Learning outcomes of the course unit
The course objective is to render engineering students capable of translating three-dimensional geometric models into normatively correct representations typical of construction and architecture, as well as to understand them from reading technical drawings and cartography.
Design, in fact, is the preferential language through which we express the operations of analyses and the nature of the intentionality of the plan as part of construction interventions inherent in civil engineering, be it expressed through traditional technical representations or computer assisted.
During the course, the study and the application of different representational methods, through descriptive geometry, will enable you to develop graphical language and the expressiveness of a student in the specific areas of civil engineering and of that inherent in construction systems in a particular manner.
Course contents summary
The course is conducted through theoretical lectures the content of which is essentially composed of Descriptive Geometry themes to provide an understanding of the various projective modalities by which it is possible to develop designs (orthogonal projections, dimensioned projections, parallel or axonometric projection, central projection or perspective and homological applications among the various projection methods), also in order to render uniform the expressive abilities of students from different secondary and advanced didactic backgrounds.
To provide continuous and progressive learning of the systems of representation, some individual exercises will be parallelly and concurrently assigned (that the student will autonomously carry out at home), which will consist in the elaboration of graphic plates, to be continuously corrected, and which themes will follow exactly those of the lectures in order to verify learning of the methods of representation.
In detail, the lectures revolve around the following subject matter:
The geometries of the plane (points, lines, curved lines)
The principal graphic constructions of the plane: tangents, Archimede’s spiral and cones.
Orthogonal Projections: essays on the historical origins of the method.
The representation of basic geometric entities (point, line, plane).
Conditions of belonging, parallelism and orthogonality.
The principal lines of the plane: horizontals, verticals, of maximum angle of inclination.
Points, lines and planes in particular positions.
Reversals of particular and generic planes. True size of plane figures.
Orthogonal projections: problems of measurement - distance from a plane, measurement of angles. Intersections between line and plane, between solid and plane.
Dimensioned Projections: basic concepts - line of maximum angle of inclination, line of level – geometrical conditions of belonging, orthonogality, parallelism - metric problems. Dimensioned plane, level curve plane.
Parallel or axonometric projections: Pohlke’s theorem
Orthogonal axonometry (isometric, dimetric, trimetric)
Oblique Axonometry (non-deformable elevation - cavalier isometric and dimetric – non-deformable plan - military isometric and dimetric).
Representation of the point, straight line and plane
Conditions of appearance, parallelism
Intersection line/solid, line/plane.
Central or perspective projection: theoretical outlines and terminology.
Homological Applications: theoretical essays - theorem on homological triangles.
Homological elements: centre, axis, couples of corresponding entities.
Types of homology: perspectivism - affinity - similarity (homothecy) – Translation.
Homological applications in orthogonal, parallel, central projections and in the theory of shadows.
The exercises will be done with traditional graphical tools (A3 white paper - 42.00 x 29.70 cm -, pencils, graduated right angles, compass, French curve, erasers, etc.), and the exercise themes will be:
1. Graphic Constructions
2. The basic elements and plane figures in orthogonal projection
3. Solids in orthogonal projection
4. Orthogonal and oblique axonometries
5. Perspectives: Central, accidental, rational
6. Homological applications
The graphic plates will be collected weekly in the classroom and will be corrected and assessed by the professor. All designs will be collected from the students and presented at the final exam.
At the end of lectures on descriptive geometry, a classroom ex tempore test will be effected on the content of these lectures.
On Descriptive Geometry:
M. Bocconcino, A. Osello, C. Vernizzi: “Disegno e Geometria”, collana “Il Disegno e l’Ingegnere”, Levrotto and Bella, Turin, 2006.
M. Docci, D. Maestri: “Scienza del disegno”, UTET Libreria, Turin, 2000.
On Architectural Design:
M. Bocconcino, A. Osello, C. Vernizzi, A. Zerbi: “Il disegno del territorio, della città e dell’architettura: applicazioni per allievi ingegneri e architetti”, series “Il Disegno e l’Ingegnere”, Levrotto and Bella, Turin, 2009.
C. Cundari, “Il Disegno. Ragioni. Fondamenti. Applicazioni.” Edizioni Kappa, Rome, 2006.
M. Docci: “Teoria a pratica del disegno”, Laterza, Rome-Bari, 1996.
For students who have, during the course, dealt with Descriptive Geometry graphics plates, as well as successively passed the ex tempore test effected at the end of the first cycle of lectures, the examination will be oral and will focus on the contents of the lectures held on the Descriptive Geometry issues and on a discussion of the final research plate that has previously been agreed upon with the professor, as well as related issues inherent in Civil Design.
The students who do not sit or do not pass the ex tempore test, must sit a written test, still concerning the contents of Descriptive Geometry (the plates of which are in any event to be realised) for admission to the final oral examination that will cover the contents of lectures conducted on Descriptive Geometry issues and a discussion of the final plate, previously agreed upon with the faculty, as well as related issues inherent in Civil Design.