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Re: ContourPlot3D: plot implicitly defined surfaces

  • To: mathgroup at
  • Subject: [mg35286] Re: ContourPlot3D: plot implicitly defined surfaces
  • From: "Raf" <r_a_f at>
  • Date: Sat, 6 Jul 2002 05:44:41 -0400 (EDT)
  • References: <ag3esq$73n$>
  • Sender: owner-wri-mathgroup at

In general, to each value of the couple {a,b} the system { F(x,y;a,b)=0,
G(x,y;a,b)=0 } can associate many couple of {x,y} as you can see with this

f := x*a* y*Sin[y] + b*y*Cos[x + b] + 1.;
g := 3b x Sin[x] + y*a *Cos[y + a] + 1.;

<< Graphics`ImplicitPlot`

ImplicitPlot[{f == 0., g == 0.} /. {a -> 1, b -> 1}, {x, -2 Pi,
    2 Pi}, {y, -2 Pi, 2 Pi}, PlotPoints -> 50,
  PlotStyle -> {GrayLevel[0], Hue[0]}]

Now, if i understand what you mean, you want to plot the cartesian surface
x=x(a,b) that, in the general case, is not well defined by this system.
If you are sure that there is only a solution for each couples of {a,b}, you
can try to find the numerical solution for each couples of {a,b} (using for
example something like Table[{a, b, x} /.       FindRoot[{f == 0, g == 0},
{x, x0}, {y, y0}]], {a, a0, a1, as}, {b, b0, b1, bs}] ), and then plot the
 with ListSurfacePlot3D, or if there are problems with this command, only
take a look to the result using Point on the solutions:
Show[Graphics3D[Point /@ Flatten[sol, 1]]


"Jun Lin" <jl_03824 at> ha scritto nel messaggio
news:ag3esq$73n$1 at
> Given two functions F=F(x,y;a,b) and G=G(x,y;a,b), the relations
>  F(x,y;a,b)=0, and
> {
>  G(x,y;a,b)=0
> implicitly define another two functions x=x(a,b) and y=y(a,b). Suppose
> functions F and G are implicit and transcendental, it is cumbersome to
> get x and y simultaniously from F=0 and G=0. Is it possible to plot
> surfaces x=x(a,b) and y=y(a,b) according to F=0 and G=0 by means of
> ContourPlot3D?
> Any suggestion and advice will be appreciated.
> Jun Lin

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