Constructive Geometry 2

Code:

30313B3

Acronym:

30313B3

Keywords
Classification	Keyword
OFICIAL	Drawing

Instance: 2014/2015 - 2S

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	51	MIARQ	3	-	3	-	81

Teaching language

Portuguese

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 second semester - Constructive Geometry 2 (GC-2) - expands the knowledge acquired during GC-1, by researching a higher degree of complexity in geometrical subjects with a strong influence in the generative and constructive processes in architecture.

The development of CG-2 curriculum unfolds through the practical 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-2, the students are expected to:
- develop a computational thinking (parametric and algorithmic) at an analytical, logic and creative levels;
- infer the geometric principles and digital processes behind the production of architectural buildings exploring complex geometries and non-standard building solutions;
- use the computer beyond explicit geometric representation in the screen, by exploring its capabilities for calculation and materialization;
- understand how the relation between digital technologies and traditional processes can promote a wider universe of conceptual and material possibilities 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, Architecture and Construction:
standardization vs. customization; variation and differentiation; form vs. component; surface vs. structure; material effects; interactivity.

2. COMPUTATION AND MATERIALIZATION
2.1 Concepts:
representation vs. calculation; geometric drawing, modeling and computation; associative design; formal and material optimization; emergence; physical computation.
2.2 Advanced digital design and modeling:
advanced geometric transformations; geometric analysis of curves and surfaces; rationalization and subdivision; digital fabrication planning.
2.3 Advanced geometric computation:
parameters and algorithms; mathematical and logic functions; curves and surfaces; lists and hierarchies of information; recursion; optimization; generation of variation (metric, topologic, quantitative).
2.4 Digital analysis:
introduction to design performance evaluation (environmental, energetic, structural…)
2.5 Material techniques:
sectioning, tessellation, bending, folding, subtraction, forming, weaving, aggregation.

3. CONSTRUCTIVE GEOMETRY
3.1 Research with geometric computation, analysis and fabrication on a theme about Geometry, Architecture and Constrution (to be defined out of 1.3 and 2.5)

Mandatory literature

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
Ceccato Cristiano 340; Advances in architectural geometry 2010. ISBN: 978-3-7091-0308-1
Critchlow Keith; Order in space
Hensel Michael 340; Morpho-ecologies. ISBN: 1-902902-53-X
Hensel Michael; Menges Achim; Weinstock Michael; Emergent Technologies and Design. Towards a Biological Paradigm for Architecture, Routledge, 2010
Hilbert D.; Geometry and the imagination. ISBN: 978-0-8218-1998-2
Iwamoto Lisa; Digital Fabrications: Architectural and Material Techniques., Princeton Architectural Press, 2009
Kalay Yehuda E.; Architecturec2b4s new media. ISBN: 0-262-11284-1
Kappraff Jay; Connections. ISBN: 981-02-4585-8
Kolarevic Branko 340; Architecture in the digital age. ISBN: 0-415-38141-X
Kolarevic Branko; Malkawi Ali; Performative Architecture. Beyond Instrumentality., Spon Press, 2005
Kolarevic Branko; Klinger Kevin; Manufacturing Material Effects. Rethinking Design and Making in Architecture., Routledge, 2008
Leach Neil; Digital Tectonics, John Wiley & Sons , 2004
Lindsey Bruce; Digital Gehry. ISBN: 3-7643-6562-5
Mitchell William j.; Digital design media. ISBN: 0-471-28666-4
Mitchell William J.; The logic of architecture. ISBN: 0-262-63116-4
Moussave Farshid ; The Function of Form, Actar , 2009
Oliveira Fernando Lisboa; A ideia de projecto em Charles S. Peirce ou da teoria do projecto considerada como uma semiótica
Pottmann Helmut 340; Architectural geometry. ISBN: 978-1-934493-04-5
Sakamoto Tomoko, Ferre Albert, Kubo Michael; From Control to Design: Parametric/Algorithmic Architecture, Actar, 2008
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
Woodbury Robert; Elements of Parametric Design, Routledge, 2010

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%).