam consists of 10/12 exercises. Time given for the examination is about three hours. Failure in the graphic test does not allow students to complete the exam by discussing the technical drawings. The attendance is obligatory in at least 75% of the course.

Programme

The course aims to provide the generative and projective foundations of representation methods and their application principles for project visualization and communication. Initially, cylindrical projections will be analyzed as the theoretical geometric foundation for the representation of both orthogonal projections, such as plans, elevations, and related sections, including practical examples, and axonometric projections (orthogonal and oblique), which, by introducing the third dimension, allow for a comprehensive understanding of the designed object. We will then move on to conic projections, the genesis of the Perspective representation method, analyzing the respective central, accidental, and tilted-frame types, focusing on the importance of point of view, also linked to stage construction. Finally, we will provide the historical geometric foundations that led to the codification of the Theory of Shadows and Chiaroscuro, applying projective rules within the various representation methods.

Core Documentation

D. Calisi, Luce ed ombra nella rappresentazione. Rilettura storica e sperimentazioni idiomatiche, Roma, Aracne editrice, 2015
M. Canciani, Il disegno in prospettiva, analisi, elementi fondamentali, metodi risolutivi e tipi, Roma, Kappa, 2005
M. Canciani, I disegni di progetto, costruzioni, tipi e analisi, Torino, De Agostini, 2009
M. Docci, M. Gaiani, D. Maestri, Scienza del disegno, Novara, Città studi edizioni, 2021
M. Docci, R. Migliari, Scienza della rappresentazione, Roma, Nis, 1992
R. Migliari, Geometria dei modelli, Roma, Kappa, 2003
R. Migliari, M. Fasolo, Prospettiva - Teoria e applicazioni, Milano, Hoepli, 2022
G. Spadafora, Fondamenti e applicazioni di geometria descrittiva, Milano, Franco Angeli, 2019

Attendance

Mandatory attendance for at least 75% of the hours. Attendance is recorded by signing the attendance sheet.

Type of evaluation

The exam consists of a written test (exemptions or final written test) and an oral exam. During the course, four thematic graphic tests will be administered on the topics covered in class. The grading range (A to D) determines the exemption from the exam on the topics covered. Students who pass all four exemptions are not required to take the final graphic test. Students who fail one or more exemptions will be required to take a final graphic test to make up for the exemptions for which they did not achieve a passing grade. The oral exam consists of the presentation of the drawings on the year's theme, with any questions asked about the drawings produced. Exemption Calendar October 22, 2025 1st Exemption – Homologies November 19, 2025 2nd Exemption – Orthogonal Projections December 10, 2025 3rd Exemption – Axonometrics January 14, 2026 4th Exemption – Perspectives