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Geometry and Representation II

Code 17833
Year 1
Semester S2
ECTS Credits 4
Workload PL(30H)/TP(30H)
Scientific area Desenho e Representação em Arquitetura
Entry requirements Attendance and passing the Geometrics course of the 1st semester constitute a prerequisite for attending this course.
Learning outcomes This curricular unit expands the knowledge acquired in the first semester, deepening the different geometric approaches and their applications in architecture. The objectives include: Understanding and applying different types of geometry, projective and topological, exploring non-Euclidean geometries and fractal geometry. Introduction to Conical Perspective – one, two, and three vanishing points, and notions of the complete point, line, and plane system. Mastery of conical perspective representation techniques, essential for visual communication. Skills to be acquired: develop mastery of conical perspective techniques for architectural representation; ability to transition from two-dimensional representations to three-dimensional understanding of spaces; understanding of the relationship between technical drawing and artistic expression in the architectural context; understanding fractal concepts and their application in architecture, addressing self-similarity, complexity, and flexib
Syllabus The curriculum unit program was designed to ensure a continuous and logical progression of students' knowledge and skills, exploring a range of geometric concepts and their applications in architecture. The objective is to provide a practical approach to representation techniques for application in freehand drawing. 1 Introduction to Conical Perspective: definition and applications in architecture. One-Point Perspective (Frontal Perspective) Application in architectural elements. Two-Point Perspective (Angular Perspective): Application in the representation of façades and interior spaces. Three-Point Perspective: Drawing tall buildings and vertical elements. 2 Light and Form Interaction: Shading techniques to enhance depth and realism. 3 Non-Euclidean and Fractal Geometries: The introduction to topology and the study of non-Euclidean and fractal geometries allows challenging the traditional conception of space and exploring new geometric possibilities.
Main Bibliography IZQUIERDO ASENSI, Fernando (1994). Ejercicios de Geometria Descriptiva I (Sistema Diedrico). Ed. El Autor, Madrid.CALAME, Jean-Francois e JACQUES, Daniel. (2005). Géométrie Spatiale – Un Vade -Mecum. Presses Polytechniques Universitaires Romandes.BALTRUSAITIS, J. (1996). Anamorphoses ou thaumaturgus opticus : les perspectives dépravées. Éditions de l’Amateur. MANDELBROT, Benoît (1982). The Fractal Geometry of Nature. Ed. W. H. Freeman.GELABERT, Lino Cabezas e UHLER Luis F. Ortega de. (2002). Análisis gráfico y representación geométrica. Ediciones de la Universitat de Barcelona. Gill, R. W. (2008). *Perspectiva Cristiva*. Editorial presença. Gill, R. W. (2008). *Desenho de Perspectiva*. Editorial presença.
Language Portuguese. Tutorial support is available in English.
Last updated on: 2026-04-13

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