Parametric Shape Grammar Formalism for Moorish Geometric Design Analysis and Generation

Abstract

The goal of this article is to propose a modeling method to automatically generate original and new forms of periodic Moorish geometric patterns. The proposed method is based on the symmetry-based approach and the shape grammar formalism. The symmetry-based approach consists of constructing a periodic pattern by using isometric transformations of its template motif. The main contribution of this article is to propose a parametric shape grammar method to generate the template motif. The process used consists first in identifying the shapes vocabulary characterizing the Moorish style. By identifying its common features by the analysis of a dataset of historical Moorish patterns, parametric shape grammar (PSG) rules are then determined. Furthermore, the use of PSGs implies additional mechanisms, such as the consideration of suitable constraints and goals. These mechanisms are imposed by the grid, which is the underlying geometric structure used traditionally by artisans to design sophisticated geometric patterns. The performance of the proposed method is measured by its capability to create original and new motifs of periodic Moorish patterns. This method preserves the authenticity of the style considered, because the generated patterns follow a parametric shape grammar based on a priori domain knowledge and extract one from representative images of Moorish style.