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## [Ost98]  Mathematical Tools for Computer-Generated Ornamental Patterns

 Ostromoukhov:1998:MTC (In a collection) Author(s) Ostromoukhov V. Title « Mathematical Tools for Computer-Generated Ornamental Patterns » In Electronic Publishing, Artistic Imaging and Digital Typography Series Lecture Notes in Computer Science Editor(s) Roger D. Hersch and Jacques André and Heather Brown Volume 1375 Page(s) 193--223 Year 1998 Publisher Springer-Verlag Address Berlin $·$ Heidelberg $·$ New York URL http://www.iro.umontreal.ca/~ostrom/publications/abstracts.html#RIDT98_Symmetry Editor(s) Roger D. Hersch and Jacques André and Heather Brown

 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.

 BibTeX code ``````@incollection{Ostromoukhov:1998:MTC, optnote = {}, author = {Victor Ostromoukhov}, optkey = {}, series = LNICS, optannote = {}, opttype = {}, editor = {Roger D. Hersch and Jacques Andr{\'e} and Heather Brown}, optedition = {}, url = {http://www.iro.umontreal.ca/~ostrom/publications/abstracts.html#RIDT98_Symmetry}, localfile = {papers/Ostromoukhov.1998.MTC.pdf}, optchapter = {}, address = SpringerAdr, publisher = SpringerPub, optmonth = {}, doi = {http://www.springerlink.com/link.asp?id=vfg6n1t19dmvnd1j}, volume = {1375}, optcrossref = {}, booktitle = {{E}lectronic {P}ublishing, {A}rtistic {I}maging and {D}igital {T}ypography}, optstatus = {url doi abstract}, optnumber = {}, 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.}, title = {{M}athematical {T}ools for {C}omputer-{G}enerated {O}rnamental {P}atterns}, year = {1998}, pages = {193--223}, }``````

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