Approaching Developable Surfaces Through Shadow and Penumbra

Abstract

This paper enquires into the relationship between the rigorous graphic construction of penumbra and shadow and the idea of a developable surface circumscribed to two cores (whether these are curves or surfaces). The first rigorously constructed graphic representations of shadow and penumbra appearing in different historical treatises are contextualised and contrasted with the first works addressing the mathematical description of such surfaces. We describe how artisans and artists have employed physical and mechanical models to construct circumscribed developable surfaces, examining both their formal exploration and constructive formalisation. Next we extrapolate the mechanisms for generating circumscribed surfaces to digital and parametric models. The two procedures presented here evince the existing geometric limits of this way of generating a surface, thus influencing its constructive applications. Lastly, several examples of ephemeral architecture based on such procedures are offered, in which the digital design and manufacturing of experimental pavilions with circumscribed developable surfaces are addressed.