most recent 30 from http://mathoverflow.net 2013-05-21T04:29:41Z http://mathoverflow.net/feeds/question/18520 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/18520/triangular-bounding-volumes Cheery 2010-03-17T21:03:04Z 2010-03-17T21:49:40Z

<p>I've come up with an alternative for beziers that might be easier to ray-trace, perhaps even though a plain vertex shader. Though I'm missing a function there.</p> <p>I need to find the parametric surface equation from the surface normals I have for edge vertices. I also have to know it's peak and valley so I can constraint the depth of my bounding triangle.</p> <p><img src="http://img89.imageshack.us/img89/9489/tribovols.png" alt="alt text"></p> <p>Image explains the overall idea: I build a bounding-volume from a control triangle. Then apply a function to each parametric coordinate of the triangle (s+t+u=1 where s,t,u >= 0) to get the height coordinate for that certain point.</p> <p>Simply put, it produces a procedurally generated height-map for the triangle's surface. I just need to find a function that generates the height-map so I can make it work.</p> <p>I've put the question up there as well: <a href="http://stackoverflow.com/questions/2465685/triangular-bounding-volumes">http://stackoverflow.com/questions/2465685/triangular-bounding-volumes</a></p>