In case anyone is interested there is a relatively standard algorithm for constructing mesh for an isosurfaces called marching cubes. For a while that was patented so there is a marching tetrahedrons analog but I think the patent issue is expired. Its complicated in that there are lots of things to keep track up but not mathematically sophisticated. Obviously that doesn't help immediately but it would be good project at some point if someone wanted to add 3d implicit plotting. Josh
On Nov 20, 9:32 am, "William Stein" <[EMAIL PROTECTED]> wrote: > On Thu, Nov 20, 2008 at 7:21 AM, kcrisman <[EMAIL PROTECTED]> wrote: > > >> > I am really newbie to Sage, but I need to both plot and declare > >> > functions like: > >> > f(x,y,z) = x*y*z > >> > and other poly's containing 3 variables. > >> > How do I do that? > > > It sounds like you are looking for a 3-D implicit plot. Is that > > correct? Or perhaps a contour plot in 3-D. Unfortunately, although > > there are reasonable (though not perfect) 2-D versions of that in > > Sage, I do not believe that we have native implicit plotting or > > contour plotting available in Sage in 3-D. That would be really nice, > > but I don't even pretend to understand how the code might be improved > > to implement that. > > > However, there is the optional experimental package for Surf, which I > > believe does plot surfaces (in an algebraic geometry context - their > > home page has a nice shot of the 27 lines on a cubic) and can be used > > with Sage. The documentation about that on the Sage site does not > > inspire confidence that this can effortlessly installed, > > unfortunately. > > > Best, > > - kcrisman > > This is just to confirm that indeed Sage doesn't have an implementation > of implicit 3d plots yet. > > There is a very powerful/flexible list_plot3d command -- you can pass it > an arbitrary collection of points in 3d and it puts a surface through them > using various interpolation options. Thus you could get some approximation > to an implicit plot, by finding lots of points (x,y,z) in a 3d grid > (use fast_float > to make this fast) such that f(x,y,z) is tiny. That would be just a few lines > of code to implement, and might be a reasonable approximation to 3d > implicit plots, for some applications (??). > > William --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/sage-support URLs: http://www.sagemath.org -~----------~----~----~----~------~----~------~--~---
