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		<title>Aesthetic Placement of Points Using Generalized Lloyd Relaxation - Versionsgeschichte</title>
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		<updated>2026-05-18T04:27:16Z</updated>
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	<entry>
		<id>http://de.evo-art.org/index.php?title=Aesthetic_Placement_of_Points_Using_Generalized_Lloyd_Relaxation&amp;diff=31957&amp;oldid=prev</id>
		<title>Gubachelier am 8. November 2015 um 17:35 Uhr</title>
		<link rel="alternate" type="text/html" href="http://de.evo-art.org/index.php?title=Aesthetic_Placement_of_Points_Using_Generalized_Lloyd_Relaxation&amp;diff=31957&amp;oldid=prev"/>
				<updated>2015-11-08T17:35:07Z</updated>
		
		<summary type="html">&lt;p&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 8. November 2015, 17:35 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-l13&quot; &gt;Zeile 13:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Zeile 13:&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;/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;== Bibtex == &amp;#160;&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;== Bibtex == &amp;#160;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot;&gt;&amp;#160;&lt;/td&gt;&lt;td class=&#039;diff-marker&#039;&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt; @inproceedings{Deussen:2009:APP:2381286.2381308,&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot;&gt;&amp;#160;&lt;/td&gt;&lt;td class=&#039;diff-marker&#039;&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt; author = {Deussen, Oliver},&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot;&gt;&amp;#160;&lt;/td&gt;&lt;td class=&#039;diff-marker&#039;&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt; title = {Aesthetic Placement of Points Using Generalized Lloyd Relaxation},&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot;&gt;&amp;#160;&lt;/td&gt;&lt;td class=&#039;diff-marker&#039;&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt; booktitle = {Proceedings of the Fifth Eurographics Conference on Computational Aesthetics in Graphics, Visualization and Imaging},&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot;&gt;&amp;#160;&lt;/td&gt;&lt;td class=&#039;diff-marker&#039;&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt; series = {Computational Aesthetics&amp;#039;09},&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot;&gt;&amp;#160;&lt;/td&gt;&lt;td class=&#039;diff-marker&#039;&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt; year = {2009},&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot;&gt;&amp;#160;&lt;/td&gt;&lt;td class=&#039;diff-marker&#039;&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt; isbn = {978-3-905674-17-0},&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot;&gt;&amp;#160;&lt;/td&gt;&lt;td class=&#039;diff-marker&#039;&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt; location = {Victoria, British Columbia, Canada},&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot;&gt;&amp;#160;&lt;/td&gt;&lt;td class=&#039;diff-marker&#039;&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt; pages = {123--128},&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot;&gt;&amp;#160;&lt;/td&gt;&lt;td class=&#039;diff-marker&#039;&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt; numpages = {6},&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot;&gt;&amp;#160;&lt;/td&gt;&lt;td class=&#039;diff-marker&#039;&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt; url = {http://dx.doi.org/10.2312/COMPAESTH/COMPAESTH09/123-128, http://de.evo-art.org/index.php?title=Aesthetic_Placement_of_Points_Using_Generalized_Lloyd_Relaxation },&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot;&gt;&amp;#160;&lt;/td&gt;&lt;td class=&#039;diff-marker&#039;&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt; doi = {10.2312/COMPAESTH/COMPAESTH09/123-128},&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot;&gt;&amp;#160;&lt;/td&gt;&lt;td class=&#039;diff-marker&#039;&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt; acmid = {2381308},&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot;&gt;&amp;#160;&lt;/td&gt;&lt;td class=&#039;diff-marker&#039;&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt; publisher = {Eurographics Association},&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot;&gt;&amp;#160;&lt;/td&gt;&lt;td class=&#039;diff-marker&#039;&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt; address = {Aire-la-Ville, Switzerland, Switzerland},&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot;&gt;&amp;#160;&lt;/td&gt;&lt;td class=&#039;diff-marker&#039;&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt; } &lt;/ins&gt;&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;/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=Aesthetic_Placement_of_Points_Using_Generalized_Lloyd_Relaxation&amp;diff=1926&amp;oldid=prev</id>
		<title>Gbachelier: Die Seite wurde neu angelegt: „  == Reference == Oliver Deussen: Aesthetic Placement of Points Using Generalized Lloyd Relaxation. In: Oliver Deussen, Peter Hall (Eds.): Eurographics Worksho…“</title>
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				<updated>2014-12-02T11:49:25Z</updated>
		
		<summary type="html">&lt;p&gt;Die Seite wurde neu angelegt: „  == Reference == Oliver Deussen: Aesthetic Placement of Points Using Generalized Lloyd Relaxation. In: Oliver Deussen, Peter Hall (Eds.): Eurographics Worksho…“&lt;/p&gt;
&lt;p&gt;&lt;b&gt;Neue Seite&lt;/b&gt;&lt;/p&gt;&lt;div&gt;&lt;br /&gt;
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== Reference ==&lt;br /&gt;
Oliver Deussen: Aesthetic Placement of Points Using Generalized Lloyd Relaxation. In: Oliver Deussen, Peter Hall (Eds.): Eurographics Workshop on Computational Aesthetics, 2009. 123-128 &lt;br /&gt;
&lt;br /&gt;
== DOI ==&lt;br /&gt;
http://dx.doi.org/10.2312/COMPAESTH/COMPAESTH09/123-128 &lt;br /&gt;
&lt;br /&gt;
== Abstract ==&lt;br /&gt;
In this paper we describe a computational method for producing aesthetically pleasing distributions of disks on a canvas. The positions of the disks are initially given at random and are moved into interesting configurations by means of a local optimization routine. The configurations are computed by a Voronoi-cell based optimization algorithm (Lloyd&amp;#039;s relaxation method). We extend this method in a way that not only evenly spaced but also clustered point sets can be produced. This is done by inverting the iterative step of the optimization algorithm. We define an energy term and show that for a certain amount of energy interesting configurations appear. This is evaluated in a small user study.&lt;br /&gt;
&lt;br /&gt;
== Extended Abstract ==&lt;br /&gt;
&lt;br /&gt;
== Bibtex == &lt;br /&gt;
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== Used References ==&lt;br /&gt;
Qiang Du , Vance Faber , Max Gunzburger, Centroidal Voronoi Tessellations: Applications and Algorithms, SIAM Review, v.41 n.4, p.637-676, Dec. 1999  http://dx.doi.org/10.1137/S0036144599352836&lt;br /&gt;
DEUSSEN O., HILLER S., VAN OVERVELD K., STROTHOTTE T.: Floating points: a method for computing stipple drawings. Computer Graphics Forum 19, 4 (2000), 40-51 (Eurographics 2000 Conf. Proc.).&lt;br /&gt;
&lt;br /&gt;
Neil A. Dodgson, Regularity and randomness in Bridget Riley&amp;#039;s early Op art, Proceedings of the Fourth Eurographics conference on Computational Aesthetics in Graphics, Visualization and Imaging, June 18-20, 2008, Lisbon, Portugal  http://dx.doi.org/10.2312/COMPAESTH/COMPAESTH08/107-114&lt;br /&gt;
&lt;br /&gt;
EYSENCK M., KEANE M.: Cognitive Psychology. Psychology Press, 2000.&lt;br /&gt;
&lt;br /&gt;
A. Gersho, Asymptotically optimal block quantization, IEEE Transactions on Information Theory, v.25 n.4, p.373-380, July 1979  http://dx.doi.org/10.1109/TIT.1979.1056067&lt;br /&gt;
&lt;br /&gt;
Johannes Kopf , Daniel Cohen-Or , Oliver Deussen , Dani Lischinski, Recursive Wang tiles for real-time blue noise, ACM Transactions on Graphics (TOG), v.25 n.3, July 2006  http://doi.acm.org/10.1145/1141911.1141916&lt;br /&gt;
	&lt;br /&gt;
LAUER D.: Design Basics. Wadsworth Publishing, 1999.&lt;br /&gt;
&lt;br /&gt;
D. Newman, The hexagon theorem, IEEE Transactions on Information Theory, v.28 n.2, p.137-139, March 1982  http://dx.doi.org/10.1109/TIT.1982.1056492&lt;br /&gt;
&lt;br /&gt;
SAW J.: Design notes. http://daphne.palomar.edu/design/gestalt.html, 2000.&lt;br /&gt;
&lt;br /&gt;
STOER J., BULIRSCH R.: Introduction to numerical analysis. Springer-Verlag, 1980.&lt;br /&gt;
	&lt;br /&gt;
Adrian Secord, Weighted Voronoi stippling, Proceedings of the 2nd international symposium on Non-photorealistic animation and rendering, June 03-05, 2002, Annecy, France  http://doi.acm.org/10.1145/508530.508537&lt;br /&gt;
&lt;br /&gt;
SMITH J.: Recent developments in numerical integration. J. Dynam. Sys., Measurement and Control 96, Ser. G-1, 1 (1974), 61-70. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
== Links ==&lt;br /&gt;
=== Full Text === &lt;br /&gt;
http://www.informatik.uni-konstanz.de/index.php?eID=tx_nawsecuredl&amp;amp;u=0&amp;amp;g=0&amp;amp;t=1417346778&amp;amp;hash=c15452eeda582f1002b140dcf262d397c2e53340&amp;amp;file=fileadmin/informatik/ag-deussen/2009/Deussen-2009-APoPUSLR.pdf&lt;br /&gt;
&lt;br /&gt;
[[intern file]]&lt;br /&gt;
&lt;br /&gt;
=== Sonstige Links ===&lt;br /&gt;
http://dl.acm.org/citation.cfm?id=2381286.2381308&amp;amp;coll=DL&amp;amp;dl=GUIDE&amp;amp;CFID=588525319&amp;amp;CFTOKEN=29804931&lt;/div&gt;</summary>
		<author><name>Gbachelier</name></author>	</entry>

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