Interwoven Islamic Geometric Patterns
Inhaltsverzeichnis
Referenz
Craig S. Kaplan: Interwoven Islamic Geometric Patterns. In: Bridges 2017, Pages 71–78.
DOI
Abstract
Rinus Roelofs has exhibited numerous planar and polyhedral sculptures made up of two layers that weave over and under each other to form a single connected surface. I present a technique for creating sculptures in this style that are inspired by the geometric structure of Islamic star patterns. I first present a general approach for constructing interwoven two- layer sculptures, and then specialize it to Islamic patterns in the plane and on polyhedra. Finally, I describe a projection operation that bulges the elements of these designs into undulating dome shapes.
Extended Abstract
Bibtex
@inproceedings{bridges2017:71,
author = {Craig S. Kaplan},
title = {Interwoven Islamic Geometric Patterns},
pages = {71--78},
booktitle = {Proceedings of Bridges 2017: Mathematics, Art, Music, Architecture, Education, Culture},
year = {2017},
editor = {David Swart, Carlo H. S\'equin, and Krist\'of Fenyvesi},
isbn = {978-1-938664-22-9},
issn = {1099-6702},
publisher = {Tessellations Publishing},
address = {Phoenix, Arizona},
note = {Available online at \url{http://archive.bridgesmathart.org/2017/bridges2017-71.pdf}}
}
Used References
[1] J. Bourgoin. Arabic Geometrical Pattern and Design. Dover Publications, 1973.
[2] Paul Bourke. Pillow shape, 2000. http://paulbourke.net/geometry/pillow/, accessed February 1, 2016.
[3] Craig S. Kaplan and David H. Salesin. Islamic star patterns in absolute geometry. ACM Trans. Graph., 23(2):97–119, 2004.
[4] Rinus Roelofs. Connected holes. In Reza Sarhangi and Carlo H. Séquin, editors, Bridges Leeuwarden: Mathematics, Music, Art, Architecture, Culture, pages 29–38, London, 2008. Tarquin Publications. Available online at http://archive.bridgesmathart.org/2008/bridges2008-29.html.
[5] Rinus Roelofs. About weaving and helical holes. In George W. Hart and Reza Sarhangi, editors, Proceedings of Bridges 2010: Mathematics, Music, Art, Architecture, Culture, pages 75–84, Phoenix, Arizona, 2010. Tessellations Publishing. Available online at http://archive.bridgesmathart.org/2010/bridges2010-75.html.
[6] Rinus Roelofs. The elevation of coxeter’s infinite regular polyhedron 444444. In Eve Torrence, Bruce Torrence, Carlo Séquin, Douglas McKenna, Kristóf Fenyvesi, and Reza Sarhangi, editors, Proceedings of Bridges 2016: Mathematics, Music, Art, Architecture, Education, Culture, pages 33–40, Phoenix, Arizona, 2016. Tessellations Publishing. Available online at http://archive.bridgesmathart.org/2016/bridges2016-33.html.
[7] Saul Schleimer and Henry Segerman. Squares that look round: Transforming spherical images. In Eve Torrence, Bruce Torrence, Carlo Séquin, Douglas McKenna, Kristóf Fenyvesi, and Reza Sarhangi, editors, Proceedings of Bridges 2016: Mathematics, Music, Art, Architecture, Education, Culture, pages 15–24, Phoenix, Arizona, 2016. Tessellations Publishing. Available online at http://archive.bridgesmathart.org/2016/bridges2016-15.html.
Links
Full Text
http://archive.bridgesmathart.org/2017/bridges2017-71.pdf
