http://blog.mmacklin.com/tags/fog-volumes/ Recent content in Fog Volumes on Miles Macklin Hugo -- gohugo.io en-us © 2019 Miles Macklin Fri, 11 Jun 2010 03:24:11 +0000 http://blog.mmacklin.com/2010/06/10/faster-fog/ Fri, 11 Jun 2010 03:24:11 +0000 http://blog.mmacklin.com/2010/06/10/faster-fog/ Cedrick at Lucas suggested some nice optimisations for the in-scattering equation I posted last time. I had left off at: \[L_{s} = \frac{\sigma_{s}I}{v}( \tan^{-1}\left(\frac{d+b}{v}\right) - \tan^{-1}\left(\frac{b}{v}\right) )\] But we can remove one of the two inverse trigonometric functions by using the following identity: \[\tan^{-1}x - \tan^{-1}y = \tan^{-1}\frac{x-y}{1+xy}\] Which simplifies the expression for $L_{s}$ to: \[L_{s} = \frac{\sigma_{s}I}{v}( \tan^{-1}\frac{x-y}{1+xy} )\] With $x$ and $y$ being replaced by: \[\begin{array}{lcl} x = \frac{d+b}{v} \\ y = \frac{b}{v}\end{array}\] http://blog.mmacklin.com/2010/05/29/in-scattering-demo/ Sat, 29 May 2010 23:32:07 +0000 http://blog.mmacklin.com/2010/05/29/in-scattering-demo/ This demo shows an analytic solution to the differential in-scattering equation for light in participating media. It's a similar but simplified version of equations found in[1], [2] and as I recently discovered [3]. However I thought showing the derivation might be interesting for some out there, plus it was a good excuse for me to brush up on my \(\LaTeX\). You might notice I also updated the site's theme, unfortunately you need a white background to make wordpress.