Constructive Geometry 1

Code:

30312B3

Acronym:

30312B3

Instance: 2017/2018 - 1S

Active?	Yes
Responsible unit:	Desenho (D)
Course/CS Responsible:	Integrated Master Degree in Architecture

Cycles of Study/Courses

Acronym	No. of Students	Study Plan	Curricular Years	Credits UCN	Credits ECTS	Contact hours	Total Time
MIARQ	40	MIARQ	3	-	3	-	81

Teaching language

Suitable for English-speaking students

Objectives

The aim of the Constructive Geometry courses consist in researching the role of Geometry in Architecture, by exploring its relation with current digital technologies. The course of the first semester - Constructive Geometry 1 (GC-1) introduces the students to the research of new themes with a strong implication in the design and characterization of the architectural space.

The development of CG-1 curriculum unfolds through the pratical exploration of the computer, which is understood here as a media for:
- geometric representation (drawing and modeling);
- calculation and geometric computation (parametric and algorithmic design;
- physical materialization (digital fabrication).

Learning outcomes and competences

By attending GC-1, the students are expected to:
- develop an heuristic thinking, visual and analytic, both in the plane and in space;
- know the implications of geometrical concepts and the use of Geometry in architectural design;
- know the basic techniques of different geometries for modeling situations where they can be creatively employed;
- use the computer beyond explicit geometric representation in the screen, by exploring its capabilities for calculation and materialization;
- develop a critical thinking about the relation of digital technologies with the traditional representation processes, and identify their both limitations and potentials for exploring the use of Geometry in Architecture.

Working method

Presencial

Program

1. GEOMETRY
1.1 Types:
metric, affine, projective, non-euclidian, fractals.
1.2 Elements:
point, curve (line, arc, helix, spline), surfaces (ruled, single curved, double curved, free), solids.
1.3 Themes related with Geometry and Architecture:
symmetry, proportion, fractals, topology, graphs.

2. COMPUTATION AND MATERIALIZATION
2.1 Concepts:
representation vs. calculation; geometric drawing, modeling and computation; parameterization, algorithms and associativity; software vs. scripting/programming; bottom-up vs. top-down methodologies.
2.2 Introduction to digital design and modeling:
coordinates; creation and edition of curves, surfaces and solids; geometric transformations; visualization.
2.3 Introduction to geometric computation:
parameters and algorithms; mathematical and logic functions; curves and surfaces; lists and hierarchies of information; generation and control of variation (metric, topologic, quantitative).
2.4 Digital materialization technologies:
fabrication (additive, subtractive, formative); assembly; construction.

3. CONSTRUCTIVE GEOMETRY
3.1 Research with digital drawing, modeling and computation of a theme about Geometry and Architecture (to be defined out of 1.3)

Mandatory literature

Blackwell William; Geometry in architecture. ISBN: 1-55953-018-9
Burry Jane; The New Mathematics of Architecture, Thames & Hudson, 2010
Burry Mark; Scripting Cultures: Architectural Design and Programming, John Wiley & Sons, 2011
Calter Paul A.; Squaring the circle
Kolarevic Branko 340; Architecture in the digital age. ISBN: 0-415-38141-X
Katz Victor J.; A history of mathematics. ISBN: 0-321-01618-1
Kalay Yehuda E.; Architecturec2b4s new media. ISBN: 0-262-11284-1
Kappraff Jay; Connections. ISBN: 981-02-4585-8
Le Corbusier; Le modulor. ISBN: 2-904-833-01-3
Mandelbrot Benoit B.; The fractal geometry of nature. ISBN: 978-0-7167-1186-5
March Lionel; Architectonics of humanism. ISBN: 0-471-97754-3
Marcolli Attilio; Teoria del campo
Mitchell William J.; Computer-aided architectural design
Mitchell William j.; Digital design media. ISBN: 0-471-28666-4
Mitchell William J.; The logic of architecture. ISBN: 0-262-63116-4
Oliveira Fernando Manuel Cortes Lisboa; Desenho de arquitectura assistido por computador. ISBN: 972-9483-27-2
Pérez-Gómez Alberto; Architectural representation and perpective hinge. ISBN: 0-262-66113-6
Pérez-Gómez Alberto; Architecture and the crisis of modern science. ISBN: 978-0-262-66055-6
Pottmann Helmut 340; Architectural geometry. ISBN: 978-1-934493-04-5
Schodek Daniel 340; Digital design and manufacturing. ISBN: 978-0-471-45636-0
Sousa José Pedro; Artigos da Secção de Tecnologia Digital, Revista Arquitectura e Vida, 2005-2006
Terzidis Kostas; Algorithmic Architecture, Architectural Press, 2006
Veloso Eduardo; Geometria. ISBN: 973-8353-26-X
Williams Kim ; Nexus - Architecture and Mathematics, 1996-2008
Xavier João Pedro; Perspectiva, perspectiva acelerada e contraperspectiva

Teaching methods and learning activities

The program unfolds through the combination of theoretical and practical teaching processes in a 3 hours weekly class. Throughout the semester 3 theoretical classes are given to present and discuss the program subjects. The practical introduction to the use of digital processes happens on a tutorial format taught in theoretical/practical classes. The rest of the classes are oriented towards the development of practical works under assistance. In specific moments, collective sessions of work presentation and discussion are organized.

The practical dimension of GC-1 is based on the iterative combination of representational processes (digital) with materialization tasks (physical).

Software

Grasshopper (software livre)
Rhinoceros (McNeel)

keywords

Technological sciences > Architecture
Technological sciences > Technology > Graphic techniques > Computer graphics

Evaluation Type

Distributed evaluation without final exam

Assessment Components

designation	Weight (%)
Participação presencial	20,00
Trabalho laboratorial	80,00
Total:	100,00

Eligibility for exams

To get approved in GC-1, the student must attend at least 75% of the classes and obtain a minimum of a 9,5 final grade resulting from his works and active participation in the class.

Calculation formula of final grade

The final grade results from the average of the students attendance and participation in the class (20%) and the completion of the practical works (80%).