Mathematical Tools for Computer-Generated Ornamental Patterns
Inhaltsverzeichnis
Reference
Victor Ostromoukhov. Mathematical Tools for Computer-Generated Ornamental Patterns, In Electronic Publishing, Artistic Imaging and Digital Typography, Lecture Notes in Computer Science 1375, Springer Verlag, pp. 193-223, 1998
DOI
Abstract
This article presents mathematical tools for computer-generated ornamental patterns, with a particular attention payed to Islamic patterns. The article shows how, starting from a photo or a sketch of an ornamental figure, the designer analyzes its structure and produces the analytical representation of the pattern. This analytical representation in turn is used to produce a drawing which is integrated into a computer-generated virtual scene. The mathematical tools for analysis of ornamental patterns consist of a subset of tools usually used in the mathematical theory of tilings such as planar symmetry groups and Cayley diagrams. A simple and intuitive step-by-step guide is provided.
Extended Abstract
Bibtex
Used References
1. [Abas&Salman 1995] S.J. Abas & A.S. Salman, Symmetries of Islamic Geometrical Patterns, World Scientific, 1995
2. [Armstrong 1988] M.A. Armstrong, Groups and Symmetry, Springer Verlag, 1988.
3. [Bourgoin 1879] J. Bourgoin, Elements de l'art arabe, Fermin-Didot, Paris, 1879. Reprint available: Arabic Geometrical Pattern and Design, Dover, 1974.
4. [Budden 1972] F.J. Budden, The Fascination of Groups, Cambridge University Press, 1972.
5. [Emmer 1993] M. Emmer (ed.), The Visual mind: art and mathematics, MIT Press, 1993.
6. [Farmer 1996] D.W. Farmer, Groups and symmetry: a guide to discovering mathematics, Providence, AMS, 1996.
7. [Grossman&Magnus 1964] I. Grossman & W. Magnus, Groups and their Graphs, The Math- ematical Association of America, 1964.
8. [Grunbaum 1984] B. Grünbaum, The Emperor's New Clothes: Full Regalia, G string, or Nothing, The Mathematical Intelligencer, Vol. 6, No. 4, pp. 47-53, 1984.
9. [Grunbaum&Shephard 1987] B. Grünbaum, G. C. Shephard, Tilings and Patterns, W. H. Freeman and company, New York, 1987.
10. [Grunbaum&Shephard 1993] B. Grünbaum, G. C. Shephard, Interlaced Patterns in Islamic and Moorish Art, in [Emmer 1993], pp. 147-155.
11. [Hahn 1995] T. Hahn (ed.), International Tables for Crystallography, Fourth Edition, Vol. A, Reidl Publishing Co., 1995.
12. [Hargittai 1986] I. Hargittai (ed.), Symmetry, Pergamon Press, 1986.
13. [Hargittai 1989] I. Hargittai (ed.), Symmetry 2, Pergamon Press, 1989.
14. [Henry&Lonsdale 1952] N.F.M. Henry & K. Lonsdale (eds.), International Tables for X-Ray Crystallography, Vol. 1, Kynock Press, 1952.
15. [Shubnikov&Koptsik 1974] A. V. Shubnikov, V. A Koptsik, Symmetry in science and art, Ple- num Press, New York, 1974.
16. [Schattschneider 1978] D. Schattschneider, The Plane Symmetry Groups: Their Recognition and Notation, Amer. Math. Monthly, Vol. 85, pp.439 - 450, 1978.
17. [Washburn &Crowe 1988] D.K. Washburn & D.W. Crowe, Symmetries of culture: theory and practice of plane pattern, Donald W. Crow, Seattle: University of Washington Press, 1988.
18. [Weyl 1952] H. Weyl, Symmetry, Princeton University Press, 1952.
Links
Full Text
http://liris.cnrs.fr/victor.ostromoukhov/publications/pdf/RIDT98_Symmetry.pdf
