تحلیل تطبیقی شیوه‌های ترسیم نقوش هندسی در هنر اسلامی و طراحی روشی بهینه در بازترسیم آثار
محورهای موضوعی : معماری اسلامی
مهدی عزیزی همدانی
1
,
غلامحسین معماریان
2
*
,
اصغر محمدمرادی
3
1 - دانشجوی دکتری معماری، دانشکده معماری و شهرسازی، دانشگاه علم و صنعت ایران، تهران
2 - استاد دانشکده معماری و شهرسازی، دانشگاه علم و صنعت ایران، تهران، ایران
3 - استاد گروه مرمت، دانشگاه علم و صنعت ایران، تهران، ایران
کلید واژه: نقوش هندسی, گره, روش بهینه, شیوه چندضلعی, شبکه‌ای, زیرساخت شعاعی,
چکیده مقاله :
نقوش هندسی با قدمت بیش از هزار سال شاخه‌ای از هنرهای اسلامی است. در قرن اخیر پژوهشگران و شرق‌شناسان علاقه‌مند به هنرهای اسلامی سعی در بیان شیوه‌های متفاوتی برای فهم این نقوش نموده‌اند. هدف این مقاله ارائه روشی بهینه برای شناخت و بازآفرینی نقوش هندسی در معماری اسلامی و ایرانی است تا زمینه به‌کارگیری این الگوها در طراحی امروزی و انتقال دانش به نسل آینده را فراهم سازد. بدین‌منظور با بررسی چهار شیوه اصلی ترسیم نقوش شامل شیوه‌های چندضلعی، زیرساخت شعاعی، شمسه مرکزی و شبکه‌ای، مزایا و محدودیت‌های هر شیوه از طریق مطالعه متون تاریخی، کتب استادکاران و ارزیابی معیارهایی مانند دقت هندسی، انعطاف‌پذیری و سهولت آموزش مورد بررسی قرار گرفت. یافته‌ها نشان می‌دهد روش‌های ترسیمی عموماً امکان ترسیم تعدادی از نقوش هندسی را فراهم می‌کنند و تنها بازترسیم دقیق طرح‌های تاریخی را ممکن می‌کنند، اما بستری برای ابداع نقوش جدید با حفظ چارچوب هندسی اصیل فراهم نمی‌سازند. اگرچه شیوه‌هایی مانند شبکه‌ای برای الگوهای ساده یا چندضلعی برای تنوع طرح‌ها مفیدند، اما در مواجهه با نقوش پیچیده و ترکیبی انعطاف کمتری دارند. در انتها با بیان هدف اصلی شیوه ترسیم نقوش هندسی که فهم و بازترسیم نمونه‌های موجود در بناهای تاریخی است، روشی بهینه در فهم و باز ترسیم این نقوش ارائه گردید. بدین‌منظور در چهار مرحله شامل شناخت و رابطه شمسه‌ها و زمینه قابل تکرار و زوایای به‌کار رفته در گره و اتصال فاصله بین شمسه‌ها شیوه بهینه تبیین شده و در انتها با سایر شیوه‌ها مقایسه می‌گردد.
Comparative Analysis of Geometric Pattern Drawing
Methods in Islamic Art and Designing an Optimal
Method for Redrawing Artifacts
Mahdi Azizi Hamedani*
Gholamhossein Memarian**
Asghar Mohammadmoradi***
This article proposes an optimal method for recognizing and redrawing geometric patterns in Islamic and Iranian architecture to facilitate their application in contemporary design and knowledge transfer to future generations. By analyzing four primary pattern-drawing methods—polygonal, radial substructure, The Point-Joining Technique, and grid-based approaches—the strengths and weaknesses of each method were evaluated through historical resource analysis, interviews with master artisans, and criteria such as geometric accuracy, generalizability, and ease of instruction. Findings reveal that the radial substructure method, relying on radiating grids and concentric circles, is optimal due to its comprehensive coverage of diverse pattern types, reduced drawing errors, and adaptability to various contexts. This method not only enables precise reproduction of historical patterns but also allows the creation of new designs while preserving geometric authenticity. Combining technical precision and practical simplicity, the proposed method offers an effective solution for preserving artistic heritage and redrawing geometric patterns.
Keywords: Geometric patterns, Interlace (Gereh), Optimal method, Polygonal method, Grid-based method, Radial substructure.
Introduction
Geometric patterns, as a hallmark of Islamic and Iranian art, hold a unique place in historical architectural ornamentation. These patterns reflect both the aesthetic sensibilities of past artists and intricate geometric systems requiring precise knowledge of construction rules. However, many of these rules remain obscure or inefficient due to the lack of systematic knowledge transfer from masters to apprentices. Previous studies have focused on historical descriptions or aesthetic analyses but rarely provided practical methods for redrawing and teaching these patterns. Existing methods fail to cover all variations of geometric patterns and often impose excessive complexity. This article addresses this gap by evaluating four primary pattern-drawing methods and proposing an optimal approach for understanding historical patterns, effective teaching, and contemporary design applications.
Research Methodology
This descriptive-analytical study combines qualitative and quantitative methods:
Literature Review: Examination of historical resources (e.g., Topkapı Scrolls), traditional artisan manuals (e.g., works of Sharbaf and Lurzadeh), and contemporary research (e.g., Bonner and Majewski).
Empirical Learning: Apprenticeship with master artisans and researchers to understand practical drawing techniques.
Field Analysis: Site visits to historical monuments (e.g., Isfahan Jameh Mosque, Fatima Masumeh Shrine) for pattern documentation.
Criteria Evaluation: Assessment of four methods based on geometric accuracy, flexibility, teachability, and innovation potential.
Comparative Analysis: Tabular comparison of methods across seven key criteria.
Results
The four methods—polygonal, radial substructure (artisan tradition), The Point-Joining Technique, and grid-based—were analyzed in detail. The radial substructure method, grounded in foundational geometry (radii and concentric circles), demonstrated superior versatility for reproducing historical patterns and creating new designs. Key findings include:
Grid-based methods excel in conventional patterns (e.g.,6- or 8-rosette) but falter with complex configurations (e.g., 10- rosettes).
The polygonal method, though diverse, demands advanced geometric knowledge and struggles with irregular rosettes.
The Point-Joining method lacks flexibility for peripheral elements and distorts composite patterns.
The radial substructure method minimizes manual errors, supports diverse contexts (square, hexagonal), and provides clear, reproducible steps for learners.
Discussion
The study of the advantages and disadvantages of four methods of drawing geometric patterns resulted in an optimal method for studying geometric patterns. This method is based on the radial substructure method. A number of masters have used this method in drawing some patterns, but it has not been the basis of their practice. Radial substructure drawings are generally drawn in a frame requiring a four-way reflection, and the shamas used in geometric patterns are drawn as a quarter. Auxiliary lines for drawing patterns are generally determined by code lines, and in some corners of the rectangular background, the method of drawing knot devices is not explained, or tasteful drawings are made. In this method, an attempt is made to identify the repeatable background in a geometric pattern in the first stage. In drawing the background of the work, the background is used in a circumscribed circle and the shamas are placed in the center of the circle. If the knot is a combination and includes two or more types of shamas, one of the shamas is designed in the center. In the second stage, the rays are drawn and extended to the point of contact with the rays of the surrounding rays, and in the next stage, an attempt is made to draw the network of the geometric pattern infrastructure. In the next stage, based on drawing the lines of the bergamot and their extension, an attempt is made to complete the geometric pattern. In the fourth stage, the pattern will be reproduced on the surface solely with translational symmetry and without the use of reflection or rotation.
Conclusion
This study analyzed four geometric pattern-drawing methods—grid-based, polygonal, radial substructure, and The Point-Joining —evaluating their strengths and weaknesses against criteria such as interpretative capability for diverse geometric patterns, clarity and logicality of drawing steps, error reduction, potential for creating new interlaced patterns (Gereh), teachability, and ease of knowledge transfer. Based on these evaluations, an optimal method for understanding and redrawing geometric patterns in historical architecture was proposed, structured into four stages to systematically facilitate comprehension and reconstruction.
The proposed method proves more efficient for manual drawing and practical engagement with geometric patterns in historical buildings, making these patterns accessible to enthusiasts. While other methods may excel in specific contexts—for example, the grid-based method is faster for 8-pointed rosettes—they lack the versatility required for complex or varied patterns. Similarly, the polygonal method offers flexibility for diverse designs but often fails to align with traditional artisans’ standards for accuracy. Although methods like the polygonal and grid-based approaches may simplify substructure creation for new patterns, mastery of the radial substructure or the proposed optimal method allows artists to innovate within authentic geometric frameworks.
The advantages of this method include reducing drawing errors by using radial grids and concentric circles, the ability to adapt to a variety of backgrounds (square, hexagonal) and combined designs, providing transparent and reproducible steps for students, and creating a platform for designing new designs while maintaining the geometric framework, which can be used in redrawing new works and designs.
Table: Comparison of Geometric Pattern-Drawing Methods
|
Index for examining the method of drawing geometric patterns |
Geometric Pattern-Drawing Methods |
||||
|
Polygonal |
Radial Substructure |
Point-Joining |
Grid-Based |
Optimal Method |
|
|
Reduction of manual drawing errors |
|
¢ |
|
|
¢ |
|
Facilitating creative design |
¢ |
|
|
¢ |
¢ |
|
Ease of learning and teaching speed |
|
¢ |
¢ |
¢ |
¢ |
|
Versatility in pattern diversity |
¢ |
|
|
¢ |
|
|
Logical and clear drawing steps |
|
¢ |
|
|
¢ |
|
Ability to create new patterns |
¢ |
¢ |
|
¢ |
¢ |
|
Ease of manual/software implementation |
|
¢ |
¢ |
|
¢ |
References
Abdullahi, Yahya& Mohamed Rashid Bin Embi (2013) “Evolution of Islamic geometric patterns. Frontiers of Architectural Research 2(2): 243–51.https://doi.org/10.1016/j.foar.2013.03.002.
Bonner, J. (2017) Islamic Geometric Patterns: Their Historical Development and Traditional Methods of Construction. In Islamic Geometric Patterns: Their Historical Development and Traditional Methods of Construction. https://doi.org/10.1007/978-1-4419-0217-7.
Bonner, J., Pelletier, M., & Box, P. O. (2012) A 7-Fold System for Creating Islamic Geometric Patterns Part 1: Historical Antecedents.
Bonner, J.F. (2012) Creating Non-Systematic Islamic Geometric Patterns with Complex Combinations of Star Forms.https://www.semanticscholar.org/paper/Creating-Non-Systematic-Islamic-Geometric-Patterns-Bonner/f0435a2886804b06a6a46010c715dd6ee3092fb4?utm_source=direct_link.
Castera, J. M., Peuriot, F. oise, Ploquin, P., &McElhearn, K (1999) Arabesques. Decorative Art in Morocco (Slp edition). Art Creation Realisation.
Cromwell, P. (2023) Geometric Architectural Ornament of the Seljuks in Asia Minor. https://doi.org/10.13140/RG.2.2.35205.52969
El-Said, Issam and AyseParman. Geometric Concepts in Islamic Art. Palo Alto, CA: Dale Seymour Pubn, 1976.
Lee, T., & August, A. S. (2014) The Geometric Rosette: Analysis of an Islamic decorative motif. https://www.semanticscholar.org/paper/The-Geometric-Rosette-%3A-analysis-of-an-Islamic-Lee-August/29f33d97a25d88ff187585277edb8d4f208d152a#citing-papers .
Majewski, M. (2020) Understanding Geometric Pattern and its Geometry, Part 2 -Decagonal Diversity. The Electronic Journal of Mathematics and Technology, 14, 87–106. .
Majewski, M. (2022) Understanding Geometric Pattern and its Geometry, Part 7—What can go wrong? The Electronic Journal of Mathematics and Technology, 16, 73–91.
Necipoğlu, G. (2017) The Arts of Ornamental Geometry. Brill. https://brill.com/display/title/32181.
Wichmann, B., & Wade, D. (2017) Islamic Design: A Mathematical Approach. Birkhäuser Basel. https://doi.org/10.1007/978-3-319-69977-6.
* Ph.D Student in Architecture, School of Architecture and Environmental Design, Iran University of Science and Technology, Tehran, Iran.
mahdyhamedany@gmail.com
** Corresponding Author: Professor, Department of Architecture, School of Architecture and Environmental Design, Iran University of Science and Technology, Tehran, Iran. corresponding Author.
memarian@iust.ac.ir
*** Professor, Department of Restoration and Rehabilitation of Historic Buildings and Sites, School of Architecture and Environmental Design, Iran University of Science and Technology, Tehran, Iran.
حاجی قاسمی، کامبیز و کامبیز نوایی (1390) خشت و خیال، تهران، سروش
. حلی، علی‌اکبر (1356) گره‌ها و قوس‌ها در معماری اسلامی، قم، مهر
. زمرشیدی، حسین و علی صادقی حبیب‌آباد (1395) تزیین‌های معماری در بارگاه و بقاع متبرکه امام‌زادگان مبتنی بر نقوش اسلامی، مطالعات شهر ایرانی- اسلامی، 7(24)، صص 5-20
. https://sid.ir/paper/499908/fa دل‌زنده، علی و همکاران (1403) مرتبه‌بندی تعاریف و شیوه‌های نگرش به معماری اسلامی برپایه شناخت‌شناسی و هستی‌شناسی اسلامی مطالعات شهر ایرانی- اسلامی54 (14)، صص83-100
. http://iic.ihss.ac.ir/fa/Article/41039 زمرشیدی، حسین (1390) مسجد بی‌نظیر جامع گوهرشاد و هنرهای قدسی معماری، مطالعات شهر ایرانی- اسلامی، صص ۷-۳۲، (۶)۲
.http://noo.rs/BKMWI السعید، عصام و عایشه پارمان (1368) نقش‌های هندسی در هنر اسلامی، مترجم مسعود رجب نیا، تهران، سروش
. شاکرسلمان، عامر (1383) هم‌آراستگی در نگاره‌های اسلامی، مترجم آقاربیع، به نشر
. شعرباف، اصغر (1385) گره و کاربندی، تهران، سازمان میراث فرهنگی کشور
. طاهری، جعفر (1390) «نقدی بر تحقیق و تصحیح «ترجمه النجارة» بوزجانی»، کتاب ماه علوم و فنون، 35، صص 53-57
. https://manuscript.isc.ac/Inventory/8/616879.htm طاهری، جعفر (1390) نقش ریاضی‌دانان در معماری به روایت متون دوره اسلامی، تاریخ علم، 9(10)، صص 39-65
. https://sid.ir/paper/ 146574/fa کریچلو، کیس (1389) تحليل مضامين جهان‌شناختي نقوش اسلامي، مترجم آذرکار، حکمت
. گلیار، محمد (۱۳۹۹) دفترگره، میراث اهل قلم
. لرزاده، حسین (۱۳۵۸) هنرهای از یاد رفته معماری اسلامی، جلد اول، تهران
. ماهرالنقش، محمود (۱۳۶۱) کاشی کاری در ایران دوره اسلامی، شرکت افست
. نجیب اوغلو، گل‌رو (1389) هندسه و تزیین در معماری اسلامی، مترجم قیومی، روزنه
. نوریان، یحیی و محمدحسین کسرائی (۱۳۹۵) «مقایسه گره‌های سنتی و الگوهای معاصر اسلامی با تمرکز بر کاربرد در معماری معاصر»، فرهنگ معماری و شهرسازی اسلامی، (2)، صص 63-75
. http://ciauj-tabriziau.ir/article-1-105-fa.html Abdullahi, Yahya & Mohamed Rashid Bin Embi (2013) “Evolution of Islamic geometric patterns. Frontiers of Architectural Research 2(2): 243–51. https://doi.org/10.1016/j.foar.2013.03.002
. Bonner, J. (2017) Islamic Geometric Patterns: Their Historical Development and Traditional Methods of Construction. In Islamic Geometric Patterns: Their Historical Development and Traditional Methods of Construction. https://doi.org/10.1007/978-1-4419-0217-7
. Bonner, J., Pelletier, M., & Box, P. O. (2012) A 7-Fold System for Creating Islamic Geometric Patterns Part 1: Historical Antecedents
. Bonner, J.F. (2012) Creating Non-Systematic Islamic Geometric Patterns with Complex Combinations of Star Forms. https://www.semanticscholar.org/paper/Creating-Non-Systematic-Islamic-Geometric-Patterns-Bonner/f0435a2886804b06a6a46010c715dd6ee3092fb4?utm_source=direct_link
. Castera, J. M., Peuriot, F. oise, Ploquin, P., & McElhearn, K (1999) Arabesques. Decorative Art in Morocco (Slp edition). Art Creation Realisation
. Cromwell, P. (2023) Geometric Architectural Ornament of the Seljuks in Asia Minor. https://doi.org/10.13140/RG.2.2.35205.52969
. El-Said, Issam and Ayse Parman (1976) Geometric Concepts in Islamic Art. Palo Alto, CA: Dale Seymour Pubn
. https://www.semanticscholar.org/paper/A-7-Fold-System-for-Creating-Islamic-Geometric-Part-Pelletier/6916c9214f267e17ae3f8c68c724fdfa78e73d9e?utm_source=direct_link
. Lee, T., & August, A. S. (2014) The Geometric Rosette: Analysis of an Islamic decorative motif. https://www.semanticscholar.org/paper/The-Geometric-Rosette-%3A-analysis-of-an-Islamic-Lee-August/29f33d97a25d88ff187585277edb8d4f208d152a#citing-papers
. Majewski, M. (2020) Understanding Geometric Pattern and its Geometry, Part 2 -Decagonal Diversity. The Electronic Journal of Mathematics and Technology, 14, 87–106
. Majewski, M. (2022) Understanding Geometric Pattern and its Geometry, Part 7—What can go wrong? The Electronic Journal of Mathematics and Technology, 16, 73–91
. Necipoğlu, G. (2017) The Arts of Ornamental Geometry. Brill. https://brill.com/display/title/32181
. Wichmann, B., & Wade, D. (2017) Islamic Design: A Mathematical Approach. Birkhäuser Basel. https://doi.org/10.1007/978-3-319-69977-6
.
