Re: [Q] CountorPlot as part of 3D Plot

*To*: mathgroup at smc.vnet.net*Subject*: [mg4398] Re: [Q] CountorPlot as part of 3D Plot*From*: Xah Lee <xah at best.com>*Date*: Mon, 15 Jul 1996 11:13:37 -0400*Organization*: Best Internet Communications*Sender*: owner-wri-mathgroup at wolfram.com

Gerd Lanfermann wrote: > problem: i want to display a 3d plot, of lets say saddle, using Plot3D. > I also want to to include a colored contour plot of this saddle ON THE > BOTTOM of the 3D-box, that matches the 3d plot. The plan is to convert your ContourGraphics to a 3D graphics primitive, then you can display it with the surface of your function. The data of ContourGraphics, DensityGraphics, and SurfaceGraphics are just a rectangular array. The difference is how they are rendered in Show. To display a ContourGraphics as a surface, just add the head SurfaceGraphics to your data and use Show. But what you want is to convert the contour data array into graphic primitives as a list of Lines and Polygons that represents the contour. This you do by adding the head Graphics to it. Once your contour data array became a list of 2D graphic primitives, you add a dimension to all the point in them so they became a list of 3D primitives. Finally display this together with your SurfaceGraphics of the function. In[8]:= myFunction[a_,b_][x_,y_]:=((x-a)^2 + y^2) ((x+a)^2 + y^2) - b^4 In[9]:= myContourData = ContourPlot[ myFunction[1,1][x,y], {x,-2,2}, {y,-1.2,1.2}, Contours->Table[ i^2-1,{i,-1, 2.5, 1/4}], PlotPoints->25, AspectRatio->Automatic, PlotRange->All, ContourLines->True, ContourShading->True, ContourStyle->({Hue[#,1,.5],Thickness[.006]}&/@Range[0,1,1/12]), ColorFunction->Hue, Ticks->{Range[-1,1], Range[-2,2],{-.5,.5}} ];0; In[10]:= myContourGP = First@ Graphics@ myContourData; myContourGP = N@ myContourGP /. {x_?AtomQ, y_?AtomQ}->{x,y,-20}; In[12]:= Show[ { SurfaceGraphics@ myContourData, Graphics3D@ myContourGP }, Axes->True, BoxRatios->{1,1,1} ];0; Hope this helps. If you are using a Mac, you might want to get Rotater--An excellent freeware for visualing wireframes in realtime, together with a mathematica to Rotater converter package. You can get them at http://www.best.com/~xah/PageTwo_dir/MathPrograms_dir/mathPrograms.html Xah xah at best.com; 74631.731 at compuserve.com http://www.best.com/~xah/SpecialPlaneCurves_dir/specialPlaneCurves.html Mountain View, CA, USA ==== [MESSAGE SEPARATOR] ====