Computational approach in presentation a parametric method to construct hybrid girihs (hybrid Islamic geometric patterns)

Hybrid girihs refer to Islamic geometric patterns that include various stars/rosettes in their final pattern. In this paper, we first identified historical hybrid girihs and then categorized them based on symmetry groups and the number of stars/rosettes folds. In the next step, we analyzed the existing hybrid girihs to identify the generative parameters and present a method for generating historical and novel systematic and non-systematic hybrid girihs. The proposed method of this paper is a computational and parametric approach based on the symmetry groups theory. Its general steps include generating the minimal essential information (template motif) within the fundamental region, applying appropriate symmetry operations on the content of the fundamental region to create the content of the unit girih, and replicating the content of the unit girih in a suitable network according to the symmetry group to create the whole pattern. Our method is used to generate hybrid girih for adorning surfaces in digital spaces and for constructing facade modules (adorned with Islamic geometric patterns) and interior decorative partitions and furniture in physical spaces according to the aesthetic judgment of users.