Abstract
Teaching descriptive geometry, in the context of this study, is characterized by the continuous investment in recognizing digital representation technologies which can enhance the didactic activities in architectural training. This study describes this trajectory which includes the use of virtual reality, augmented reality and parametric modelling, as well as freehand drawing and the production of physical models both by automating the unfolding process and by digital fabrication processes of 3D printing and laser cutting. In addition to questioning the relevance and sustainability of the infrastructure needed to ensure the continuation of this trajectory, the potentialities identified in each of the learning activities that have been structure, are shown. Although these potentialities are specific to this context, it is considered that this type of record contributes to understand the issues being faced in teaching practices.
TopIntroduction
The history of teaching descriptive geometry certainly differs very little in different contexts of architectural training. Aiming specifically at developing spatial reasoning and skills to control and represent geometric form, this history was initially established with, perhaps, differences in the study strategy, whether or not it was applied directly to the architectural form. The bibliographic references of this geometry present the fundamental concepts of representation of point, line and plane. The teachers, geometers with different professional backgrounds, declared insistently the comprehension of the projections of these geometric entities as a solution to any kind of problem regarding the representation of form in two or three dimensional space. This discipline is taught in the beginning of the architectural training and throughout its history registers a strong investment in the development of didactic strategies to accelerate the abstraction abilities required by the intrinsic characteristics of the knowledge in question. The students come from different backgrounds and were often not stimulated to develop such abilities. In Brazil, this problem is registered specially in the GRAPHICA forums promoted by the Brazilian Association of Graphic Expression (ABEG), initially founded as Brazilian Association of Teachers of Descriptive Geometry and Technical Drawing. The reoccurrence of this problem, intensified even after the possibilities offered by graphics computing, is attributed to the changes in the structure of basic education on a national level. Kopke (1996) observed that since the Law of National Education Basis and Guidelines (LDB) from 1971, law n° 5.692, drawing started being addressed in the discipline of Artistic Education and lost its importance. Freshmen students, because of this lack of previous training in abstract geometric thinking, find it hard to understand.
In the context of this study, teaching descriptive geometry in the course of Architecture and Urban Design in the Federal University of Pelotas (UFPel), Brazil, the scenery reflects exactly the situation described above. Until 2011 the disciplines that taught descriptive geometry were offered by the Department of Technical Drawing and Computational Graphics. Professors with different backgrounds such as architecture, art and engineering were responsible for all the representation disciplines offered to all the courses that needed them in the university. Due to the tradition of the department itself, the content taught in these disciplines did not give priority to applying it to the professional context. However, in some moments when the background of the professor was the same as the course for which the discipline was being taught, some initiatives of applying directly to the professional context were registered.
The disciplines offered to Architecture students were called Descriptive Geometry III and IV, and they dealt with graphic-projective procedures aimed at the representation of polyhedral and curved surfaces respectively. Studies of two dimensional geometry were not included being offered only for the undergraduates in Arts. This is made worst by the guidelines for Brazilian basic education because the architecture students were studying spacial geometry without having the basis of 2D geometry. In Descriptive Geometry III these skills were developed from the methods of orthogonal projection with a single plane and from Monge projection and in Descriptive Geometry IV from Monge projection. In both, until 2010 the didactic activities were mainly based on drawing with traditional drawing instruments. Thus, exploring form was limited, considering the time it took to build the representation of a surface on a single point of view, especially when it involved more complex surfaces.
Since 2010 these disciplines started including activities developed through digital graphic representation. In this way, taking advantage of automated methods of projection, accelerating form exploring and transforming in a dynamic and precise way. Furthermore, the disciplines advanced in the use of interactive and digital systems of visualization, allowing the investment in variating parameters. With this, developing the comprehension of the logic of more complex surfaces in a playful way.
Key Terms in this Chapter
Digital Fabrication: Digital fabrication is a type of manufacturing process where the machine used is controlled by a computer. Are classed according to the processes acting upon the physical and/or chemical properties of the materials used. These are: additive procedures, subtractive procedures and formative procedures (according Brankolevic and Malkawi, 2003 AU39: The in-text citation "Brankolevic and Malkawi, 2003" is not in the reference list. Please correct the citation, add the reference to the list, or delete the citation. ), and joining procedures (Schodek, 2005 AU40: The in-text citation "Schodek, 2005" is not in the reference list. Please correct the citation, add the reference to the list, or delete the citation. ).
3D Printing: Also known as additive manufacturing is a process used to make a three-dimensional object without the use of dies, molds or machining. In 3D printing additive processes are used, in which successive layers of material are laid down under computer control. These objects can often be of virtually any shape or geometry, and are produced from a 3D model or another electronic data source. 3d printing thus enables to production of parts which would not be possible with traditional manufacturing techniques.
Descriptive Geometry: The descriptive geometry is a branch of geometry that aims to accurately represent objects of three dimensions on a two dimensional plane. For that draws on the projection of the objects, which consists of passing the projecting straight object, which intersect the projection plane, where it creates a projection of the object. This projection can be made according to several projection methods, which differ according to the number of projection planes used and the different characteristics of projecting straight.
Developable Surfaces: Forms are called ‘developable’ or ‘single curved’ when they can be created through ordinary bending of a planar surface without stretching, cutting or wrinkling the material. These surfaces are characterized by only bending in one direction at a time, like the cylinder or the cone. Developable surfaces are useful because they allow round forms to be made out of flat materials like plywood, sheet metal or cloth (Kolher, 2010 AU38: The in-text citation "Kolher, 2010" is not in the reference list. Please correct the citation, add the reference to the list, or delete the citation. ). For non-developable surfaces is studied your approximate planning, and one of the processes used is approximated by spherical zones. The zones that make up the spherical surface are not developable hence these zones are developed by means of a sufficiently rough flat surface ( Kremer, 2008 ).
Laser Cutting: Is a non-contact process which utilizes a laser to cut materials, resulting in high quality, dimensionally accurate cuts. The process works by directing the laser beam through a nozzle to the work piece. A combination of heat and pressure creates the cutting action. The material melts, burns, vaporizes, or is blown away by a jet of gas, leaving an edge with a high-quality surface finish.
Virtual Reality: It is an advanced interface technology between a user and a computer system. The goal of this technology is to recreate the most of the sense of reality for an individual, leading him to adopt this interaction as one of its temporal realities. For this, this interaction takes place in real time, using computational techniques and equipment to assist in expanding the user presence feeling.
Augmented Reality: Augmented Reality is an advanced display technology, defined by Tori, Kirner and Ciscouto (2006, p. 10) AU35: The in-text citation "Tori, Kirner and Ciscouto (2006, p. 10)" is not in the reference list. Please correct the citation, add the reference to the list, or delete the citation. as “[...] enrich the real environment with virtual objects using a technological device, working in real time.”
Parametric Design: For parametric design is meant the generation process forms whose constituent elements are not geometrically determined in a static manner, but using variables whose values are specified in each case. In parametric design systems elements can be changed later without that overall consistency is changed. This requires the specification of the restrictive properties that affect selectively some of the elements of the form or the relationship that some have with each other (Monedero, 2000 AU41: The in-text citation "Monedero, 2000" is not in the reference list. Please correct the citation, add the reference to the list, or delete the citation. ).
Complex Geometries: In mathematics, complex geometry is the study of complex manifolds and functions of many complex variables. Application of transcendental methods to algebraic geometry falls in this category, together with more geometric chapters of complex analysis (Huybrechts, 2005 AU36: The in-text citation "Huybrechts, 2005" is not in the reference list. Please correct the citation, add the reference to the list, or delete the citation. ). Geometry lies at the core of the architectural design process. It is omnipresent, from the initial form-finding stages to the actual construction. Modern constructive geometry provides a variety of tools for the efficient design, analysis, and manufacture of complex shapes. This results in new challenges for architecture. However, the architectural application also poses new problems to geometry. Architectural geometry is therefore an entire research area, currently emerging at the border between applied geometry and architecture. Complex geometries in architecture include central concepts on freeform curves and surfaces, differential geometry, kinematic geometry, mesh processing, digital reconstruction, and optimization of shapes (Pottman et al, 2007 AU37: The in-text citation "Pottman et al, 2007" is not in the reference list. Please correct the citation, add the reference to the list, or delete the citation. ).