Re: Crossing of 3D functions

*To*: mathgroup at smc.vnet.net*Subject*: [mg57317] Re: Crossing of 3D functions*From*: Maxim <ab_def at prontomail.com>*Date*: Tue, 24 May 2005 05:12:55 -0400 (EDT)*References*: <200505110925.FAA24136@smc.vnet.net> <d5uu43$90b$1@smc.vnet.net> <200505161106.HAA09312@smc.vnet.net> <d6bi29$mno$1@smc.vnet.net> <200505190708.DAA13139@smc.vnet.net> <d6k969$uk$1@smc.vnet.net> <d6rsqo$41b$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

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

**References**:**Crossing of 3D functions***From:*fonfastik@interia.pl (Paawel)

**Re: Crossing of 3D functions***From:*fonfastik@interia.pl (Paawel)

**Re: Crossing of 3D functions***From:*fonfastik@interia.pl (Paawel)