Drawing Girih is a challenging mathematical and geometrical principle for artists and artisans in the present and past. This paper is to determine how Girih have been embedded on curved surfaces such as dome, according to their curvature. For achieving this goal, the Dast-Gardan pattern is represented as a prominent and complex type. This pattern enables the designer to use diverse types of star polygons in one pattern depending on the curvature of the surface. The research hypothesis is examined by analyzing the patterns of three historic domes in Iran. The result shows that there is a relationship between the number of points of star polygons and the change of the dome curvature.

THE LOGIC OF TRADITIONAL DESIGN OF
ISLAMIC PATTERNS FOR CURVED SURFACES
First Conference on Traditional Structures and Technology : DOMES

Islamic pattern is one of the most famous and beautiful geometric patterns in art and architecture. It was an important technique in Muslim architects point of view and unknown art in orientalists perspective for its complexity and mysteries. Nevertheless there are many documents and traditional samples, most new attempts for reinventing pattern are in progress. However most of them focuses on drawing pattern on infinite flatten surfaces, there are some tries to spread Islamic pattern on curved surface.

In this paper, we first introduce the multi-context pattern as a well-known issue in the old artisan’s method; then compare its traditional and new drawing method. According to this comparison, unlike the new drawing methods, we conclude that traditional drawing method makes pattern by considering context. So designing traditional Islamic pattern for curved surfaces has been based on multi-context logic because of aggregation and expansion in different parts of surface. This aggregation and expansion relate to surface curvature decreases and increases. At the end, we represent and analyze a great Islamic pattern that spread under the dome of Ja’me Yazd mosque as a complete sample of our approach in this paper.