Generative parametric design of Gothic window tracery

Gothic architecture, and especially window tracery, exhibits quite complex geometric shape configurations by combining only a few basic geometric patterns, namely circles and straight lines. They are combined using only a limited set of operations, such as intersection, offsetting, and extrusions. The reason lies in the process how these objects have been physically realized, i.e., through construction with compass and ruler. Consequently, Gothic architecture is a great, although challenging, domain for parametric modeling. 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 this 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., 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.