Generation of Architectural Forms Through Linear Algebra

Abstract

Our efforts are aimed at applying a mathematical taxonomy or a geometrical model to significant classes of classical or modern architectural structures. Mathematical formulas are used to describe them, even though it is very clear that such formulas have not influenced the creativity of the designers. The purpose of our exercise is simply to better highlight the shape of the architectural object, to extract from it an inherent rule, to make evident its structural rigor. The final result of this exercise is a three-dimensional geometrical model, that is, a description of the geometrical object (a locus, or set of points) expressed through geometric analytical formulae, and its subsequent display on media such as paper or computer screen. The approach involves establishing a few basic elementary shapes, imposing movements and deformations on them, to determine a final shape dynamically; then giving the equations and supplying the related graphical representations.

First published as: Franca Caliò and Elena Marchetti , “Generation of Architectural Forms Through Linear Algebra”, pp. 9–22 in Nexus III: Architecture and Mathematics, ed. Kim Williams, Ospedaletto (Pisa): Pacini Editore, 2000.