On Jul 12, 7:29 pm, Carl Witty <carl.wi...@gmail.com> wrote: > 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.
Yes, I agree, although that overhaul could well be worth it! > > 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 ofhttp://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. OK, thanks, I had come to a similar conclusion, though the trick with max_ and min_symbolic is neat. For the moment I think this will do most of the things that I need, but the fact that there are no symbolic and's and or's makes it quite (=very) messy if there are multiple intersecting volumes which restrict each other. Thanks, David. > > 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
