1. Subject Description 1. Subject´s Facts 1.1. Code: GAE02 1.2. Kind of subject: Basic 1.3. Duration: Annual 1.4. ECTS Credits: 8,5 1.5. Responsible professor: David Simón Grábalos 1.6. Language: Catalan, Spanish, English
Type Subject
Primer - Obligatoria

Titular Professors

Previous Knowledge

Previous knowlwdge
Geometric construction, technical drawing


Objectives & knolwdge

Competences that will be developed with this subject:

General competences:

Interpersonal competentes:
IT1 To be able to acquire the critic and auto-critic capacity.
IT4. Capacity to work in an interdisciplinary team

Systematical competences
CS1. Capacity to apply knowledge into practice.
CS3. To be able to develop learning capacities.
CS4. Capacity to adapt to new situations
CS5. To be able to generate new ideas.
CS8. Capacity to work autonomously.
CS9- Capacity to design and manage projects.

Instrumental capacities
IS1. Analysis and synthesis capacity
IS3. General basic knowledge of the studied area.
IS4. Students must be able to acquire basic knowledge of their profession.
IS8- Ability to manage information (ability to search and analyze information from different sources).
IS10. Students must be able to make decisions.
IS11- Fundamental and basic knowledge in the formative environment

Specific competences

Disciplinary knowledge (know):
B-4 Form analysis.
B-5 Representation systems.
B-6 Graphic restitution.
B-7 Geometry.

Disciplinary knowledge (know how to do):
A-7 Spatial representation
B-3 Capacity to use special representation systems, sketches development, proportionality, the language and techniques to represent graphics of the building elements and processes.
E-1 Capacity to interpret and elaborate the graphic documentation for a project, data capture, build architectural plans and geometric control of building work units.

Learning Outcomes of this subject are:

RA.02 Adequate knowledge of the history and the theories of architecture, as well as of the arts, technology and related human sciences

RA.03Carry out technical activities of calculation, measurements, valuations, appraisals and economic feasibility studies; carry out expert reports, inspections, pathology analysis and other analogous ones and write the corresponding reports, opinions and technical documents; carry out plan surveys on sites and buildings.
RA.04 Prepare technical projects and carry out the management of building works within the scope of their legal authorization.




The architectural creations or furniture, are built in the mind of the Architect. In both cases it is an object, real or virtual of three dimensions, the subject teaches to project it on a paper or screen in two dimensions or vice versa.

There are three basic ways to project:
A.- Cylindrical (orthogonal or oblique) Objective.
A1 Dihedral system.
A2 Horizontal Projection.
A3 Axonometric system.
B.- Perspective. Subjective
C.- Spherical. Fish eye. Gnomonic or stereographic
In descriptive geometry we observe parallelism, orthogonality, intersections, depth, shapes, symmetries, points of view, etc.
In this subject, along with the drawing, the tools are provided that lead to capture, by means of the eyes, the proportions, the sizes, the rhythms of the light and the shadows, the reflections, the volumes, the masses, the scale ... All these tools in your domain are important in the condition of architect. Once the conception of space is understood, the analysis of the representation of the represented forms in the subject of drawing and representation techniques, as well as the forms used in the construction and in the architectural analysis, will be sought.

The graduates of our Descriptive Geometry I program acquire the knowledge and develop the skills indicated below:

1. To have the knowledge of representation on a plane of the forms of the space, for the practice of the representation of the future forms that their projects will have.
2. Design and represent forms composed of planes and quadrics, intersections between them, representation processes to communicate how the projects are for the student imagined and analyze and interpret the results obtained.
3. Identify, formulate and solve problems of flat representation (called planes) in the different representation systems mentioned above in a multidisciplinary environment individually or as a member of a team.
4. Understand the impact of representation in the communication of imagined forms and the importance of working in a professional environment.
5. Use representation techniques and their tools for the conception of space.
6. Communicate effectively in a drawn way. Understand all contemporary aspects related to the representation of the projects of your profession, as well as the need for ongoing training.

Thematic blocks to organize the subject:

Point, straight line& plane
Slope and intervals, LMS, Scale
Intersection of two planes, intersections straight line-plane
Roofs resolutions.
Gruond shapes
Land Hidden zones.
Point, straight line & plane
Point and straight line.Straight line and straight line. Plane and plane. Straight line and plane. Point and plane.
Revolving a line.
Auxiliary projections and axonometry
Distances between points, lines and planes
Angles between lines and planes
Axonometric projections, orthogonal and oblique. Cube
Tetrahedron, octahedron. Figures Relationship.

Vanishing point, vanishing line. Proportions (Tales) and measures.
Distance circumference. rebattement of station point. Angle between two coplanar lines and line perpendicular to a plane.
Definition and contours. Location of a point
Planeintersection. Development. Intersections with lines
Intersection with lines and planes
Traces method. Planes through vertix. Edgewise planes.
Casting edge
Cast shadows
Shadow plane. Vanishing line
Plane that recives shadows. Vanishing line



The subject has a two teaching sessions per week.
Each session is divided into three parts: a first part is devoted to the resolution of problems made by the students at home, a second masterful part in which the teacher explains the new contents and a third part in which the students work on new exercises for consolidate the matter.

Teaching-learning methodological approach to accomplish the objectives:

The classes are organized on a dual structure.
The first one explaining and synthesizing the main theoretical Concepts with explanatory diagrams).
The second one will be to solve short exercices intended for his understanding.
They will complete the exercises at home.
The complementary exercises will be given at the beginnig of the course.

The subject´s methodology includes:

Basic Concepts will be developed to understand the space and the representation Systems.
Theoretical classes for all the students about the different contents of the subject: Different representation Systems, shades, etc.
Group explanations emphasizing in particular aspects of the exercises that must be done.
Practical exercices to apply the Concepts.
Drawing practical sessions with small explanations or specific corrections by the professor during the exercises development.
Group comments about the results of the exercises.
Individual comment about the global tracking of the course at least once a year.

Dedication to the subject = 8,5 credits at 26 hours / credit = 221 hours
Annual dedication = 32 weeks (26 teaching hours + 6 exams)
Weekly dedication = 221 hours / 32 weeks = 7 hours / week

CONCEPE - Total - Hours - %
Master classes: 26 weeks lecture. x 1h./w. = 26h 10%
Practical classes: 26 weeks lecture. x 3h./w. = 78h 35%
Dedication at home: 32 weeks x 3h / w. = 105h 50%
Exams: 4 exams x 3h = 12h 5%

Total annual dedication 221


Evaluation systems:

1. Exams
2. Practices
3. Aula BCN

NOTE: Depending on the course, these assessment systems and their percentage can be modified. The first day of class will be published on the intranet of the subject, with access to all students enrolled, the assessment systems and percentages assigned for that course.

Evaluation Criteria

Evaluation of achievement-level of the objectives:

Basic objectives for the evaluation:
Demonstrate ability to draw and represent.
Demonstrate capacity to understand three-dimensional objects represented in two dimensions and vice versa.
To learn the easy way of placing objects in space and how to look at them to represent them easily.
Check that the drawing represents the given object.
Participation during the class.
Autonomous learning; initiative; motivation.
The teachers will take into account the ability or the student to respond to the given problem to solve it, the understanding of the data, the ability to conduct the work and the ability to develop it.

Basic Bibliography


G. MONGE: Géométrie descriptive. Nouvelle edition, J. Klostermann fils, Paris 1811.
John Montague, Basic Perspective Drawing. A Visual Approach 1998
Rendow Yee, Architectural Drawing A visual compendium of types and methods 2007
Adrian Gheorghiu, Virgil Dragomir, Geometry of Structural Forms, ‪Applied Science Pub, 1978‬‬
Solomon Woolf, Elementary course in Descriptive Geometry 1895
Charles William MacCord, Elements of Descriptive Geometry, 1914
Engel, H. Sistemas de estructuras. Madrid: Blume, 1970.
González, V.; López, R.; Nieto, M. Sistemas de representación. Sistema diédrico. Vol. I. Valladolid: Texgraf, 1982.
Izquierdo, F. Geometría descriptiva. 19a. ed. Madrid: Labor, 1990.
Izquierdo, F. Geometría descriptiva superior y aplicada. 2a. ed. Madrid: Dossat, 1980.
Sánchez, J. A. et al. Curso de geometría descriptiva. 16 Ejercicios del curso 1994-95 para la evaluación de los alumnos y programas lectivos. Barcelona: Departament EGA I, UPC, 1996.
Sánchez, J. A. Geometria descriptiva. Sistemes de Projeccions Cilíndrica. Barcelona: Edicions UPC, 1993.
Sánchez J. A.; Villanueva, L. Temes clau de Dibuix Tècnic. Barcelona: Edicions UPC, 1991.
Reiner, T. Perspectiva y axonometría. Barcelona: Gustavo Gili, 1981.
Schmidt, R. Geometría descriptiva con figuras esteoscópicas. Barcelona: Reverte, 1993.
Taibo, A. Geometría descriptiva y sus aplicaciones. Vol. I: Punto, recta y plano. Vol. II: Curvas y superfícies. Madrid: Tebar, 1983.

Additional Material