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	<title>Comments for The Lowly Mathematician</title>
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	<link>http://lowlymath.net</link>
	<description>The Disparate Notions of the Lowly Mathematician</description>
	<pubDate>Tue, 06 Jan 2009 15:34:34 +0000</pubDate>
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		<title>Comment on Peano&#8217;s Axioms IV: Advanced Functions and Integers by Ondra</title>
		<link>http://lowlymath.net/2007/peanos-axioms-iv-advanced-functions-and-integers/#comment-27</link>
		<dc:creator>Ondra</dc:creator>
		<pubDate>Sat, 29 Dec 2007 18:00:48 +0000</pubDate>
		<guid isPermaLink="false">http://lowlymath.wordpress.com/2007/07/28/peanos-axioms-iv-advanced-functions-and-integers/#comment-27</guid>
		<description>Well, it's interesting, but I can't see the whole code; it is cropped by the sidebar, at least in Konqueror and Firefox...</description>
		<content:encoded><![CDATA[<p>Well, it&#8217;s interesting, but I can&#8217;t see the whole code; it is cropped by the sidebar, at least in Konqueror and Firefox&#8230;</p>
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		<title>Comment on On Raytracers, The Quantum Kind by Joe Fredette</title>
		<link>http://lowlymath.net/2007/on-raytracers-the-quantum-kind/#comment-43</link>
		<dc:creator>Joe Fredette</dc:creator>
		<pubDate>Tue, 02 Oct 2007 19:25:00 +0000</pubDate>
		<guid isPermaLink="false">http://lowlymath.wordpress.com/2007/10/01/on-raytracers-the-quantum-kind/#comment-43</guid>
		<description>Brad,&lt;br/&gt;&lt;br/&gt; I certainly wasn't trying to imply that people who write raytracers are ignorant of optics. I'm pretty sure the two are mutally exclusive. It just seemed like something that had been passed over- and like you said, for good reason- since it was so slow. My goal was more to expose the issue to those who don't write/work on raytracers. People like me. :)&lt;br/&gt;&lt;br/&gt; Out of Curiosity, is your Raytracer publicly available? If so, where can I find it? I always enjoy reading through all the different approaches to the raytracing problem. &lt;br/&gt;&lt;br/&gt;~~Joe</description>
		<content:encoded><![CDATA[<p>Brad,</p>
<p> I certainly wasn&#8217;t trying to imply that people who write raytracers are ignorant of optics. I&#8217;m pretty sure the two are mutally exclusive. It just seemed like something that had been passed over- and like you said, for good reason- since it was so slow. My goal was more to expose the issue to those who don&#8217;t write/work on raytracers. People like me. <img src='http://lowlymath.net/wordpress/wp-includes/images/smilies/icon_smile.gif' alt=':)' class='wp-smiley' /> </p>
<p> Out of Curiosity, is your Raytracer publicly available? If so, where can I find it? I always enjoy reading through all the different approaches to the raytracing problem. </p>
<p>~~Joe</p>
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		<title>Comment on On Raytracers, The Quantum Kind by Brad</title>
		<link>http://lowlymath.net/2007/on-raytracers-the-quantum-kind/#comment-42</link>
		<dc:creator>Brad</dc:creator>
		<pubDate>Tue, 02 Oct 2007 18:46:00 +0000</pubDate>
		<guid isPermaLink="false">http://lowlymath.wordpress.com/2007/10/01/on-raytracers-the-quantum-kind/#comment-42</guid>
		<description>Most of what you talk about has been done in raytracers before.  People who write raytracers are not ignorant of optics, rather we concentrate on getting as realistic results as possible with as little machine time as needed - it is always a trade off.  Since most of the wave-like optic effects only appear rarely, we avoid calculating them if they take a long time.  Most of these (such as the slit and prism) can only be calculated using a light-forwards algorithm, and most everyone uses a camera-forwards algorithm, these rarely get implemented.&lt;br/&gt;&lt;br/&gt;Given time, I would like to add prism effects to my own raytracer, since I think they add a lot to some scenes.  I likely will never add the double slit effect, since I cannot image a scene I'd want to render that really needs it.</description>
		<content:encoded><![CDATA[<p>Most of what you talk about has been done in raytracers before.  People who write raytracers are not ignorant of optics, rather we concentrate on getting as realistic results as possible with as little machine time as needed - it is always a trade off.  Since most of the wave-like optic effects only appear rarely, we avoid calculating them if they take a long time.  Most of these (such as the slit and prism) can only be calculated using a light-forwards algorithm, and most everyone uses a camera-forwards algorithm, these rarely get implemented.</p>
<p>Given time, I would like to add prism effects to my own raytracer, since I think they add a lot to some scenes.  I likely will never add the double slit effect, since I cannot image a scene I&#8217;d want to render that really needs it.</p>
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		<title>Comment on On Raytracers, The Quantum Kind by Joe Fredette</title>
		<link>http://lowlymath.net/2007/on-raytracers-the-quantum-kind/#comment-41</link>
		<dc:creator>Joe Fredette</dc:creator>
		<pubDate>Tue, 02 Oct 2007 16:24:00 +0000</pubDate>
		<guid isPermaLink="false">http://lowlymath.wordpress.com/2007/10/01/on-raytracers-the-quantum-kind/#comment-41</guid>
		<description>*Points at Boojum*&lt;br/&gt;&lt;br/&gt;Look, someone who knows what there doing!&lt;br/&gt;&lt;br/&gt;Thats wicked cool, I'll have to read up on spectral rendering, Optics is fun :)</description>
		<content:encoded><![CDATA[<p>*Points at Boojum*</p>
<p>Look, someone who knows what there doing!</p>
<p>Thats wicked cool, I&#8217;ll have to read up on spectral rendering, Optics is fun <img src='http://lowlymath.net/wordpress/wp-includes/images/smilies/icon_smile.gif' alt=':)' class='wp-smiley' /></p>
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		<title>Comment on On Raytracers, The Quantum Kind by Boojum</title>
		<link>http://lowlymath.net/2007/on-raytracers-the-quantum-kind/#comment-40</link>
		<dc:creator>Boojum</dc:creator>
		<pubDate>Tue, 02 Oct 2007 04:26:00 +0000</pubDate>
		<guid isPermaLink="false">http://lowlymath.wordpress.com/2007/10/01/on-raytracers-the-quantum-kind/#comment-40</guid>
		<description>Ah yes.  Sorry for the double post, but I found the better paper I was originally looking for.  It was "3D graphics and the wave theory" in the SIGGRAPH '81.  I believe the algorithm described there could reproduce the double slit effects.</description>
		<content:encoded><![CDATA[<p>Ah yes.  Sorry for the double post, but I found the better paper I was originally looking for.  It was &#8220;3D graphics and the wave theory&#8221; in the SIGGRAPH &#8216;81.  I believe the algorithm described there could reproduce the double slit effects.</p>
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		<title>Comment on On Raytracers, The Quantum Kind by Boojum</title>
		<link>http://lowlymath.net/2007/on-raytracers-the-quantum-kind/#comment-39</link>
		<dc:creator>Boojum</dc:creator>
		<pubDate>Tue, 02 Oct 2007 04:19:00 +0000</pubDate>
		<guid isPermaLink="false">http://lowlymath.wordpress.com/2007/10/01/on-raytracers-the-quantum-kind/#comment-39</guid>
		<description>Hey there, found this via Reddit.  To paraphrase Fark, "I research ray tracing, so I'm really getting a kick out of these replies."&lt;br/&gt;&lt;br/&gt;Anyway, you're absolutely correct that standard ray tracing is based around classical optics.  Specifically, it's based on the branch called "geometric optics."&lt;br/&gt;&lt;br/&gt;As for what you describe about ray tracing based on the wavelengths, we call that "spectral rendering".  There are various ways to handle the representation of the spectra for it.  But once you have that, the conversion to RGB is fairly well known.  It basically involves integrating the product of the computed spectra for the ray with each of the CIE tristimulus curves to reduce it to a color in the CIE XYZ color space.  From there, ignoring color calibration, it's a simple linear transformation to get to one of the RGB color spaces.&lt;br/&gt;&lt;br/&gt;In addition to the prismatic dispersion, spectral renderers can often handle things like chromatic aberration, thin film interference, and some degree of diffraction grating type effects.&lt;br/&gt;&lt;br/&gt;As for the anonymous commenters wave tracer idea, there's been a tiny amount of work in that area.  I know there was a paper in the SIGGRAPH 94 about simulating wavefronts to compute global illumination.  More recently, this year's SIGGRAPH had a paper on eikonal rendering which seems to be related.  Neither one will really reproduce the double slit effect, but they are at least a tad closer than the standard geometric optics approach.</description>
		<content:encoded><![CDATA[<p>Hey there, found this via Reddit.  To paraphrase Fark, &#8220;I research ray tracing, so I&#8217;m really getting a kick out of these replies.&#8221;</p>
<p>Anyway, you&#8217;re absolutely correct that standard ray tracing is based around classical optics.  Specifically, it&#8217;s based on the branch called &#8220;geometric optics.&#8221;</p>
<p>As for what you describe about ray tracing based on the wavelengths, we call that &#8220;spectral rendering&#8221;.  There are various ways to handle the representation of the spectra for it.  But once you have that, the conversion to RGB is fairly well known.  It basically involves integrating the product of the computed spectra for the ray with each of the CIE tristimulus curves to reduce it to a color in the CIE XYZ color space.  From there, ignoring color calibration, it&#8217;s a simple linear transformation to get to one of the RGB color spaces.</p>
<p>In addition to the prismatic dispersion, spectral renderers can often handle things like chromatic aberration, thin film interference, and some degree of diffraction grating type effects.</p>
<p>As for the anonymous commenters wave tracer idea, there&#8217;s been a tiny amount of work in that area.  I know there was a paper in the SIGGRAPH 94 about simulating wavefronts to compute global illumination.  More recently, this year&#8217;s SIGGRAPH had a paper on eikonal rendering which seems to be related.  Neither one will really reproduce the double slit effect, but they are at least a tad closer than the standard geometric optics approach.</p>
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		<title>Comment on On Raytracers, The Quantum Kind by Joe Fredette</title>
		<link>http://lowlymath.net/2007/on-raytracers-the-quantum-kind/#comment-38</link>
		<dc:creator>Joe Fredette</dc:creator>
		<pubDate>Mon, 01 Oct 2007 21:57:00 +0000</pubDate>
		<guid isPermaLink="false">http://lowlymath.wordpress.com/2007/10/01/on-raytracers-the-quantum-kind/#comment-38</guid>
		<description>Alfredo, &lt;br/&gt;&lt;br/&gt;Hmm, I didn't know Povray had a dispersion effect- I guess thats just the nature of such a big system. That said- thats wicked cool. WRT The Prism Effect, I suppose it just seemed counterintuitive to me that a wave could slow down, to be honest- I have a hard time grasping how waves (that is, an infinitely long wavetrain) can move at all. Back with dispersion, I'll have to read up on it some. Thanks!</description>
		<content:encoded><![CDATA[<p>Alfredo, </p>
<p>Hmm, I didn&#8217;t know Povray had a dispersion effect- I guess thats just the nature of such a big system. That said- thats wicked cool. WRT The Prism Effect, I suppose it just seemed counterintuitive to me that a wave could slow down, to be honest- I have a hard time grasping how waves (that is, an infinitely long wavetrain) can move at all. Back with dispersion, I&#8217;ll have to read up on it some. Thanks!</p>
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		<title>Comment on On Raytracers, The Quantum Kind by Anonymous</title>
		<link>http://lowlymath.net/2007/on-raytracers-the-quantum-kind/#comment-37</link>
		<dc:creator>Anonymous</dc:creator>
		<pubDate>Mon, 01 Oct 2007 19:55:00 +0000</pubDate>
		<guid isPermaLink="false">http://lowlymath.wordpress.com/2007/10/01/on-raytracers-the-quantum-kind/#comment-37</guid>
		<description>Since taking difeq, I've thought it would be cool to try to write a sort of "wave tracer", rendering the scene using the &lt;a HREF="http://en.wikipedia.org/wiki/Wave_equation" REL="nofollow"&gt;wave equation&lt;/a&gt;.  Of course, I'm also pretty sure I'm nowhere near smart enough to do it.&lt;br/&gt;&lt;br/&gt;I don't know if that gives you anything as far as rendering prisms (I think you'd probably still trace only one wavelength at a time...), but it would give you a working double slit experiment.</description>
		<content:encoded><![CDATA[<p>Since taking difeq, I&#8217;ve thought it would be cool to try to write a sort of &#8220;wave tracer&#8221;, rendering the scene using the <a HREF="http://en.wikipedia.org/wiki/Wave_equation" REL="nofollow">wave equation</a>.  Of course, I&#8217;m also pretty sure I&#8217;m nowhere near smart enough to do it.</p>
<p>I don&#8217;t know if that gives you anything as far as rendering prisms (I think you&#8217;d probably still trace only one wavelength at a time&#8230;), but it would give you a working double slit experiment.</p>
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		<title>Comment on On Raytracers, The Quantum Kind by Alfredo</title>
		<link>http://lowlymath.net/2007/on-raytracers-the-quantum-kind/#comment-36</link>
		<dc:creator>Alfredo</dc:creator>
		<pubDate>Mon, 01 Oct 2007 18:45:00 +0000</pubDate>
		<guid isPermaLink="false">http://lowlymath.wordpress.com/2007/10/01/on-raytracers-the-quantum-kind/#comment-36</guid>
		<description>Actually, you can simulate dispersion in POV-Ray. See "dispersion" in the documentation. &lt;br/&gt;&lt;br/&gt;Of course, POV-Ray works by ray tracing. It wouldn't make much sense to render a macroscopic scene by adding countless waves.&lt;br/&gt;&lt;br/&gt;It's perfectly possible to explain Snell's law with a wave model of light. See Huygens' Principle. Certainly the speed of a wave can vary locally.</description>
		<content:encoded><![CDATA[<p>Actually, you can simulate dispersion in POV-Ray. See &#8220;dispersion&#8221; in the documentation. </p>
<p>Of course, POV-Ray works by ray tracing. It wouldn&#8217;t make much sense to render a macroscopic scene by adding countless waves.</p>
<p>It&#8217;s perfectly possible to explain Snell&#8217;s law with a wave model of light. See Huygens&#8217; Principle. Certainly the speed of a wave can vary locally.</p>
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		<title>Comment on Programming Lanugages Part II: Beginner Friendly by Anonymous</title>
		<link>http://lowlymath.net/2007/programming-lanugages-part-ii-beginner-friendly/#comment-16</link>
		<dc:creator>Anonymous</dc:creator>
		<pubDate>Sun, 30 Sep 2007 09:13:00 +0000</pubDate>
		<guid isPermaLink="false">http://lowlymath.wordpress.com/2007/06/02/programming-lanugages-part-ii-beginner-friendly/#comment-16</guid>
		<description>I believe what you are looking for is Hackity Hack&lt;br/&gt;&lt;br/&gt;http://hacketyhack.net/&lt;br/&gt;&lt;br/&gt;It fulfills all your criterea.&lt;br/&gt;&lt;br/&gt;Check it out.</description>
		<content:encoded><![CDATA[<p>I believe what you are looking for is Hackity Hack</p>
<p><a href="http://hacketyhack.net/" rel="nofollow">http://hacketyhack.net/</a></p>
<p>It fulfills all your criterea.</p>
<p>Check it out.</p>
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