Generative Parametric Design of Gothic Window Tracery

• Venue: SMI '04 Proceedings of the Shape Modeling International 2004
• Year: 2004

Gothic architecture, and especially window tracery,exhibits quite complex geometric shape configurations bycombining only a few basic geometric patterns, namely circlesand straight lines. They are combined using only a limited setof operations, such as intersection, offsetting, and extrusions.The reason lies in the process how these objects have beenphysically realized, i.e., through construction with compass andruler. Consequently, Gothic architecture is a great, althoughchallenging, domain for parametric modeling.We present some principles of this long-standing domain, togetherwith some delicate details, and show how the constructionsof some prototypic Gothic windows can be formalized usingour Generative Modeling Language (GML). The emphasis ofthis procedural approach is on modularization, so that complexconfigurations can be obtained from combining elementary constructions.Different combinations of specific parametric featurescan be grouped together, which leads to the concept of styles.They permit to differentiate between the basic shape and itsappearance, i.e., a particular ornamental decoration.This leads to an extremely compact representation for a wholeclass of shapes, which can nevertheless be quickly evaluatedto obtain a connected manifold mesh of a particular windowinstance. The resulting mesh may also contain free-form surfaceparts, represented as subdivision surfaces.