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MathGroup Archive 2005

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Re: Crossing of 3D functions


On Mon, 23 May 2005 06:22:16 +0000 (UTC), Paawel <fonfastik at interia.pl>  
wrote:

> My question is, wheather it is possible to find analytical form of
> equation (EC) describing crossing of these two (F1 and F2) functions.
> Another thing is, if I have this equation (EC) is it possible to plot
> surfaces of F1 and F2, only up to values less or equal to this
> function (EC)? (So that plotted are only lower part of these functions
> (F1&F2))
> I hope it is understandable
> Regards
>

If you want to plot Min[F1, F2], it can be done as

{{r1, r2}, {f1, f2}} = {{1, 2}, {90, 180}};

F1[r_, f_] = 3.92 + 3.758/E^(6.152*(-1.184 + r)) - (6.288336759430112*(1 -  
0.00008280000000000001*(180 - f)^2))/E^(3.076*(-1.184 + r));

F2[r_, f_] = 0.479 + 0.479/E^(9.986*(-1.375 + r)) - (0.958*(1 -  
0.00107*(133 - f)^2))/E^(4.993*(-1.375 + r));

R[f_?NumericQ] := R[f] =
   r /. FindRoot[F1[r, f] == F2[r, f], {r, (r1 + r2)/2, r1, r2}]

R1[f_, u_] = (R[f] - r1)*u + r1;
R2[f_, u_] = (r2 - R[f])*u + R[f];

ParametricPlot3D[
   {{R1[f, u], f, F1[R1[f, u], f], SurfaceColor[Hue[0]]},
    {R2[f, u], f, F2[R2[f, u], f], SurfaceColor[Hue[2/3]]}},
   {f, f1, f2}, {u, 0, 1},
   BoxRatios -> {1, 1, .4}]

Here r runs from r1 to R[f] for F1 and from R[f] to r2 for F2. This is  
essentially the same as

Plot3D[{Min[F1[r, f], F2[r, f]],
     If[F1[r, f] < F2[r, f], Hue[0], Hue[2/3]]},
   {r, r1, r2}, {f, f1, f2},
   PlotRange -> All]

but with a smooth boundary (plus simulated illumination).

Maxim Rytin
m.r at inbox.ru


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