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

Abstract

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 Iannis 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.