Applied geometry consists of the application of the best known representation systems, and using them to describe objects from an artistic and professional approach. Nowadays, however, the classic techniques of square and bevel, plan projection, elevations, profiles, etc... have been displaced by digital techniques, which help enormously in the process. Of course, always complemented with sketching, design and freehand sketch.



Today, we can see the usefulness of it when presenting artistic dossiers for exhibitions and museums, giving the presentation of the same a high-level professional finish through well done sketches, or 3D renderings with simulations of lighting and shading in real time.

In fact, in the professional industry, more and more profiles are required to control the tools of applied geometry, such as the ability to draw under orthogonal representation systems, axonometric or freehand conic perspective, but also the ability to project 3D renderings that give credibility and realistic volume to the parts, objects and projected buildings.



That is why from fields as apparently distant as building engineering, architecture or product design, they begin to require these techniques that we will see in the course.

This subject is configured as an experimental workshop that proposes an analytical vision through Geometry in Art and an experimental formulation with proposals and projects in which drawing and descriptive tools are a fundamental part.

It also contemplates the training that our graduates must have to teach in secondary education and the quality of that training from a critical, practical orientation and adaptation of the descriptive and constructive tools to the medium in question, that is to say, its disciplinary adequacy.

The theoretical and practical content of the course "Applied Geometry" will try to give a creative and practical approach to the traditional techniques of perspective drawing and representation systems. Thus, instead of focusing on the more technical drawing - typical of engineering - with square and bevel, angle protractor, 1/1 measures and others, in the course we will see very current techniques of freehand drawing as well as professional software such as Krita, Blender and Zbrush.



We have chosen these programs because with them the students can create models for both artistic and professional production with the free versions of them. Not only that, but we will see all the support that these digital techniques give us when creating objects and inorganic spaces.



The applicability of these techniques, framed in the field of traditional drawing, digital drawing and 3D modeling, will give an outlet to the geometry itself, but applying it to the presentation of dossiers with parts and scenarios through preview, rendering objects for product design, or the preparation of a professional portfolio.



We will also carry out a group work with a specific client in mind, through which students will adjust to real needs, and will use what they have learned in the first ten weeks to develop an artistic work applicable to a commission.



In addition, they will receive feedback from a professional in the field, as well as a lecture, which will allow them to have direct contact with a professional reality.

METHODOLOGY:



Being the "application" component determinant in this subject, the practices will be the ones that will condition to a greater extent the development of the course.



The theoretical contents will run parallel to the development of the practices, using a minimum previous knowledge and counting on the capabilities of a person whose profile is linked to the field of the visual, we can delve into the possibilities of the Representation Systems.

It is highly recommended that interested students have a personal computer and, if possible, a graphic tablet of the most basic range.



The timetable for this course, in which the subject is to be taught in weekly blocks of five hours, determines the type of instrumental and digital media.

We will understand from its base the use of the dihedral-orthogonal, axonometric and conic perspective systems, but through a simple and easy to understand approach, and we will see its applicability in the creation of scenes, objects and vehicles, both for product design, artistic dossiers, or film and video game production.



Afterwards, we will go into the possibilities and tools offered by digital drawing, with perspective aids, drawing guides and different tools that will help us to create and design parts, vehicles, buildings or even characters for film and video games.



Finally, we will learn the techniques of digital modeling, rendering and lighting to create showroom modules, scenography sets, and scenery and vehicles for professional production with Blender. All this will be complemented with an introduction to digital sculpting through the Zbrush tool.





Among the functions of the NP hours, will be to get materials or prepare them conveniently for use in class; make bibliographical consultations, the pursuit of work that does not require to be done in classroom hours, etc.

The "tutorials" (6h/week), allow to deal with issues that require personalized attention (Vgr.: Evolution of exercises, consultations on non-attendance work, guidance on various issues such as monitoring the work of students who with justified cause, according to regulations, do not attend the P hours, etc.). It should be noted that in no case are tutorials supposed to replace teaching hours.



SPECIAL; MEASURES FOR COVID 19



In view of possible contingencies with this issue, we have proposed that, depending on the enrollment of the subject, if the group of students exceeds 35, in order to maintain the mandatory distance between students, the group would be divided in two, with half of the group attending in person and the second half the following week. Classes will be held at the usual time, but will be recorded live via Webex. In this way, both those who are in the classroom and those who are at home will be able to follow the content of the class live, being able to consult live the questions they deem appropriate.



WHAT IF THERE IS CONFINEMENT AGAIN?



In this case, the classes will become completely online, maintaining the teaching schedule, and the obligation to attend them online, for which it will be required to enter the Egela session and have headphones, speakers or similar to follow the teaching. It is not mandatory to use a microphone in these sessions. In addition, some of the techniques will be recorded on the platform so that students can consult them during the course.

• Continuous Assessment System
• Final Assessment System
• Tools and qualification percentages:
  • Individual works (%): 60
  • Team projects (problem solving, project design)) (%): 40

EVALUATION:



The evaluation will be continuous for students who regularly attend classes and participate in the P (face-to-face) and NP (non-face-to-face) activities that are proposed or agreed.

Attendance must be higher than 80% of the face-to-face hours, in which case personal involvement in the work will be weighted with up to one point, but at the discretion of the faculty of the subject.

The continuous evaluation will be based on the development of the practical work proposals to be carried out and on the degree of acquisition of the expected learning outcomes (competences).

The theoretical contents taught will be evaluated through the practices developed, which will be presented by their authors, in the corresponding deliveries that will appear in Egela of the course itself.

The exercises carried out during the course will be weighted as 100% of the final grade.

Those who, in writing, have presented the resignation of the subject,

will be able to take the final evaluation. In order to do so, they must present the work developed during the course, complete and corrected. The evaluation, in this case, will be given by the assessment of the work submitted, which will be validated by a validation test in which the student will demonstrate its authenticity.

The evaluation of the extraordinary evaluation will be as follows. It will consist on the one hand of an exam, which will have a value of up to 50% of the grade, and on the other hand of the delivery in the corresponding Egela folder, which will complete 100%. In order to take the exam, the teacher will require the delivery of 100% of the work done during the course.

If the student does not take the exam, he/she will be considered as a "No Show" in the second exam.

OBLIGATORY MATERIAL

It is mandatory to have a computer at home to be able to do the digital part, and a basic tablet of the simplest range (Wacom Intuos or lower).

Basic bibliography

Bouleau, CH.Bibliografía básica



-Bärtschi, Willy A. "El estudio de las sombras en la perspectiva". Gustavo Gili. México 1982

-Bonet Minguet. "Perspectiva cónica". Ediciones del autor. Valencia 1985

-Cabezas, L. Ortega de Uhler, L.F. "Análisis gráfico y representación geométrica". Universitat de Barcelona. Barcelona 2001

-Flocon-Taton. "La perspectiva". Tecnos. Madrid 1966

-Giménez Morell, Roberto. "Espacio. Visión y representación". Universidad Politécnica de Valencia, Valencia 1988.

-Guasch, P. "Dibujo geométrico y perspectiva". UPV/EHU. Leioa 1985

-Izquierdo Asensi, F. "Geometría Descriptiva". Ed. Dossat .11ª ed. Madrid 1977

-Kubovy,Michael. "Psicología de la perspectiva y el arte del renacimiento". Ed. Trotta, M. 1996.

-Moral. R. "Perspectiva". Gustavo Gili. Barcelona 1981

-Navarro de Zuvillaga. J. "Mirando a través. La perspectiva en las artes". Ediciones del Serbal. Barcelona 2000

-Pedoe, Dan. "La geometría en el arte". Gustavo Gili. Barcelona 1979.

-Pirenne, M.H. "Optica perspectiva y visión en la pintura, arquitectura y fotografía". Victor Lerú. Buenos Aires. 1974

-Robertson, Scott and Bertling, Thomas, “How To Draw”, Drawing and Sketching Objetcs and Environments from Your Imagination”, Design Studio Press 2013

-Robertson, Scott and Bertling, Thomas, “How To Render”, The Fundamentals of Light, Shadow and Reflectivity”, Design Studio Press 2014

-Schmidt, R. "Geometría descriptiva con figuras estereoscópicas". Ed.: Reverté, B. 1986

-Thomae, R. "El encuadre en la perspectiva". Gustavo Gili. B. 1980

-Vero. R. "El modo de entender la perspectiva". Gustavo Gili. Barcelona 1991

-Vidal, Mª. D. y Giménez, R., "Perspectiva artística". Ed.: Universidad Politécnica de Valencia, 2007.

-Villanueva Bartrina, L. "Perspectiva lineal: su relación con la fotografía". UPC. Barcelona 1996.

-Wrigth, L. "Tratado de perspectiva". Stylos. Barcelona 1985

In-depth bibliography

Bibliografía

Bärtschi, Willy A. El estudio de las sombras en perspectiva cónica. Gustavo Gili. Barcelona 1980
Baxandall, Michael. Las sombras y el siglo de las luces. Visor. Madrid 1997
Bonci, Elia. Teoria delle hombre e del chiaroscuro. Ulrico Hoepli. Milán 1937
Bonet Minguet. Perspectiva cónica. Ediciones del autor. Valencia 1978
Bouleau, Ch. Tramas. Akal. Barcelona 1996
Cabezas, L. Ortega de Uhler, L.F. Análisis gráfico y representación geométrica. Universitat de Barcelona. Barcelona 2001
Della Francesca, Piero. De prospectiva pigendi. De Lettere. Firenze. 1984
Flocon, Albert. La perspective. Presse Universitaire de France. Paris 1984
Flocon-Taton. La perspectiva. Tecnos. Madrid 1966
Gibson, J.J. La percepción del mundo visual . Infinito. Buenos Aires 1974
Guasch, P. Dibujo geométrico y perspectiva. UPV/EHU. Leioa 1985
Hockney, D. El conocimiento secreto. Destino. Barcelona 2001
Kemp, M. La ciencia del arte. Akal. Madrid 2000
Metzger. P. La perspectiva a su alcance. Benedikt Taschen Verlag. 1991
Montague. J. Basic perspective drawing. John Wiley & Sons Inc. N.Y. 1998
Moral. R. Perspectiva. Gustavo Gili. Barcelona 1981
Navarro de Zuvillaga. J. Mirando a través. La perspectiva en las artes. Ediciones del Serbal. Barcelona 2000
Pedoe, D. La geometría en el Arte. Gustavo Gili. Barcelona 1979
Pirenne, M.H. Optica perspectiva y visión en la pintura, arquitectura y fotografía. Victor Lerú. Buenos Aires. 1974
Raya Moral, Baltasar. Perspectiva. Gustavo Gili. Barcelona 1980
Thomae, Reiner. Perspectiva y axonometria. Gustavo Gili. Barcelona 1976
Schaarwachter, G. Perspectiva para arquitectos. Gustavo Gili. Barcelona 1976
Stoichita, Victor. Breve historia de las sombras. Siruela 1997
Vero. R. El modo de entender la perspectiva. Gustavo Gili. Barcelona 1991
Villanueva Bartrina, L. Perspectiva lineal. Su relación con la fotografia. UPC. Barcelona 1996.
Wrigth, L. Tratado de perspectiva. Stylos. Barcelona 1985