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		<title>Beautification of Islamic Patterns via Constraint Satisfaction - Versionsgeschichte</title>
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		<updated>2026-08-01T04:19:41Z</updated>
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		<id>http://de.evo-art.org/index.php?title=Beautification_of_Islamic_Patterns_via_Constraint_Satisfaction&amp;diff=33157&amp;oldid=prev</id>
		<title>Gubachelier: /* Bibtex */</title>
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				<updated>2016-12-27T19:45:39Z</updated>
		
		<summary type="html">&lt;p&gt;‎&lt;span dir=&quot;auto&quot;&gt;&lt;span class=&quot;autocomment&quot;&gt;Bibtex&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;
&lt;table class=&quot;diff diff-contentalign-left&quot; data-mw=&quot;interface&quot;&gt;
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				&lt;td colspan=&#039;2&#039; style=&quot;background-color: white; color:black; text-align: center;&quot;&gt;← Nächstältere Version&lt;/td&gt;
				&lt;td colspan=&#039;2&#039; style=&quot;background-color: white; color:black; text-align: center;&quot;&gt;Version vom 27. Dezember 2016, 19:45 Uhr&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l27&quot; &gt;Zeile 27:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Zeile 27:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&#039;diff-marker&#039;&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;#160;&amp;#160; publisher&amp;#160;  = {Tessellations Publishing},&lt;/div&gt;&lt;/td&gt;&lt;td class=&#039;diff-marker&#039;&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;#160;&amp;#160; publisher&amp;#160;  = {Tessellations Publishing},&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&#039;diff-marker&#039;&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;#160;&amp;#160; address&amp;#160; &amp;#160;  = {Phoenix, Arizona},&lt;/div&gt;&lt;/td&gt;&lt;td class=&#039;diff-marker&#039;&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;#160;&amp;#160; address&amp;#160; &amp;#160;  = {Phoenix, Arizona},&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
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&lt;tr&gt;&lt;td class=&#039;diff-marker&#039;&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;#160;&amp;#160; note&amp;#160; &amp;#160; &amp;#160; &amp;#160; = {Available online at \url{http://archive.bridgesmathart.org/2016/bridges2016-371.html}}&lt;/div&gt;&lt;/td&gt;&lt;td class=&#039;diff-marker&#039;&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;#160;&amp;#160; note&amp;#160; &amp;#160; &amp;#160; &amp;#160; = {Available online at \url{http://archive.bridgesmathart.org/2016/bridges2016-371.html}}&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
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&lt;tr&gt;&lt;td class=&#039;diff-marker&#039;&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;td class=&#039;diff-marker&#039;&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&#039;diff-marker&#039;&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;== Used References ==&lt;/div&gt;&lt;/td&gt;&lt;td class=&#039;diff-marker&#039;&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;== Used References ==&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>Gubachelier</name></author>	</entry>

	<entry>
		<id>http://de.evo-art.org/index.php?title=Beautification_of_Islamic_Patterns_via_Constraint_Satisfaction&amp;diff=33107&amp;oldid=prev</id>
		<title>Gubachelier: Die Seite wurde neu angelegt: „  == Reference == Yongquan Lu and Erik D. Demaine: Beautification of Islamic Patterns via Constraint Satisfaction. In: Bridges 2016, Pages 371–374.  …“</title>
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				<updated>2016-12-27T09:47:19Z</updated>
		
		<summary type="html">&lt;p&gt;Die Seite wurde neu angelegt: „  == Reference == Yongquan Lu and Erik D. Demaine: &lt;a href=&quot;/index.php?title=Beautification_of_Islamic_Patterns_via_Constraint_Satisfaction&quot; title=&quot;Beautification of Islamic Patterns via Constraint Satisfaction&quot;&gt;Beautification of Islamic Patterns via Constraint Satisfaction&lt;/a&gt;. In: &lt;a href=&quot;/index.php?title=Bridges_2016&quot; title=&quot;Bridges 2016&quot;&gt;Bridges 2016&lt;/a&gt;, Pages 371–374.  …“&lt;/p&gt;
&lt;p&gt;&lt;b&gt;Neue Seite&lt;/b&gt;&lt;/p&gt;&lt;div&gt;&lt;br /&gt;
&lt;br /&gt;
== Reference ==&lt;br /&gt;
Yongquan Lu and Erik D. Demaine: [[Beautification of Islamic Patterns via Constraint Satisfaction]]. In: [[Bridges 2016]], Pages 371–374. &lt;br /&gt;
&lt;br /&gt;
== DOI ==&lt;br /&gt;
&lt;br /&gt;
== Abstract ==&lt;br /&gt;
Islamic star patterns are traditionally drawn with compass-and-straightedge constructions, which yield geometrically&lt;br /&gt;
precise results, but are often unintuitive to work out. We present a more declarative paradigm for construction, where&lt;br /&gt;
users can draw patterns by hand and then apply constraints to improve and beautify the design. This system applies&lt;br /&gt;
concepts from CAD systems like geometric constraint satisfaction and numerical optimization in a highly symmetric&lt;br /&gt;
and aesthetic context. We exhibit some representative results generated by our system.&lt;br /&gt;
&lt;br /&gt;
== Extended Abstract ==&lt;br /&gt;
&lt;br /&gt;
== Bibtex == &lt;br /&gt;
 @inproceedings{bridges2016:371,&lt;br /&gt;
  author      = {Yongquan Lu and Erik D. Demaine},&lt;br /&gt;
  title       = {Beautification of Islamic Patterns via Constraint Satisfaction},&lt;br /&gt;
  pages       = {371--374},&lt;br /&gt;
  booktitle   = {Proceedings of Bridges 2016: Mathematics, Music, Art, Architecture, Education, Culture},&lt;br /&gt;
  year        = {2016},&lt;br /&gt;
  editor      = {Eve Torrence, Bruce Torrence, Carlo S\&amp;#039;equin, Douglas McKenna, Krist\&amp;#039;of Fenyvesi and Reza Sarhangi},&lt;br /&gt;
  isbn        = {978-1-938664-19-9},&lt;br /&gt;
  issn        = {1099-6702},&lt;br /&gt;
  publisher   = {Tessellations Publishing},&lt;br /&gt;
  address     = {Phoenix, Arizona},&lt;br /&gt;
  url         = {http://de.evo-art.org/index.php?title=Beautification_of_Islamic_Patterns_via_Constraint_Satisfaction},&lt;br /&gt;
  note        = {Available online at \url{http://archive.bridgesmathart.org/2016/bridges2016-371.html}}&lt;br /&gt;
 }&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
== Used References ==&lt;br /&gt;
[1] Eric Broug. Islamic Geometric Design. Thames &amp;amp; Hudson, 2013.&lt;br /&gt;
&lt;br /&gt;
[2] Craig S Kaplan. Computer generated islamic star patterns. In Proceedings of Bridges 2000, pages&lt;br /&gt;
105–112, 2000.&lt;br /&gt;
&lt;br /&gt;
[3] Yongquan Lu and Erik D. Demaine. A system for generating paper sliceform artwork. Symmetry:&lt;br /&gt;
Culture and Science, 26(2):203–215, 2015.&lt;br /&gt;
&lt;br /&gt;
[4] M. J. D. Powell. An efficient method for finding the minimum of a function of several variables without&lt;br /&gt;
calculating derivatives. The Computer Journal, 7(2):155–162, January 1964.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
== Links ==&lt;br /&gt;
=== Full Text === &lt;br /&gt;
http://archive.bridgesmathart.org/2016/bridges2016-371.pdf&lt;br /&gt;
&lt;br /&gt;
[[intern file]]&lt;br /&gt;
&lt;br /&gt;
=== Sonstige Links ===&lt;br /&gt;
http://archive.bridgesmathart.org/2016/bridges2016-371.html&lt;/div&gt;</summary>
		<author><name>Gubachelier</name></author>	</entry>

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