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

They are described, through the various representative methods, orthogonal projections, axonometry and perspective, the conditions of belonging, of parallelism, intersection and the determination of the true size and shape of the plane figures. Particular importance will be given to the sections and their geometric construction, to the planar development of figures, belonging to a volumetric model, so that this can be reconstructed manually. Various historical references to representative methods will be given and some drawings by various authors will be analysed.
In detail we will study: the method of the double orthogonal projection construction of the fundamental geometric elements - representation of points, straight lines and planes - projection and intersection the measurement of the slope angle and the true shape of a flat figure - planar development - rotational solids - the sections of volumes and simple architectural bodies and the intersections between different volumes the theory of shadows.
The representation of the main geometric elements in the axonometry: points, straight and plane the oblique axonometry, military and knight - relationship of axonometric affinity determination of the true shape of a figure orthogonal axonometry direct construction - reference elements - intersection problems - axonometry of solids - graphic construction of vaulted roofs: cross vault and pavilion.
Spatial genesis of the reference elements in the perspective - representation of the fundamental geometric elements: points, straight, plane - conditions of belonging, parallelism, perpendicularity - straight points of measurement, angles - resolving processes of the perspective - perspective to vertical, horizontal and oblique - problems of intersection and true shape construction and measurement of angles return perspective.

Core Documentation

G. Spadafora, Fondamenti e applicazioni di geometria descrittiva, Franco Angeli, 2019
CANCIANI M., I DISEGNI DI PROGETTO, COSTRUZIONI, TIPI E ANALISI, DE AGOSTINI, TORINO, 2009.
CANCIANI M., IL DISEGNO IN PROSPETTIVA, ANALISI, ELEMENTI FONDAMENTALI, METODI RISOLUTIVI E TIPI, KAPPA, ROMA 2005.
M. DOCCI, M. GAIANI, D. MAESTRI, SCIENZA DEL DISEGNO, CITTÀ STUDI EDIZIONI, NOVARA, 2021.
DOCCI M., MIGLIARI R., SCIENZA DELLA RAPPRESENTAZIONE, NIS, ROMA 1992.
MIGLIARI R. GEOMETRIA DEI MODELLI, KAPPA, ROMA 2003.

Reference Bibliography

CANCIANI M., I DISEGNI DI PROGETTO, COSTRUZIONI, TIPI E ANALISI, DE AGOSTINI, TORINO, 2009. CANCIANI M., IL DISEGNO IN PROSPETTIVA, ANALISI, ELEMENTI FONDAMENTALI, METODI RISOLUTIVI E TIPI, KAPPA, ROMA 2005. DOCCI M., GAIANI M., MAESTRI D., SCIENZA DEL DISEGNO, CITTÀ STUDI EDIZIONI, NOVARA, 2011. DOCCI M., MIGLIARI R., SCIENZA DELLA RAPPRESENTAZIONE, NIS, ROMA 1992. MIGLIARI R. GEOMETRIA DEI MODELLI, KAPPA, ROMA 2003.

Type of delivery of the course

The discipline will be conducted in two areas, closely related to each other: the theoretical one, where a series of information, principles and rules will be given, which are the foundation of the representation of architecture and design, and the practical one, where application exercises and ex-tempora will be carried out, in which various drawings will be analyzed, according to their geometric and projective characteristics. The course makes use of the teams platform AA23/24 - FUNDAMENTATIONS OF DESCRIPTIVE GEOMETRY - 21001992 - CHANNEL II (CANCIANI), in which are updated as they come, the schedule of lectures (updated to the current lecture), and the supporting material for the lectures (PDF files of the lecture or application, the drawings and SKP files of some three-dimensional models of the geometric constructions). The course is structured according to a series of lectures, applications and graphical proofs, as described below: - some frontal lectures, in which topics related to the theoretical foundations of descriptive geometry and the solving of some problems specific to representation will be covered; - a series of applications carried out independently by the students; - some graphical proofs, related to the three representative methods studied; - the reviews (to be carried out obligatory during the year and in a congruous number), where the student will be able to personally show the lecturer the papers produced within the course and those prepared for the examination.

Attendance

Mandatory attendance for at least 75% of the hourss

Type of evaluation

The examination is individual. The examination will consist of a graphical test, after passing which the student will have access to an oral discussion in which the level of learning and awareness of the geometric principles underlying the drawings presented will be assessed. All graphical evidence performed in the classroom, as well as participation in lectures and reviews, will contribute to the final evaluation. The work for examination, done exclusively by hand and in black or colored pencil, consists of: - The book with lecture notes taken and exercises and applications redrawn in clean - A folder with transparent envelopes that puts together the drawings regarding the case study analysis, notes, appropriately put in clean and corrected) - Three panels in 50cm. x 70cm format, menabò of the final panels of the building under study - One 50cm. x 70cm format table of the building under study, in which the elaborations of the orthogonal projections will be shown, together with overturnings such as sections or determinations of the true form, - Two 50cm. x 70cm. size panels, related to the object of study. The panels should contain three-dimensional representations, such as cutaways, exploded views, axonometric or perspective sections, in a number of at least 5 elaborations per panel (accompanied by plans and elevations, used in overturnings), with the geometric constructions in evidence. All students who registered in previous years (from A.Y. 2023-2024, and so for previous years), will have to take the examination according to the procedures above: the subject of study can be about the paper they took in the year they followed or the current year.