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	<title>A Party to the World &#187; computational geometry</title>
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		<title>Octtrees For Space Rasterization</title>
		<link>http://dan.lecocq.us/wordpress/2009/04/30/octtrees-for-space-rasterization/</link>
		<comments>http://dan.lecocq.us/wordpress/2009/04/30/octtrees-for-space-rasterization/#comments</comments>
		<pubDate>Thu, 30 Apr 2009 21:49:09 +0000</pubDate>
		<dc:creator>Dan</dc:creator>
				<category><![CDATA[computer science]]></category>
		<category><![CDATA[computational geometry]]></category>
		<category><![CDATA[graphics]]></category>
		<category><![CDATA[octtree]]></category>
		<category><![CDATA[ray tracing]]></category>

		<guid isPermaLink="false">http://dan.lecocq.us/wordpress/?p=525</guid>
		<description><![CDATA[Raytracing is slow. Incredibly slow. Painfully slow. That&#8217;s because you&#8217;ve got to check a lot of things to accurately determine what you&#8217;re seeing, if it&#8217;s in shadow, if it reflects off of something, etc., so it helps quite a bit to be able to get an idea beforehand of where everything is. Enter octtrees. We&#8217;ve [...]]]></description>
			<content:encoded><![CDATA[<p>Raytracing is slow.  Incredibly slow.  <em>Painfully</em> slow.  That&#8217;s because you&#8217;ve got to check a lot of things to accurately determine what you&#8217;re seeing, if it&#8217;s in shadow, if it reflects off of something, etc., so it helps quite a bit to be able to get an idea beforehand of where everything is.  Enter octtrees.</p>
<p>We&#8217;ve got a picture of a model (in this case, the Stanford bunny model).  It consists of thousands of tiny triangles that make a surface.  Then, imagine a cube surrounding the entire model.  If there are two many triangles in that cube, you cut the cube in to eight smaller cubes, and repeat.  What this build is a tree where &#8220;busy&#8221; portions of the space get divided more.</p>
<p>And now for pretty pictures:<br />
<div id="attachment_526" class="wp-caption aligncenter" style="width: 310px"><a href="http://dan.lecocq.us/wordpress/wp-content/uploads/2009/04/bunny.png"><img src="http://dan.lecocq.us/wordpress/wp-content/uploads/2009/04/bunny-300x291.png" alt="The bunny on its own.  There are tricks to smooth it out, but I left it highly triangulated to better represent the idea." title="bunny" width="300" height="291" class="size-medium wp-image-526" /></a><p class="wp-caption-text">The bunny on its own.  There are tricks to smooth it out, but I left it highly triangulated to better represent the idea.</p></div><br />
<div id="attachment_527" class="wp-caption aligncenter" style="width: 310px"><a href="http://dan.lecocq.us/wordpress/wp-content/uploads/2009/04/bunnytree.png"><img src="http://dan.lecocq.us/wordpress/wp-content/uploads/2009/04/bunnytree-300x291.png" alt="Bunny with balanced wireframe octtree around it." title="bunnytree" width="300" height="291" class="size-medium wp-image-527" /></a><p class="wp-caption-text">Bunny with balanced wireframe octtree around it.</p></div><br />
<div id="attachment_528" class="wp-caption aligncenter" style="width: 310px"><a href="http://dan.lecocq.us/wordpress/wp-content/uploads/2009/04/bunnytreeside.png"><img src="http://dan.lecocq.us/wordpress/wp-content/uploads/2009/04/bunnytreeside-300x291.png" alt="Profile of the bunny with a very deep octtree." title="bunnytreeside" width="300" height="291" class="size-medium wp-image-528" /></a><p class="wp-caption-text">Profile of the bunny with a very deep octtree.</p></div></p>
<p>I&#8217;m finishing up the implementation, and then I&#8217;ll be using it as part of my octtree as a intersection speedup.</p>
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