Algebraic analysis and reconstruction of the Philips Pavilion's hyperbolic paraboloid surfaces

Fischer, Thomas1; Wortmann, Thomas2

2022-03-01

10.1177/14780771221082253

International Journal of Architectural Computing   影响因子和分区

1478-0771

2048-3988

In this article, we present a procedure to derive algebraic descriptions from geometric descriptions of trimmed hyperbolic paraboloid (or 'hypar') surfaces. We contextualise this procedure historically, and we illustrate its application using the 1958 Philips Pavilion by Le Corbusier and lannis Xenakis as a case study. The procedure uses parametric modelling and computational optimisation to converge on close algebraic approximations of hyperbolic paraboloid geometry through a successive breakdown of vast search spaces. It departs from coordinate data of three or four vertices of a geometrically described hyperbolic paraboloid and yields the surface's two quadratic coefficients, the coordinates of its centroid location and the rotation angles of its spatial orientation. The procedure exemplifies the under-explored analytical (as opposed to generative) use of computational optimisation and parametric modelling in the field of architectural computing.

Parametric analysis optimisation ruled surfaces hyperbolic paraboloids geometry reconstruction

ESCI ; EI

英语

第一 ; 通讯

Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany's Excellence Strategy[EXC 2120/1 - 390831618]

Architecture

Architecture

WOS:000776663800001

SAGE PUBLICATIONS LTD

20221511948442

Algebra

Computer Applications:723.5 ; Algebra:921.1 ; Combinatorial Mathematics, Includes Graph Theory, Set Theory:921.4

Web of Science

1.Southern Univ Sci & Technol, Sch Design, 1088 Xueyuan Ave, Shenzhen 518055, Guangdong, Peoples R China
2.Univ Stuttgart, Inst Computat Design & Construct, Fac Architecture & Urban Planning, Chair Comp Architecture, Baden Wurttemberg, Germany

Fischer, Thomas,Wortmann, Thomas. Algebraic analysis and reconstruction of the Philips Pavilion's hyperbolic paraboloid surfaces[J]. International Journal of Architectural Computing,2022,20(1):61-75.

Fischer, Thomas,&Wortmann, Thomas.(2022).Algebraic analysis and reconstruction of the Philips Pavilion's hyperbolic paraboloid surfaces.International Journal of Architectural Computing,20(1),61-75.

Fischer, Thomas,et al."Algebraic analysis and reconstruction of the Philips Pavilion's hyperbolic paraboloid surfaces".International Journal of Architectural Computing 20.1(2022):61-75.