Generative Parametric Design of Gothic Window Tracery

Abstract

Gothic architecture, and especially window tracery, exhibits quite complex geometric shape configurations. But this complexity is achieved by combining only a few basic geometric patterns. We present some principles of this long-standing domain, together with some delicate details, and show how the constructions of some prototypic Gothic windows can be formalized using our Generative Modeling Language (GML). The emphasis of our procedural approach is on modularization, so that complex configurations can be obtained from combining elementary constructions. Different combinations of specific parametric features can be grouped together, which leads to the concept of styles. They permit to differentiate between the basic shape and its appearance, i.e., in a particular ornamental decoration. This leads to an extremely compact representation for a whole class of shapes, which can nevertheless be quickly evaluated to obtain a connected manifold mesh of a particular window instance. The resulting mesh may also contain free-form surface parts, represented as subdivision surfaces.