id 
caadria2020_304 
authors 
Fischer, Thomas and Wortmann, Thomas 
year 
2020 
title 
From Geometrically to Algebraically Described Hyperbolic Paraboloids  An optimisationbased analysis of the Philips Pavilion 
source 
D. Holzer, W. Nakapan, A. Globa, I. Koh (eds.), RE: Anthropocene, Design in the Age of Humans  Proceedings of the 25th CAADRIA Conference  Volume 1, Chulalongkorn University, Bangkok, Thailand, 56 August 2020, pp. 435444 
summary 
In this paper, we present a procedure to derive algebraic parameters from geometrically described truncated hyperbolic paraboloid surfaces. The procedure uses parametric modelling and optimisation to converge on close algebraic approximations of hyperbolic paraboloid geometry through a successive breakdown of vast search spaces. We illustrate this procedure with its application to the surfaces of the 1958 Philips Pavilion designed by Le Corbusier and Iannis Xenakis. This application yielded previously unavailable parametric data of this building in algebraic form. It highlights the power of the parametric design and optimisation toolkit, both in terms of automated search and epistemological enablement. 
keywords 
parametric analysis; optimisation; ruled surfaces; hyperbolic paraboloid; geometry reconstruction 
series 
CAADRIA 
email 
thomas.fischer@xjtlu.edu.cn 
full text 
file.pdf (2,266,871 bytes) 
references 
Contenttype: text/plain

Burry, J (2011)
Logic and Intuition in Architectural Modelling: Philosophy of Mathematics for Computational Design
, Ph.D. Thesis, RMIT University




Burry, MC (2002)
Rapid prototyping
, Automation in Construction, 11(3), p. 313333




Burry, MC (2005)
Homo faber
, Architectural Design, 75(4), p. 3037




Burry, MC (2011)
Architecture and practical design computation
, Menges, A and Ahlquist, S (eds), Computational Design Thinking, AD Reader, Wiley, Chichester, pp. 102119




Fischer, T, Herr, CM, Burry, MC and Frazer, JH (2003)
Tangible interfaces to explain Gaudí's use of ruledsurface geometries
, Automation in Construction, 12(5), p. 467471




Fischer, T (2012)
Geometry rationalization for nonstandard architecture
, Architecture Science, 5, p. 2546




Fischer, T (2019)
Transcomputability, (Glanville's Corollary of) Ashby's Law of Requisite Variety, and epistemic processes
, Kybernetes, 48(4), pp. 793804




Pottmann, H, Asperl, A, Hofer, M and Kilian, A (2007)
Architectural Geometry
, Bentley Institute Press, Exton, PA




Sdegno, A (2012)
Ruled surfaces in Le Corbusier's architectures
, Rossi, M (eds), Descriptive Geometry and Digital Representation: Memory and Innovation, McGrawHill, New York, p. 167175




Sprague, TS (2013)
Beauty, versatility, practicality: the rise of hyperbolic paraboloids in postwar America (19501962)
, Construction History, 28(1), p. 165184




Treib, M (1996)
Space Calculated in Seconds. The Philips Pavilion, Le Corbusier, Edgard Var?se
, Princeton University Press, Princeton, NJ




Wortmann, T (2017)
Opossum. Introducing and evaluating a modelbased optimization tool for Grasshopper
, Janssen, P, Loh, P, Raonic, A and Schnabel, MA (eds), Proceedings of the 22nd CAADRIA Conference, XJTLU, Suzhou, p. 283292




Xenakis, I (2008)
Music and Architecture: Architectural Projects, Text, and Realizations
, Pendragon Press, Hillsdale, NY




last changed 
2020/08/14 18:39 
