Suggesting a Model for Drawing Interlace Patterns in Islamic Architectural Ornaments

One of the noteworthy cases for historian researcher is ornament in architecture، which its execution is implicated in knowledge of geometry. Geometrical ornaments are subsets of Islamic architectural ornaments، and one of their examples is interlace. One of The most important and prevalent methods for drawing interlaces is radial based method which draws and divides circles into equal parts. In historical methods for applied geometrical treatises like Interlace of analogous and homogeneous shapes (originally fi tadakhole alashkale almotashabehe and almotavafeghe) which is pendant to translation of Abolvafa Boozjani’s treatise in tenth century AD، radial infrastructure is used for drawing the knots. The method of drawing is written alongside to the drawing. This method is used by Abdorahman Sufi in tenth century AD، for compass geometry which explains dividing circles into equal parts and drawing regular polygons. In this treatise، a basic method is proposed for dividing and reproducing using compass and constant aperture. In Mirza AkbarKhan’s scroll written in Qajar era، radial based approach for drawing knots is used too. Another method is Hankin’s method which in contrast uses polygons. In this technique، two lines are drawn from all side’s midpoints of all polygons. These lines cross each other like a letter x and are continued till they meet other lines of similar origins. In this paper، at first، a new method is proposed for drawing interlace using comparative analysis of the most important methods which is based on radial and Hankin’s polygon tiling and investigation their advantages and drawbacks. The proposed method is defined by direct parameters like “shamse’s” side and length of aperture. Using the proposed approach، problems of Hankin’s method، like calculation of polygon tiling based and contact angle will be solved. This proposed method can be converted into arbitrary patterns. Since the circumference of geometric ornament is more vulnerable than its center، drawing it from center and defining it parametrically can provide the possibility of drawing around parts of ornament in probable damage، which is performed in the proposed method by selecting number of sides and the length of aperture. In fact، it has been tried to promote the method of drawing geometric ornaments in Islamic architecture using computer especially with GDL written in Graphisoft ArchiCad 16. Indeed interlaces can be drawn with knowing two parameters composed of direct parameters like numbers of shamse’s side and length of aperture. The characteristic of this generating method is the fine feature for Islamic geometric ornaments which is known rarely. Presenting the process of conversion to arbitrary shapes is not easy in the first method، because radial infrastructure is a traditional method، where special points are connected to each other. Hankin’s method has more possibility for presenting this feature، but this method has its own limitations، such as selection of polygon tiling bases and contact angles before drawing interlaces. Indeed، there is not any difference among the resulting shapes in three methods. In fact the advantage of the proposed method is in simplicity for users with knowing direct parameters as numbers of shamse’s side and length of aperture for producing shapes.