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An approach to automating the construction of 3D girihs (3D Islamic geometric patterns) on NURBS surfaces.

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Title: An approach to automating the construction of 3D girihs (3D Islamic geometric patterns) on NURBS surfaces.
Authors: Azizi Naserabad, Ali1 (AUTHOR), Ghanbaran, Abdulhamid1 (AUTHOR) ghanbaran@sru.ac.ir
Source: International Journal of Architectural Computing. Mar2026, Vol. 24 Issue 1, p274-301. 28p.
Subjects: Curved surfaces, Computational geometry, Islamic architecture
Abstract: Islamic geometric patterns known as "girihs" are typically seen as 2D designs. However, in traditional Iranian architecture, girihs have been used to decorate curved and 3D surfaces. While there have been many studies on 2D girihs and methods for creating them, there has been less focus on 3D girihs. Additionally, there isn't a comprehensive digital technique for constructing 3D girihs. This paper aims to fill this gap by proposing an automated approach for constructing girihs on curved surfaces to create 3D girihs. We use the UV coordinate relative to the NURBS (Non-Uniform Rational B-Spline) surfaces to identify the corresponding generative points of 2D girihs on 3D surfaces, then connect the points to construct 3D girihs. With this method, any geometric girih can be mapped onto a 3D surface, and under the right conditions, any 2D designs and motifs can also be mapped. We implement the proposed method in Grasshopper for Rhino 8 for Win, controlling the density and mapping quality of 3D girihs through parameters NMU and DL. By integrating this algorithm with a 2D girih generation algorithm, we provide the possibility of real-time customization and interactive construction of 3D girihs. [ABSTRACT FROM AUTHOR]
Copyright of International Journal of Architectural Computing is the property of Sage Publications Inc. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: An approach to automating the construction of 3D girihs (3D Islamic geometric patterns) on NURBS surfaces.
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  Data: <searchLink fieldCode="JN" term="%22International+Journal+of+Architectural+Computing%22">International Journal of Architectural Computing</searchLink>. Mar2026, Vol. 24 Issue 1, p274-301. 28p.
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  Data: <searchLink fieldCode="DE" term="%22Curved+surfaces%22">Curved surfaces</searchLink><br /><searchLink fieldCode="DE" term="%22Computational+geometry%22">Computational geometry</searchLink><br /><searchLink fieldCode="DE" term="%22Islamic+architecture%22">Islamic architecture</searchLink>
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  Label: Abstract
  Group: Ab
  Data: Islamic geometric patterns known as "girihs" are typically seen as 2D designs. However, in traditional Iranian architecture, girihs have been used to decorate curved and 3D surfaces. While there have been many studies on 2D girihs and methods for creating them, there has been less focus on 3D girihs. Additionally, there isn't a comprehensive digital technique for constructing 3D girihs. This paper aims to fill this gap by proposing an automated approach for constructing girihs on curved surfaces to create 3D girihs. We use the UV coordinate relative to the NURBS (Non-Uniform Rational B-Spline) surfaces to identify the corresponding generative points of 2D girihs on 3D surfaces, then connect the points to construct 3D girihs. With this method, any geometric girih can be mapped onto a 3D surface, and under the right conditions, any 2D designs and motifs can also be mapped. We implement the proposed method in Grasshopper for Rhino 8 for Win, controlling the density and mapping quality of 3D girihs through parameters NMU and DL. By integrating this algorithm with a 2D girih generation algorithm, we provide the possibility of real-time customization and interactive construction of 3D girihs. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of International Journal of Architectural Computing is the property of Sage Publications Inc. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Text: English
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      – SubjectFull: Computational geometry
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              Text: Mar2026
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