From Cartesian to Topological Geometry: Challenging Flatness in Architecture

This paper argues that recent topological expressions of surface in architecture have an intellectual lineage to late-modernism. Several key developments of that era challenged the limitations of a simplified Cartesian understanding of form. This paper commences with a discussion of Cartesian geometry in Modernism, relative to innovations in the building industry that promoted constancy, repetition and standardisation. Despite the same logic being transferred to digital working platforms where the architectural elements are normally designed as geometric prisms and their immediate derivatives, an interest in computation has enabled architecture to bypass orthogonal regularity. Concepts investigated during late-modernism—such as adaptability, disequilibrium, and smooth transitioning—are now central to performance and parametric-based design, examined through the interaction with data inputs, further pointing at critical updates of common software production tools.