Architectural Sciences

In the course the methods of computer representation are analyzed, namely the mathematical representation of three-dimensional shapes (3D modeling) and the numeric (or polygonal) representation of space and the effects of light on shapes (chiaroscuro or rendering). The program of the course can be divided into three parts, organized as follows: The first part of the course (about 25% of the total amount) deals with the methods of digital representation and the definition of their principles. Laboratory activities are carried out for a correct approach to mathematical representation with particular reference to the quality control of curves and surfaces (concepts of tangent, curvature, continuity, etc.). The second part (about 25% of the total amount) deals with the study of polyhedra and their geometric and topological features. The methods of mathematical representation are applied for the accurate construction of the regular, semiregular and Catalan polyhedra with an in-depth study on the topic of geodesic domes and roofing design processes. In the third part (equal to about 50% of the total amount) the study of surfaces is tackled starting from the methods with which it is possible to classify them. Experiences and activities on architecture applications are conducted with particular reference to vaulted systems. Particular attention is paid to the analysis of the geometric properties of the quadric surfaces, of the ruled surfaces and of the developable surfaces for their importance in classical and contemporary architecture. For teaching support materials, you can refer to the course website based on the e-learning platform at the following link: https://elearning.uniroma1.it/course/index.php?categoryid=38

The course does not provide for propaedeutics and passing other exams but it is considered very useful to have consolidated some topics and concepts addressed during the course of Drawing in the first year. In particular, the projection and section operations are indispensable in the process of generating any type of image (graphic, digital and photographic). It is also important to know the graphical methods of representation (perspective, plan and elevation method, axonometric) for the creation of views.

The reference text for the course is: Riccardo Migliari (a cura di), Geometria descrittiva, vol. II, CittàStudi - De Agostini, Novara 2009 The course uses the 'Sapienza' e-learning system, based on Moodle. The teaching reports will be managed through this platform, which allows students to take the documents made available by the teacher (texts, images, 3D drawings and models, etc.), to communicate with the teacher himself or to interact in discussion groups, upload documents to be verified, etc.

The course does not provide mandatory frequency but it is strongly recommended to make a complete and rapid preparation possible to take the final exam. The lessons are traditional type and are generally divided into two parts: in the first, for an hour or two, the professor explains the theoretical contents of the topic. In this phase the students' computers must remain strictly closed. After a pause of quarter of an hour, in the second part of the lesson the students perform an exercise on their computer, assisted by the teacher of the Course. In this way the students will be able to prepare the final drawings already during the course attendance, thus facilitating their commitment.

Attendance is not mandatory for the course, but it is highly recommended to ensure thorough and rapid preparation for the final exam. The teaching materials uploaded lesson by lesson on the course website, along with summaries of the topics covered, will also be useful for non-attending students to prepare the final assignments required for the exam.

The exam consists of an oral test, in which the student is asked to illustrate the construction of the surfaces that have been described during the lessons and the theoretical principles of mathematical and numerical representation to assess the levels of knowledge and competence achieved. The exam also consists in evaluating the quality of graphic works for the assessment of the critical and communicative skills acquired. These are: · The taccuino, which is a notebook, of white paper sheets on which the student records the notes taken in lessons; · The drawings made during the classroom exercises and completed, where necessary, in the individual study; These drawings will be made with computer and printed on A4 sheet sizes; · The files relating to the models produced and their elaborations in the 3dm, c4d, stp (for non-Rhinoceros), psd, tif formats, stored on CDs or DVDs. Lastly, the teacher will propose ex-tempore of digital elaborations that prove the acquired knowledge.

Riccardo Migliari (a cura di), Geometria descrittiva, vol. I, CittàStudi - De Agostini, Novara 2009. Riccardo Migliari, Geometria dei modelli, Kappa, Roma 2003. Riccardo Migliari (a cura di), Disegno come modello, Kappa, Roma, 2004 Graziano Mario Valenti, De.form.are., Roma Design Più, Roma 2010 Andrea Casale Graziano Mario Valenti, Architettura delle superfici piegate. Le geometrie che muovono gli origami, Kappa, 2012 Helmut Pottmann, Andreas Asperl, Michael Hofer, Axel Kilian, Architectural geometry, Eston, Bentley Institute Press, 2007 Sitografia: www.descriptivegeometry.eu www.mathcurve.com https://elearning2.uniroma1.it/course/view.php?id=1469 https://elearning2.uniroma1.it/course/view.php?id=324

The lessons are traditional type and are generally divided into two parts: in the first, for an hour or two, the professor explains the theoretical contents of the topic. In this phase the students' computers must remain strictly closed. After a pause of quarter of an hour, in the second part of the lesson the students perform an exercise on their computer, assisted by the teacher of the Course. In this way the students will be able to prepare the final drawings already during the course attendance, thus facilitating their commitment.

The course introduces the scientific foundations of representation, with the aim of developing, in the architect student, the ability to understand the forms of the space and to represent them, through the construction of models. Descriptive geometry is the science that teaches how to build these models, whether graphics, digital or physical, through the metrical and morphological control of three-dimensional forms and through the study of their properties in analogical, i.e. visual, form. The course is articulated into two main topics respectively aimed to the knowledge and to the communication of the form, which are organized in theoretical lessons, guided practical exercises and a final synthesis work. The first topic concerns the capability to understand the shape, acquired through the knowledge of the lines and surfaces theory and their geometric properties. This section deals with polyhedrons and their geometrical and topological characteristics, with in-depth analysis of their applications in architecture, such as the roofs and the geodetic domes. Ample space is devoted to the study of lines and surfaces theory, analyzing their geometric, analytical and differential properties (genesis, degree, curvature, continuity, etc..). Some lines and surfaces classes are explored, selected from the ones that have found wide use in architecture. Regarding the lines: conics, flat and skew helices and spirals, quartic courbes etc.; regarding the surfaces: ruled and developable surfaces, quadric surfaces, helicoids, taurus etc. The theoretical lessons about the lines and surfaces properties are supported by the analysis of some architectures where they find direct application. The second topic concerns the capability to describe the shape, acquired through the knowledge of the methods of graphic and digital representation, with regard to the different communication scopes of the form itself. The digital methods of representation are deepened: the mathematical representation (Nurbs) for the metric control and the numerical representation (polygonal) for the perceptual control of the shape. Hybrid forms of representation, derived by the integration between graphical and digital drawing, are experimented. These contents find direct experimentation in a final synthesis work, devoted to the morphological analysis of an architecture agreed with the teacher. The analysis of realized or designed architectures aims to develop student's ability to deeply understand the architectural shape and communicate it through digital and graphical representation methods, able to describe its morphological characters.

The course does not requires prerequisites, but the student must have learned the theoretical foundations of representation. He must have acquired full mastery of the projection and section operations, that are necessary to generate any type of image, whether graphic, digital or photographic. Finally, he must have acquired full mastery of the graphical methods of representation, in particular: orthogonal projections, perspective and axonometry.

Migliari Riccardo. 2009. Geometria descrittiva. Novara: CittàStudi De Agostini Glaser Georg, Polthier Konrad. 2013. Immagini della matematica. Milano: Springer - Verlag Italia & Raffaello Cortina Editore Pottmann Helmut, Asperl Andreas, Hofer Michael, Kilian Axel, Bentley Daryl. 2007. Architectural geometry. Bentley: Bentley Institute Press Laura de Carlo, Leonardo Paris (a cura di). 2019. Le linee curve per l'architettura e il design. Roma: FrancoAngeli. The summaries of the lessons, the exercises and the bibliographical references with explicit reference to the pages to be studied are weekly reported on the Moodle platform, in order to facilitate learning during the course. Moodle also provides students with supplementary teaching materials such as articles, images, drawings, 3D models, etc.

The lessons are generally articulated into two parts, the first one devoted to the theoretical contents communication and the second one to the digital exercises. These exercises, guided by the teacher and concern theoretical principles treated during the first part of the lesson, are elaborated through digital or hybrid representation techniques. They are the graphic works required for the final exam, that the student can elaborate, in whole or in part, directly in the classroom, aided by the teacher. The course uses 'Sapienza' e-learning system (http://elearning.uniroma1.it). Teaching reports are also managed through the Moodle platform, which allows students to download documents uploaded by teacher (texts, images, drawings, etc.), to communicate with him or interact in discussion groups, to send documents to be verified, etc. Here, students find a weekly summary of contents of each lessons and the related bibliography with explicit reference to the pages to be studied and any additional teaching materials, such as articles, 3D models, images, drawings.

The course does not require attendance, but this is recommended, in order to facilitate a complete and rapid preparation for the final exam. Non-attending students may access lecture summaries, related exercises, and corresponding bibliographical references, as well as supplementary teaching materials on the Moodle platform.

The exam consists in an oral test in which students must demonstrate their knowledge about the theoretical contents treated during the course: the capability to control the shapes in space through the knowledge of polyhedrons, lines and surfaces theory; the knowledge of digital representation methods, useful to describe the shape itself. Graphic elaborations produced by the students during the course will be evaluated, to prove, in a graphical way, the acquired knowledge: - The graphic works related to the exercises developed during the course, in order to prove the mastery of the theoretical contents acquired. - The visual presentation related to the morphological analysis of architecture, in order to prove the capability in reading, understanding and describing the architectural shape. - The notebook, which describes the cognitive path carried out by the students during the course, containing lesson notes and reasoning developed around the proposed exercises. The teacher may require an ex tempore realization of digital elaborations in order to verify that theoretical knowledge and computer skills have been acquired.

Reference texts: Migliari Riccardo. 2009. Geometria descrittiva. Novara: CittàStudi De Agostini Glaser Georg, Polthier Konrad. 2013. Immagini della matematica. Milano: Springer - Verlag Italia & Raffaello Cortina Editore Pottmann Helmut, Asperl Andreas, Hofer Michael, Kilian Axel, Bentley Daryl. 2007. Architectural geometry. Bentley: Bentley Institute Press Laura de Carlo, Leonardo Paris (a cura di). 2019. Le linee curve per l'architettura e il design. Roma: FrancoAngeli. Recommended texts: Casale Andrea, Valenti Graziano Mario. 2012. Architettura delle superfici piegate. Le geometrie che muovono gli origami. Roma: Kappa. Migliari Riccardo. 2003. Geometria dei modelli. Roma: Kappa Migliari Riccardo. 2004. Disegno come modello. Roma: Kappa Ugo Vittorio. 2008. La costruzione geometrica della forma architettonica. Milano: Maggioli editore Valenti Graziano Mario. 2008. De.form.are. Roma: Designpress Valenti Graziano Mario. 2021. Di segno e modello. Esplorazioni sulla forma libera fra disegno analogico e digitale. Milano: Franco Angeli Cresci Luciano. 2009. Le curve matematiche tra curiosità e divertimento. Milano: Hoepli

The lessons are generally articulated into two parts, the first one devoted to the theoretical contents communication and the second one to the digital exercises. These exercises, guided by the teacher and concern theoretical principles treated during the first part of the lesson, are elaborated through digital representation techniques. They are the graphic works required for the final exam, that the student can elaborate, in whole or in part, directly in the classroom, aided by the teacher. The course uses 'Sapienza' e-learning system (http://elearning.uniroma1.it). Teaching reports are also managed through the Moodle platform, which allows students to download documents uploaded by teacher (texts, images, drawings, etc.), to communicate with him or interact in discussion groups, to send documents to be verified, etc. Here, students find a weekly summary of contents of each lessons and the related bibliography with explicit reference to the pages to be studied and any additional teaching materials, such as articles, 3D models, images, drawings.