Definition and representation of complex architectural shapes. Experiences in advanced courses at the Faculty of Architecture in Milano (original) (raw)

The shape: from behind to beyond Architecture students and spoiled complexity

Contemporary architecture deals so much with representation and fabrication of complexity, which is not always easy to cope with; there is a huge number of buildings, as attractive as obscure in construction techniques. The form that’s behind these buildings is worth of understanding, worth to be drawn, but how? The case study is a Master’s Degree Architecture course of Politecnico di Milano named Representation, where 12 students have the task to represent – imaging the fabrication method – a building of their choice, with a certain degree of surface complexity. The representation requires the comprehension of shape-generator elements. These can be recognised as geometrical forms, axes of symmetry, algorithmic patterns, etc. Aim of the students is finding and representing these important signs that mark architecture. It is evident that as complex the architecture is as more complex becomes retrieval. The path the students have to walk starts from real continuous architectural shape, passing through discrete elements, then returning to continuous architectonic ideas. Due to the limited students analysis ability, the building chosen must be provided with references which help in form finding. The students task is divided in two parts: 1) Recognition of shape-generator elements Starting from component relationship that lies beneath architecture, students must produce sketches of the chosen building, taking gradual knowledge of shape-generator elements supporting the architectural image. Geometrical bi-dimensional drawings are helpful to clarify the knowledge acquired, to be completed with more complex schemes. Identification of architectural segments - that rule structure - is made through analytic drawing, which is the redrawing of essential lines of building chosen. Once this analysis has been taken for the whole building, one single character is chosen and grown deeper. 2) Redrawing of elements After the knowledge of shape-generator elements has been accomplished, students are required to produce interpretation drawings in axonometry. This method of representation shows simultaneously (at least) one plan and one section, especially when drawn from below. Therefore students must have precise comprehension of how elements works together to complete this task. The results - at the end of this process - were deeply influenced by the shape-complexity of chosen building. Some of the students chose buildings with a high grade of surface complexity, so the final results were accurate in representation, poor as form analysis. This is due to a general lack in digital tool capability, generally suffered by most of Italian engineering/architecture students, which is reflected in a general failure to control shape in a skilful way. Most of the students, indeed, skilfully chose controllable buildings, so their analysis was rich in variety and details. The richness consists in a series of variations on the starting shape-generator elements. The detail component was the deepening of analysis which embraced the widest possible portion of the building. The teaching method applied for this course was based on getting deeper knowledge of built architecture, because it enhanced student in space analysis and design workout. Therefore all works gave a method useful to collect a personal interpretation of architectural masterpieces.

Basis of Architectural Survey Between Geometry and Representation. A First Educative Approach

Education and New Developments 2020, 2020

This paper illustrates the educative path-aimed at learning the basis of architectural survey-we propose to the students in the first year, as part of the Drawing and Survey Laboratory (bachelor's degree in Architecture). The primary focus of the Laboratory is to guide them in studying and using the graphic languages and related fundamental tools. In this case, architectural survey comes as a cognitive tool of fundamental importance for the analysis and understanding of architectural artefacts. The main objective of the exercises carried out during the Laboratory is to prepare student by a gradual theoretical and technical path for the direct and indirect operations of survey. During the first semester the course includes a first operation of surveying an architectural drawing (during the exercise of critical redraw of a published project), giving birth to an ideal scalar approach to the themes of survey, both manual (direct survey) and digital (PR, SfM), which combines and develops horizontal and vertical skills. Here, we discuss the main passages of the path of survey through an emblematic case study from Torino.

Educational Means for the Study of the Geometry of Architectural Forms

Procedia - Social and Behavioral Sciences, 2014

This paper presents an exercise which aims to stimulate architect students' creativity, raise awareness on architectures' formal possibilities based on geometric shapes and to illustrate how the theoretical knowledge can be practically applied on a certain architectural program. As basic information for this exercise, the types and the features of the main structural geometric forms are enumerated while student work exemplifies their use in a particular case.

Analyzing today geometry on architectural heritage between mathematics and representation to define architect's background

2023

We present and analyze an example of activity aiming at introducing graphic language and standards to students of the first year bachelor's in architecture. Our example concerns the 2D representation of an architectural object, an essential competency in the architect's profession, and specifically deals with roofing systems made up of vaults generated by cylinders and their intersections. It is a first attempt to create activities that involve all students regardless of their different levels of geometric understanding and of familiarity with graphic language; in particular, this example exploits the introduction of physical or virtual models to support the mathematical thinking of students in completing the task and takes place during regular lesson times, without modifying or adding mathematical subject contents. Research literature on mathematical modeling, in particular on the so-called prescriptive one, provides us tools to frame and implement our study case; it also allows presenting mathematical modeling as a goal in an extra-mathematical educational context.

Studies of Geometry Integrated in Architectural Projects

Journal For Geometry and Graphics, 2001

Geometry plays the role of a basic science in engineering, especially in architecture. In the past years the importance of geometry was pushed back because of a wrong estimation of new technologies like CAD. Geometry researchers and teachers failed to convince the practical engineers of the importance of geometrical reasoning, even in the use of computerised methods. This paper will show the concept of an integrated teaching of geometry in architectural projects which is able to point out the importance of geometry in practising architecture as well as in the use of new technologies. Descriptive Geometry turns out not to be an antiquated science but a current one. In our integrated geometry concept we start with the architectural project that leads us to geometrical problems to be solved. The experiences with project-oriented studies for students of architecture in their major courses at our university in the past years are presented in this paper. In the examples like developing geometrical forms, projection methods for representations of architecture, photoreconstruction and photomontage, we reflect the way from the geometrical task, arising from the design project, to the geometrical solution.

Principles of a Geometry Program for Architecture--Experiences, Examples, and Evaluations

Journal For Geometry and Graphics, 2003

Geometry is a basic science for architecture. During the past centuries there were various evaluations of the role of geometry for architecture. Especially in the last decades the importance of descriptive geometry was pushed back more or less in most countries. Some countries try to keep the traditional descriptive geometry discipline, others replace it by training CAD-systems. Both ways have some understandable reasons, but both let missing important points of an actual geometry education. On the one hand it is not enough to keep only the traditional discipline, on the other hand geometrical knowledge is still a necessary condition for architecture, and this geometrical basis is not reached only by training CADsystems. As responsibles for the education of the students of architecture we have to react to the challenges of our times and we have to be aware of the new, but also the remaining requests of teaching geometry for architecture. In this paper the principles of such a geometry program will be presented and explained by examples from the past teaching experiences at University of Kaiserslautern in Germany. The concept is exposed in a textbook and exercise material for the students.

Learning Through Design Problems. Geometry and architectural reasoning

Applying Education in a Complex World: Teaching and Learning/ AMPS PROCEEDINGS SERIES 33, 2023

The problem of teaching and apprenticeship of abstract contents, namely of Geometry in the context of Architecture training, doesn't lie in the provision of formal or mechanical prescriptions, but in the opportunity to equip students with methodologies of abstract reasoning and research, that will allow them to autonomously respond to the broad field of architectural action. As a fundamental science of architectural training and practice, geometry implies, simultaneously, to approach projective systems (spatial mechanics and support of architectural graphic materialization), to characterize geometrical lexicon (properties and generative procedures), to inquire ways of reasoning space (configuration and the forethought of its bodily experience), foreseeing their repercussions upon architectural design. A holistic overview of the discipline, which requires the convergence of two fundamental domains: Relation Geometries - that due to their synthetic nature, are aimed at understanding and conception of form and space; along with Representative Geometries - whose analytical purpose provide accurate resources for the representation and questioning of the material and immaterial world. Departing from such principles, the communication aims to share the ongoing re-equation of the followed teaching strategies, namely at the application of a project-based learning methodology, in the context of the School of Architecture, Art and Design of the University of Minho.

STRUCTURAL AND GEOMETRIC CONCEPTS FOR ARCHITECTURAL DESIGN PROCESSES

The actual trends in architecture show more and more complex, irregular and seemingly “non-geometric” forms. It seems that the digital tools seduce the users to create anything possible. The more spectacular a building appears, often without perceptible structures, the better and more innovative it is evaluated. Therefore we are asking for fundamentals for design processes, in order to escape from an arbitrary design and finding a rational basis for design processes. When we look back in the history of architecture, we can find the background of geometric structures as important fundaments for designing, for example in symmetry concepts or using transformations. There is a tradition of using structural thinking for design disciplines referring to a mathematical-geometric basis. Structural thinking can be seen as a method and tool, especially with the help of digital tools. It is also the background for an aesthetic foundation of design processes. This way gives the chance to create dynamic architectural design processes, working with the formulated relations and interactions between geometry, material, construction, and other components in multidisciplinary interrelations with an integrative role for geometry. This theoretical background for architectural design processes with an important role for geometry will be illustrated by examples and some experiments by our students.

Structures and Geometry in Design Processes

Structural thinking in architecture is based on structuring information with the help of mathematical-geometric methods. Some of those methods are presented in this paper which had been one of the background for the DAAD Summer School "Structure – sculpture" in Buenos Aires, where students worked on the design task analyzing and redesigning the Ulm Pavilion by Max Bill. An overview of several mathematical-geometric approaches will be given accompanied by examples of teaching practice at Ulm School of Design in Germany, an innovative international school experiment between 1953 and 1968, where those methods had an important impact.

MAP ARIA UMR n°694/CNRS/CULTURE, Ecole Nationale Supérieure d’Architecture

2010

This paper reports on a work carried out during a one-week workshop with students of the architecture school of Nancy in France. Based on the advancements of CAD/CAM technologies, this exercise explores the link between two stages of the process of creation of an architectural object; geometric modelling and respective manufacturing preparations. The main idea is to deal with the continuum of the form creation, from the first idea (designer’s mental image), through the geometric description, to the final physical model. The development of architectural vocabulary is largely related to recent advances in the world of digital design. Advanced CAD tools and geometric modellers allow the creation of forms that overtake Euclidian models. But digital also affects the universe of manufacturing; CNC technologies provide the possibility of creating physical version of