Plotting an intersection seam on a contour plot ?

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SUMMARY

The discussion focuses on plotting an intersection seam between two 2D functions, s1(x,y) and s2(x,y), using Mathematica's Plot3D and ContourPlot functions. The user successfully plots the intersection seam in a 3D space with the command provided, utilizing the MeshFunctions option. However, they seek guidance on how to incorporate the intersection seam into the contour plots of both functions. A reference link to Wolfram's documentation on combining graphics is suggested as a starting point for further exploration.

PREREQUISITES
  • Understanding of 2D interpolation techniques for functions.
  • Familiarity with Mathematica's Plot3D and ContourPlot functions.
  • Knowledge of MeshFunctions in Mathematica for visualizing intersections.
  • Basic skills in combining graphics in Mathematica.
NEXT STEPS
  • Explore the use of the MeshFunctions option in ContourPlot in Mathematica.
  • Learn how to combine multiple graphics in Mathematica using the CombineTwoOrMoreGraphics method.
  • Investigate advanced interpolation techniques for 2D functions in Mathematica.
  • Study examples of visualizing intersections of functions in Mathematica documentation.
USEFUL FOR

Mathematica users, data visualizers, and mathematicians interested in advanced plotting techniques for 2D functions and their intersections.

evgenx
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Hi,

I have two 2D functions (surfaces), s1(x,y) and s2(x,y) defined
via Interpolation. They intersect forming an intersection seam (which is a line).
I can plot both functions using Plot3D and I can also plot the seam on the same
3D plot by means of the MeshFunctions option. The comand I use reads the following:

Plot3D[{s1[R, a], s2[R, a]}, {R, 2.62, 3.19}, {a, 1.36, 1.78},MeshFunctions->{(s1[#1, #2]-s2[#1, #2])&},Mesh->{{0}},MeshStyle->{Red,Thick}]

But what I would like also to plot is the intersection seam on the contour
plots of S1 and S2. I mean I can plot a contour plot of S1 or S2 (using ContourPlot)
but I don't know how to add the seam to the contour plot.

I will very appreciate any hint/instructions how to do that.
Many thanks!

Evgeniy
 
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