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<html><head><title>Wavelets for Computer Graphics</title></head><body bgcolor="#ffffff" text="#000000"link="#0000ee" vlink="#551a8b" alink="#ff0000"><center><h1>Wavelets for Computer Graphics</h1><img src="icon.gif" tppabs="http://grail.cs.washington.edu/projects/wavelets/icon.gif" width=49 height=49><p></center><hr><h2>Overview</h2>Wavelets are a mathematical tool for hierarchically decomposingfunctions. They allow any function to be described in terms of acoarse overall shape, plus details that range from broad to narrow.As the figures below illustrate, wavelets can be applied to a wide varietyof objects used in graphics, including images, curves, surfaces, and thesolutions to lighting simulations.<p><center><table cellpadding=3 cellspacing=3> <tr align=center valign=top> <td bgcolor="#cccccc"><b>Images</b></td> <td><img width=128 height=128 src="mona-20.jpg" tppabs="http://grail.cs.washington.edu/projects/wavelets/mona-20.jpg"><br> 20 coefficients</td> <td><img width=128 height=128 src="mona-200.jpg" tppabs="http://grail.cs.washington.edu/projects/wavelets/mona-200.jpg"><br> 200 coefficients</td> <td><img width=128 height=128 src="mona-orig.jpg" tppabs="http://grail.cs.washington.edu/projects/wavelets/mona-orig.jpg"><br> 16,000 coefficients</td> </tr> <tr><td></td></tr> <tr align=center valign=top> <td bgcolor="#cccccc"><b>Curves</b></td> <td><img width=128 height=59 src="hello1.gif" tppabs="http://grail.cs.washington.edu/projects/wavelets/hello1.gif"><br> level 3.1</td> <td><img width=128 height=59 src="hello2.gif" tppabs="http://grail.cs.washington.edu/projects/wavelets/hello2.gif"><br> level 5.4</td> <td><img width=128 height=59 src="hello3.gif" tppabs="http://grail.cs.washington.edu/projects/wavelets/hello3.gif"><br> level 8.0</td> </tr> <tr><td></td></tr> </tr> <tr align=center valign=top> <td bgcolor="#cccccc"><b>Surfaces</b></td> <td><img width=128 height=178 src="dino1.gif" tppabs="http://grail.cs.washington.edu/projects/wavelets/dino1.gif"><br> 229 triangles</td> <td><img width=128 height=178 src="dino2.gif" tppabs="http://grail.cs.washington.edu/projects/wavelets/dino2.gif"><br> 2,000 triangles</td> <td><img width=128 height=178 src="dino3.gif" tppabs="http://grail.cs.washington.edu/projects/wavelets/dino3.gif"><br> 10,000 triangles</td> </tr> <tr><td></td></tr> </tr> <tr align=center valign=top> <td bgcolor="#cccccc"><b>Simulation</b></td> <td><img width=128 height=80 src="illum1.gif" tppabs="http://grail.cs.washington.edu/projects/wavelets/illum1.gif"><br> no refinement</td> <td><img width=128 height=80 src="illum2.gif" tppabs="http://grail.cs.washington.edu/projects/wavelets/illum2.gif"><br> 6 refinements</td> <td><img width=128 height=80 src="illum3.gif" tppabs="http://grail.cs.washington.edu/projects/wavelets/illum3.gif"><br> final gather</td> </tr></table><p></center><hr><h2>Publications</h2>Although a great deal has been written about wavelets, most of theliterature uses terminology from signal processing and pure mathematics.Our aim in writing the tutorial article and the book listed below was toprovide a consistent theoretical framework for those working in computergraphics, as well as examples of graphics applications that make use ofwavelets.<p><table cellspacing=5> <tr valign=center> <td align=center><a href="index-1.htm" tppabs="http://grail.cs.washington.edu/projects/wavelets/article/"><img src="page1.gif" tppabs="http://grail.cs.washington.edu/projects/wavelets/article/page1.gif" alt="Article" width=82 height=102 border=0><br> <b>The Article</b><p></a></td> <td colspan=3 align=left><b>Wavelets for Computer Graphics: A Primer</b>. Eric J. Stollnitz, Tony D. DeRose, and David H. Salesin. <i>IEEE Computer Graphics and Applications</i>, 15(3):76-84, May 1995 (part 1), and 15(4):75-85, July 1995 (part 2).<p></td> </tr> <tr valign=center> <td></td> <td align=center><a href="index-2.htm" tppabs="http://grail.cs.washington.edu/projects/wavelets/book/"><img src="cover.gif" tppabs="http://grail.cs.washington.edu/projects/wavelets/book/cover.gif" alt="Book" width=82 height=102 border=0><br> <b>The Book</b><p></a></td> <td colspan=2 align=left><b><i>Wavelets for Computer Graphics: Theory and Applications</i></b>. Eric J. Stollnitz, Tony D. DeRose, and David H. Salesin. Morgan Kaufmann, San Francisco, 1996.<p></td> </tr> <tr valign=center> <td></td> <td></td> <td align=center><a href="matlab.html" tppabs="http://grail.cs.washington.edu/projects/wavelets/book/matlab.html"> <img src="matlab.gif" tppabs="http://grail.cs.washington.edu/projects/wavelets/book/matlab.gif" alt="Matlab" width=82 height=102 border=0><br> <b>Matlab</b><p></a></td> <td align=left>Matlab code used to generate endpoint-interpolating B-spline wavelet matrices and figures for the book and the <i>IEEE CG&A</i> article.<p></td> </tr></table><hr><h2>The Authors</h2><center><table cellpadding=10 cellspacing=10> <tr align=center valign=top> <td><a href="javascript:if(confirm('http://www.amath.washington.edu/~stoll/ \n\nThis file was not retrieved by Teleport Pro, because it is addressed on a domain or path outside the boundaries set for its Starting Address. \n\nDo you want to open it from the server?'))window.location='http://www.amath.washington.edu/~stoll/'" tppabs="http://www.amath.washington.edu/~stoll/"> <img src="eric.gif" tppabs="http://grail.cs.washington.edu/projects/wavelets/eric.gif" width=80 height=80 border=0 alt="Eric"><br> <b>Eric Stollnitz</b></a></td> <td><img src="tony.gif" tppabs="http://grail.cs.washington.edu/projects/wavelets/tony.gif" width=80 height=80 border=0 alt="Tony"><br> <b>Tony DeRose</b></td> <td><a href="javascript:if(confirm('http://www.cs.washington.edu/homes/salesin/ \n\nThis file was not retrieved by Teleport Pro, because it is addressed on a domain or path outside the boundaries set for its Starting Address. \n\nDo you want to open it from the server?'))window.location='http://www.cs.washington.edu/homes/salesin/'" tppabs="http://www.cs.washington.edu/homes/salesin/"> <img src="david.gif" tppabs="http://grail.cs.washington.edu/projects/wavelets/david.gif" width=80 height=80 border=0 alt="David"><br> <b>David Salesin</b></a></td> </tr></table></center><hr><h2>Related Work</h2>Here's a <a href="related.html" tppabs="http://grail.cs.washington.edu/projects/wavelets/related.html">list of other publications</a> involvingwavelets and graphics, all by members of the University of Washington'sgraphics group.<p>More coprehensive information about wavelets can be obtained from <ahref="javascript:if(confirm('http://www.wavelet.org/ \n\nThis file was not retrieved by Teleport Pro, because it is addressed on a domain or path outside the boundaries set for its Starting Address. \n\nDo you want to open it from the server?'))window.location='http://www.wavelet.org/'" tppabs="http://www.wavelet.org/">Wavelet Digest</a> and MathSoft's <ahref="javascript:if(confirm('http://www.mathsoft.com/wavelets.html \n\nThis file was not retrieved by Teleport Pro, because it is addressed on a domain or path outside the boundaries set for its Starting Address. \n\nDo you want to open it from the server?'))window.location='http://www.mathsoft.com/wavelets.html'" tppabs="http://www.mathsoft.com/wavelets.html">Wavelet Resources</a>.<p><hr><table width=100% cellpadding=0 cellspacing=0> <tr> <td align=left><font size=-1> <a href="mailto:stoll@amath.washington.edu"> <stoll@amath.washington.edu></a> </font></td> <td align=right><font size=-1><!-- hhmts start -->4:01 pm, 1 October 1998<!-- hhmts end --> </font></td> </tr></table></body></html>
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