Re: Getting only 1 of 3 curves of intersection
- To: mathgroup at smc.vnet.net
- Subject: [mg126315] Re: Getting only 1 of 3 curves of intersection
- From: "djmpark" <djmpark at comcast.net>
- Date: Mon, 30 Apr 2012 04:43:43 -0400 (EDT)
- Delivered-to: l-mathgroup@mail-archive0.wolfram.com
- References: <1198356.198995.1335681120499.JavaMail.root@m06>
Bill, Use Reduce: Reduce[Cos[x y] == Sin[x y] && 0 <= y <= \[Pi], {x, y}, Reals] Then write ConditionalExpressions for the intersections. intersection1[k_][x_] = ConditionalExpression[{x, (-2 ArcTan[1 + Sqrt[2]] + 2 \[Pi] k)/x, Sin[-2 ArcTan[1 + Sqrt[2]] + 2 \[Pi] k]}, (k <= 0 && x <= (-2 ArcTan[1 + Sqrt[2]] + 2 \[Pi] k)/\[Pi]) || (k >= 1 && x >= (-2 ArcTan[1 + Sqrt[2]] + 2 \[Pi] k)/\[Pi])]; intersection2[k_][x_] = ConditionalExpression[{x, (-2 ArcTan[1 - Sqrt[2]] + 2 \[Pi] k)/x, Sin[-2 ArcTan[1 - Sqrt[2]] + 2 \[Pi] k]}, (k <= -1 && x <= (-2 ArcTan[1 - Sqrt[2]] + 2 \[Pi] k)/\[Pi]) || (k >= 0 && x >= (-2 ArcTan[1 - Sqrt[2]] + 2 \[Pi] k)/\[Pi])]; The particular intersections you want for your plot are: intersection2[0][x] intersection2[1][x] intersection1[1][x] In Presentations I would draw this as: << Presentations` Draw3DItems[ {{Opacity[0.6, ColorData["Crayola"]["RedViolet"]], Draw3D[Sin[x y], {x, 0, Pi}, {y, 0, Pi}, Mesh -> None]}, {Opacity[0.6, Cyan], Draw3D[Cos[x y], {x, 0, Pi}, {y, 0, Pi}, Mesh -> None]}, {Black, Thick, ParametricDraw3D[intersection2[0][x], {x, 0, \[Pi]}], ParametricDraw3D[intersection2[1][x], {x, 0, \[Pi]}], ParametricDraw3D[intersection1[1][x], {x, 0, \[Pi]}]}}, NeutralLighting[0, 0.5, 0.4], NiceRotation, Axes -> True, AxesLabel -> {"x", "y", "z"}, BoxRatios -> {1, 1, 0.5}, ImageSize -> 500] David Park djmpark at comcast.net http://home.comcast.net/~djmpark/index.html From: Bill [mailto:WDWNORWALK at aol.com] Hi: Consider the following plot: g1=Plot3D[Sin[x*y],{x,0,Pi},{y,0,Pi},PlotStyle->None,MeshStyle->Red,Axes->Tr ue,AxesLabel->{"x","y","z"}]; g2=Plot3D[Cos[x*y],{x,0,Pi},{y,0,Pi},Mesh->None,PlotStyle->{Cyan,Opacity[.8] }]; nsSol=NSolve[{z-Sin[x*y],z-Cos[x*y]},{y,z}];//Quiet g3=ParametricPlot3D[{x,y,z}/.nsSol[[2]],{x,0,Pi},PlotStyle->{Magenta,Thickne ss[.007]}]; Show[g1,g2,g3,Background->LightYellow,ImageSize->500] Using the above Mathematica 8.0.4 code, I can plot one curve of intersection shown in magenta. Within the plotted area, I can see 2 more places where intersection curves should be. I've tried using Reduce in place of NSolve, but can't get it to work. Question: If this can be done, can someone please give me the code? Thanks, Bill