On Jul 12, 2:28 am, David Sanders <dpsand...@gmail.com> wrote: > Hi, > > I have been playing around with the implicit_plot3d command, and it's > very nice. > > Is there something similar to plot regions defined by inequalities in > 3D, along the lines of the Mathematica > RegionPlot3D command? I see that there is an old discussion from 2 > years ago about this. > > It seems to me (in my ignorance) that the kind of algorithm required > to do this should not be too different from that for implicit_plot3d > with the region option. (Though implicit_plot3d draws surfaces, > whereas region_plot3d would draw volumes. But apparently the marching > cubes algorithm is used for both?)
I haven't looked at this stuff in more than a year, but I think this is all accurate: Our plotting framework doesn't really "understand" volumes, only surfaces. So it would be a major overhaul to produce a plot that showed (via some sort of volumetric shading, say) the difference between the "inside" and the "outside" of your region. However, if you want to produce a plot of the surface of your region, that's pretty easy. If your region is defined by a single inequality F(x,y,z)<0, then you can just implicit_plot3d F(x,y,z). If your region is defined as a boolean combination of inequalities, then arrange all the inequalities to be of the form F(x,y,z) < 0, then drop all the "< 0", replace "and" with "max_symbolic", replace "or" with "min_symbolic", and replace "not F(x,y,z)" with "-F(x,y,z)". Also, when you plot, because of http://trac.sagemath.org/sage_trac/ticket/9483 you need to add "smooth=False". Here's a complete example. This forms the intersection between a cube and the union of two cylinders. sage: var('x,y,z') (x, y, z) sage: implicit_plot3d(max_symbolic(min_symbolic(x*x+y*y-1, x*x+z*z-2), x-1.8, y-1.8, z-1.8, -x-1.8, -y-1.8, -z-1.8), (x, -2, 2), (y, -2, 2), (z, -2, 2), smooth=False) It would be great to put all of this into a region_plot3d command, but as far as I know, Sage does not yet support symbolic conjunctions and disjunctions ("and"s and "or"s); so it would be difficult to tell region_plot3d about any region more complicated than a single inequality. Carl -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
