Drawing Parametric Polygonal Pointed Star Patterns

Document Type : علمی - پژوهشی


1 PhD Candidate, Faculty of Conservation and Restoration, Art University of Isfahan

2 Assistant Professor, Faculty of Architecture and Urban Planning, Art University of Isfahan

3 Assistant Professor, Faculty of Arts and Architecture, Yazd University

4 Associate Professor, Faculty of Conservation and Restoration, Art University of Isfahan


The traditional methodology for drawing intricate Islamic patterns has been handed down through generations mainly by word of mouth by master masons to their apprentices. This method is nowadays cumbersome to apply in higher education where students are trained with an analytical mentality and rely on computer-aided design and drafting. It is equally infeasible to employ such traditional methodologies in current construction practices where engineers mainly depend on CAD/CAM applications. This paper proposes an alternative methodology based on analytical mathematics and parametric design for drawing Islamic patterns. It tests this methodology by drawing polygonal pointed star patterns both on flat surfaces as well as on curved surfaces of revolution such as those found in domes and minarets. It is demonstrated that this methodology provides promising areas for developing traditional designs while being more suited to current CAD/CAM production processes.

رئیس‌زاده، مهناز و حسین مفید. احیای هنرهای از یاد رفته، تهران: مولی، 1389‌.
شعرباف، اصغر‌. گره و کاربندی، تهران: انتشارات سازمان میراث فرهنگی کشور، 1385‌.
نجیب اوغلو، گلرو. هندسه و تزیین در معماری اسلامی (طومار طوپقاپی)، ترجمۀ مهرداد قیومی، تهران: روزنه، 1379.
Bodner, B.L. “A Nine- and Twelve-Pointed Star Polygon Design of the Tashkent Scrolls”, in Reza Sarhangi and Carlo Séquin, (eds.), Proceedings of Bridges 2011: Mathematics, Art, Architecture, Music, Culture, Conference, Phoenix: Tesselations Publishing, 2011, pp. 147-154.
________ . “Bourgoin’s 14-Pointed Star Polygon Designs”, in Bridges: Mathematical Connections in Art, Music, and Science Conference Proceedings, 2010, pp. 135 - 142.
Hankin, E.H. “The Drawing of Geometric Patterns in Saracenic Art”, in Memoirs of the Archaeological Society of India, Vol 15‌, 1925, Government of India.
________ . “Examples of Methods of Drawing Geometrical Arabesque Patterns”, in The Mathematical Gazette, No. 12 (1925), pp. 371–373.
________ . “Some Difficult Saracenic Designs II", in The Mathematical Gazette, No. 18, pp.165–168.
________ . “Some Difficult Saracenic Designs III”, in The Mathematical Gazette, No 20 (1936), pp. 318–319.
Kaplan, Craig S. Computer Graphics and Geometric Ornamental Design, PhD dissertation thesis, University of Washington, 2002.
Lee, A.J. “Islamic Star Patterns”, in Muqarnas, 4 (1995),pp. 182–197.