Re: Re: Plotting bounded domains

*To*: mathgroup at smc.vnet.net*Subject*: [mg23261] Re: [mg23211] Re: [mg23110] Plotting bounded domains*From*: Hartmut Wolf <hwolf at debis.com>*Date*: Sat, 29 Apr 2000 22:05:04 -0400 (EDT)*Organization*: debis Systemhaus*References*: <8dnvsh$hua@smc.vnet.net> <200004240512.BAA15297@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

Gurzen Nezrug schrieb: > > Hello bob and group, > > I would like to second the question and object the answer. > Bob Hanlon nice trick result with a function which is f(x,y)=x*y in the > wanted region and f(x,y)=0 outside. But what I want, and possibly what > jgregory wants (If I'm allowed to guess) is to see only the inner part and > nothing on the outer part (i.e. clear background). To justify my question, > suppose that f(x,y) is now 0 for x<1, how can we tell between the real 0 and > the "outside the region" 0 ?!? > Is there a way to get such plot other then parametrizing the area "by hand" > (which might not be simple) and using ParametricPlot3D? > I would like to add, knowing software such as MATLAB (I hope it is not > forbidden to mention this name here) assigning a value of NaN to a function > or a matrix (stands for "Not a Number") means that this point will simply > not be shown in graphics plot. Is there a way to achieve the same within > mathematica? > > Thank you all, > > BobHanlon at aol.com wrote in message <8dnvsh$hua at smc.vnet.net>... > >f[x_, y_] := x*y; > > > >region[x_, y_] := > > (UnitStep[x] - UnitStep[x - 2.])*(UnitStep[y] - UnitStep[y - x]); > > > >Plot3D[f[x, y]*region[x, y], {x, -0.5, 2.5}, {y, -0.5, 3.5}, > > PlotPoints -> 35, AxesLabel -> {"x", "y", "z"}, > > ViewPoint -> {1.300, -2.400, 2.000}]; > > > >Bob Hanlon > > > >In a message dated 4/19/2000 2:44:33 AM, jgregory at ismi.net writes: > > > >> In Mathematica, how does one plot a bounded and closed domain in R^2 > >>that includes variables? For example let R be y=x; x=2; y = 0; for the > >>function, f(x,y) = x*y. > >> > > I would like to add two methods: (1) define f as: f[x_, y_] := x*y /; 0 <= y <= x f[_, _] = Null Off[Plot3D::"plnc", Plot3D::"gval"] Plot3D[f[x, y], {x, 0, 2}, {y, 0, 2}] (2) manipulate the output g = Graphics3D[ Plot3D[x*y, {x, 0, 2}, {y, 0, 2}, DisplayFunction -> Identity]]; g2 = g /. p : Polygon[_] :> (p /. {x_, y_, z_} -> If[y <= x, {x, y, z}, Unevaluated[Sequence[]]]); Show[g2, DisplayFunction -> $DisplayFunction] I consider the result (2) as most pleasing. Kind regards, Hartmut