Fișa disciplinei:

BP1-15 A Modele matematice in arhitectura.pdf

Department:

Basics of Architectural Design

Course Leader:

conf.dr.arh. Anca Vitcu

Teaching Staff:

https://www.uauim.ro/departamente/bp/grupe/

Teaching language:

Romanian

Learning outcomes:

General Objective
Generating a background that catalyzes and fosters through experimentation creativity and the shaping of the relationship between mathematics & computer science on side and architecture on the other, a relationship inspired by biosciences/natural sciences.

Acquisition of basic knowledge and skills:
- in the field of mathematical modeling, in the analytical description of the the architectural project idea, in the search of suitable algorithmic, geometric or topological solutions,
- in the rapid visualization of the architectural idea by creating a 3D model in one of the dedicated software packages (Blender, 3ds Max, Maya).

Specific Objectives
O1. Knowledge of mathematical modeling concepts and how they are used in contemporary architecture;
O2. Knowledge of principles of algorithmic generation of forms and how they are used in architectural and urban design;
O3. Knowledge of 3D modeling methods and techniques for visualizing shapes and configurations in architectural space.

Content:

Course
1. Architecture inspired by nature - an overview of associated mathematical concepts and presentation of examples of mathematical models used in built architecture and urban planning.
2. Fractal structures, presentation of the differences between fractal and Euclidean geometry, examples of how to interpret fractal geometry in architecture and examples of interpretations of fractal geometry in architecture.
3. Geometric and topological features of complex surfaces in 3-dim space:
- ruled surfaces (hyperboloid, paraboloid, hyperbolic paraboloid, conoid surfaces,...),
-modeling of free-form curves and surfaces (Bézier, B-spline, NURBS, ...).
4. Geometric and topological features of complex surfaces in 3-dim space:
-minimal surfaces (catenoid, helicoid, Enneper and Scherk surfaces),
- Plateau's bubbles, Weaire-Phelan structure.
5. Geometric and topological features of complex surfaces in 3-dim space:
-non-orientable surfaces (Klein's glass, Möbius strip,...).
6. Discrete analogies of smooth geometric objects.
7. Explanation of some basic concepts in the field of machine learning, contextualization and understanding of their role in architectural and urban design.

Seminar/Lab
1. An overview of fundamental computer modeling algorithms, techniques, and tools;
Exercises: topological transformations, cellular automata, Voronoi diagrams, triangulation of a region
2. The choice of project topics – students can opt for the preparation of a practical project consisting of a 3D model created in one of the dedicated programs or to prepare a theoretical project consisting of an in-depth analysis of the connection between mathematics and architecture of the proposed topic. The projects are inspired by the topic discussed in the course.
3. Project development – revise/proofread
4. Project development – revise/proofread
5. Project development – revise/proofread
6. Project development – revise/proofread
7. Project development – revise final version

Teaching Method:

Customized lectures and applications

Assessment:

Project evaluation (theoretical module - 30%) – the motivation for choosing the topic, the description of the source from nature as the basis of inspiration, examples of architectural projects that have the same source of inspiration and the use of associated mathematical concepts, sketches of the architectural form inspired by nature (proposed by the student).
- Ability to understand, recognize and explain concepts of topology, differential geometry in selected contemporary architecture projects. (colloquium)

Project evaluation (practical part - 70%) - the complexity of the 3D model, the description of the mathematical concept/associated/implemented algorithm, the correct use of modeling techniques. (colloquium)
- Understanding of basic strategies to create content through polygonal, spline, NURBS or procedural modeling.

Minimal performance standards
- To understand fundamental mathematical and algorithmic concepts in the context of modeling complex architectural forms.
- To know and have the ability to correctly use the modeling techniques and basic principles used in dedicated programs (Blender, 3ds Max, Maya).
- Have the skills to stage an idea correctly using reference software packages.

Bibliography:

BIBLIOGRAFIE:
Adam A. John (2003) – Mathematics in Nature: Modeling Patterns in the Natural World, Princeton University Press
Carta Silvio (Ed.) (2022) - Machine Learning and the City: Applications in Architecture and Urban Design, Wiley;
Emmer Michele, Abate Marco (Eds.) (2018) – Imagine Math 6: Between Culture and Mathematics, Springer;
Hensel Michael (2013) - Performance-Oriented Architecture: Rethinking Architectural Design and the Built Environment, Wiley;
Lang J. Robert (2018) – Twists, Tilings and Tessellation: Mathematical Methods for Geometric Origami, CRC Press;
Lastra Alberto (2021) - Parametric Geometry of Curves and Surfaces: Architectural Form-Finding, Springer;
Lesmoir-Gordon Nigel (Ed.) (2010) – The Colors of Infinity: The Beauty and Power of Fractals, Springer;
Niss Mogens, Blum Werner (2020) - The Learning and Teaching of Mathematical Modelling, Routledge;
Prautzsch Hartmut, Boehm Wolfgang, Paluszny Marco (2002) - Bezier and B-Spline Techniques, Springer;
Pugnale Alberto, Bologna Alberto (2023) – Architecture Beyond the Cupola: Inventions and Designs of Dante Bini (Mathematics and the Built Environment series), Springer Nature;
Rossi Michela, Buratti Giorgio (Eds.) (2018) - Computational Morphologies Design Rules Between Organic Models and Responsive Architecture, Springer;
Verner I, Maor S (2006) – Mathematical Mode of Thought in Architectural Design Education, Nexus Network Journal 8;
Williams Kim, Ostwald J. Michael (2015) - Architecture and Mathematics from Antiquity to the Future (vol. II), Springer
Vitcu Anca (2023) - The Challenge of Next-Generation Machine Learning Algorithms for Architecture Design and Living Environment, in Vol. Architecture Inspired by Nature, Ed. Springer Nature;
Vitcu Anca (2015) - Bio-Inspired Architecture as Performance Orientated System, in Vol. On Form and Pattern, Ed. Academiei Române.
Vitcu Anca – Course notes
https://www.evolo.us/
https://www.archdaily.com/
https://www.arup.com/news-and-events/ai-ml-tool-for-better-decision-making-on-land-use-and-planning
https://www.balmondstudio.com/about-cecil-balmond.php
http://www.i-mad.com/categories/status/
https://www.zaha-hadid.com/archive
https://www.designboom.com/

Bibliografie selectivă (seminar/lab):
Architectural Design: Parametricism 2.0 - Rethinking Architecture's Agenda for the 21st Century, Wiley, March/April 2016;
Architectural Design: Pavilions, Pop-Ups and Parasols: The Impact of Real and Virtual Meeting on Physical Space, Wiley, May/June 2015;
Architectural Design: Empathic Space - The Computation of Human-Centric Architecture, Wiley, September/October 2014;
Architectural Design: Space Architecture - The New Frontier for Design Research, Wiley, November/December 2014;
Architectural Design: Computation Works-The Building of Algorithmic Thought, Wiley, March/April 2013;
Architectural Design: Inside Smartgeometry: Expanding the Architectural Possibilities of Computational Design, Wiley, March 2013;
Architectural Design: Mathematics of Space, Wiley, July/August 2011;
Architectural Design: Protocell Architecture, Wiley, March/April 2011;
Architectural Design: The New Structuralism - Design, Engineering and Architectural Technologies, Wiley, July/August 2010;
Architectural Design: Exuberance - New Virtuosity in Contemporary Architecture, Wiley, March/April 2010;
Architectural Design: Patterns of Architecture, Wiley, November/December 2009;
Architectural Design: Digital Cities, Wiley, July/August 2009;
Architectural Design: Closing the Gap, Wiley, March/April 2009;
Architectural Design: Versatility and Vicissitude, Wiley, March/April 2008;
Architectural Design: Elegance, Wiley, January/February 2007;
Architectural Design: Collective Intelligence in Design, Wiley, September/October 2006;
Architectural Design: Programming Cultures, Wiley, July/August 2006;
Vitcu Anca – Fișe de lucru
https://www.guggenheim.org/teaching-materials/the-architecture-of-the-solomon-r-guggenheim-museum/frank-lloyd-wright-and-nature
https://parametrichouse.com/bending-active-plates/
https://www.blender.org/
https://www.autodesk.com/products/3ds-max/overview?term=1-YEAR&tab=subscription
https://www.autodesk.com/products/maya/overview?term=1-YEAR&tab=subscription

Notes:

- Students learn to use mathematics creatively by generating varied complex shapes, as well as a method to answer design problems – efficiency, functionality, optimization, adaptability, stability, sustainability.