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You are not logged in. #1 20070809 08:03:44
rendering polynomial implicit shapes 2DIve been thinking, how would one go about rendering an implict 2d polynomial graph? Last edited by lucadeltodesco (20070809 08:06:21) The Beginning Of All Things To End. The End Of All Things To Come. #2 20070809 09:26:48
Re: rendering polynomial implicit shapes 2DIdeas off the top of my head: "The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  Leon M. Lederman #3 20070809 10:01:44
Re: rendering polynomial implicit shapes 2DYou could go about graphing it in 3D, storing only those points which satisfy the requirement = 0. The important thing when doing this is to build in a "step size" parameter allowing you to get approximations first. "In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..." #4 20070809 17:59:32
Re: rendering polynomial implicit shapes 2Dive figured out a good method that renders the objects perfectly, at arbitrary depth, and works for any implicit function http://denvish.net/ulf/090807/33048_laser.php i absolutely adore the second graph, and third graph is just immense  thinking about it, this could be directly extended into 3D aswell, only you would have a few more cases to check for, but otherwise it is directly extendable Last edited by lucadeltodesco (20070809 18:12:48) The Beginning Of All Things To End. The End Of All Things To Come. #5 20070809 21:57:50
Re: rendering polynomial implicit shapes 2DA good technique, a bit like my "brute force" method would you say? But some kind of brute force may be the only way, as the function could pop up anywhere. "The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  Leon M. Lederman #6 20070809 22:10:32
Re: rendering polynomial implicit shapes 2Dthe narrowing in of boxes looks cool, but the only reason it 'narrows' in is because i am rendering the graphs at different accuracies, it draws a box whenever it detects that the graph passes through it. so having different accuracies, different sized boxes, they congrugate around where the graph parts are drawn The Beginning Of All Things To End. The End Of All Things To Come. #7 20070809 22:34:02
Re: rendering polynomial implicit shapes 2Dyep, there we are: http://denvish.net/ulf/090807/48788_laserrend.php The Beginning Of All Things To End. The End Of All Things To Come. #8 20070809 22:43:32
Re: rendering polynomial implicit shapes 2Dmy god, this is just plain cool: The Beginning Of All Things To End. The End Of All Things To Come. #9 20070810 07:20:01
Re: rendering polynomial implicit shapes 2DShould be hanging in The Museum of Modern Art! "The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  Leon M. Lederman #10 20070823 14:39:42
Re: rendering polynomial implicit shapes 2DYou're a genuous!! Aside from the pun, what if you set some equations equal to values close to zero, but not exactly, and compare the graphs you get to the zero set equations. igloo myrtilles fourmis #11 20070828 02:27:34
Re: rendering polynomial implicit shapes 2DIntriguing... that they are antialiased is even more impressive (supersampling?) 