Lecture

Modeling 3D Spaces: Inverted Dihedra

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In course

AR-211: Stereotomy

La Stéréotomie est l'art de concevoir et fabriquer des volumes complexes en pierre et des assemblages en bois. Ce cours propose une réinterprétation de la Stéréotomie avec différents outils, une réflexion sur la géométrie, les processus de fabrication, les ...

Description

This lecture delves into the complexities of 3D space, highlighting the challenges posed by angles and dihedra. The instructor demonstrates a practical approach to creating a geometric pre-component, focusing on key geometric information. Through a step-by-step process, the lecture explores the transformation of a convex dihedron into a concave one, emphasizing the importance of precise rotations and limitations. By adjusting the orientation of planes and components, the instructor showcases the reversal of dihedral configurations, ensuring proper alignment and containment within the 3D space.

Instructors (5)

Ignacio Ferrer Perez-Blanco

Teaching & PhD Courses Stereotomy AR-211 Stereotomy is the art of designing and crafting complex stone volumes and wooden assemblies. This course offers a reinterpretation of Stereotomy with various tools, a reflection on geometry, manufacturing processes, modes of representation, visualization, and communication.

Stefana Parascho

Teaching & PhD PhD Students Jingwen Wang, Gabriel Vallat, Maxence Grangeot, Eleni Maria Skevaki, Wenqian Yang, Megi Sinani Courses Capitalizing on Uncertainty AR-809 SUMMER SCHOOL - Capitalizing on Uncertainty is a 6-day Summer school exploring uncertainty as a productive resource in design and fabrication through lectures, hands-on experiments, and the collaborative design and construction of a full-scale structure in a human-robot fabrication setting. Digital design and making: A criti

Marie-Pierre Zufferey

Diplôme d'Architecture à l'EPFL en 1988 (prix SIA, section Vaud, du meilleur travail pratique de diplôme). Collaboration avec plusieurs bureaux d'architecture et, en parallèle, rédaction d'une thèse de doctorat suivie de l'obtention en 1992 du titre de Docteur ès Sciences. Bureau indépendant de 1996 à 2008; enseignement dans plusieurs écoles (dessin technique, peinture, couleurs). De 1999 à 2004, première assistante chez les professeurs Arduino Cantàfora (CRE) et Georges Abou Jaoudé (LIV, cours théorique, visualisation et représentation informatique). De 2005 à 2011, collaboratrice scientifique et chargée de cours auprès du professeur A. Cantàfora (CRE, chaire de représentation et expression) : enseignement pratique du dessin, peinture, et taille de la pierre, et théorique, analyse d'images, techniques de représentation, modes de communication, auprès des étudiants d'architecture de différents niveaux; rédaction de documentation pédagogique (cahiers d'appui des cours). Charge de cours pour une Unité d'Enseignement ENAC intitulée "Lectures du paysage par le biais de l'image et de l'art" avec Robert Ireland de 2006 à 2008. Responsable d'une nouvelle Unité d'Enseignement ENAC sur "les murs de soutènement urbains", printemps 2009 et 2010, avec O. Burdet, A. Parriaux, J-L. Moret. Participation ponctuelle en 2011, 2013 et 2014, pour l'UE-ENAC "Learning from vernacular", du professeur Pierre Frey sur la pierre et les traces de la main dans l'architecture vernaculaire. Recherche personnelle en cours sur les socles à la Renaissance italienne et française, en lien avec les professeurs Volker Hoffmann (Würzburg) et Roberto Gargiani (EPFL). Domaines d'intérêt spécifique: l'architecture à la Renaissance; la taille de la pierre et la stéréotomie; le dessin d'observation scientifique, la peinture et la gravure; la philosophie.

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Related concepts (18)

Geometry

Geometry (; ) is a branch of mathematics concerned with properties of space such as the distance, shape, size, and relative position of figures. Geometry is, along with arithmetic, one of the oldest branches of mathematics. A mathematician who works in the field of geometry is called a geometer. Until the 19th century, geometry was almost exclusively devoted to Euclidean geometry, which includes the notions of point, line, plane, distance, angle, surface, and curve, as fundamental concepts.

Geometric transformation

In mathematics, a geometric transformation is any bijection of a set to itself (or to another such set) with some salient geometrical underpinning. More specifically, it is a function whose domain and range are sets of points — most often both or both — such that the function is bijective so that its inverse exists. The study of geometry may be approached by the study of these transformations. Geometric transformations can be classified by the dimension of their operand sets (thus distinguishing between, say, planar transformations and spatial transformations).

Differential geometry

Differential geometry is a mathematical discipline that studies the geometry of smooth shapes and smooth spaces, otherwise known as smooth manifolds. It uses the techniques of differential calculus, integral calculus, linear algebra and multilinear algebra. The field has its origins in the study of spherical geometry as far back as antiquity. It also relates to astronomy, the geodesy of the Earth, and later the study of hyperbolic geometry by Lobachevsky.

Non-Euclidean geometry

In mathematics, non-Euclidean geometry consists of two geometries based on axioms closely related to those that specify Euclidean geometry. As Euclidean geometry lies at the intersection of metric geometry and affine geometry, non-Euclidean geometry arises by either replacing the parallel postulate with an alternative, or relaxing the metric requirement. In the former case, one obtains hyperbolic geometry and elliptic geometry, the traditional non-Euclidean geometries.

Elliptic geometry

Elliptic geometry is an example of a geometry in which Euclid's parallel postulate does not hold. Instead, as in spherical geometry, there are no parallel lines since any two lines must intersect. However, unlike in spherical geometry, two lines are usually assumed to intersect at a single point (rather than two). Because of this, the elliptic geometry described in this article is sometimes referred to as single elliptic geometry whereas spherical geometry is sometimes referred to as double elliptic geometry.

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