MuPAD: Drawing a surface with a line on

I took me years to figure out how did we plot such a picture in this entry. Thanks to MuPAD, we can do it quite easily. What I got is the following

Firstly, we need to choose a function which has a mountain-pass shape. Thank to a special solution to the Toda system considered in this entry, we can choose

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MuPAD

MuPAD was a Computer algebra system (CAS). Originally developed by the MuPAD research group at the University of Paderborn, Germany, it was developed by the company SciFace Software GmbH & Co. KG in cooperation with the MuPAD research group and partners from some other universities since 1997.

I found MuPAD a very cool tool for plotting graph of functions. I will show you in details some examples.

1. We start with the following function

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To plot its graph, I use the following

f := plot::Function3d(exp(-x^2-y^2)*(cos(3*y)+sin(7*x)), x=-2..2, y=-2..2, Submesh=[1,1], FillColorFunction=((x, y, z) -> [(z+2)/4, 0.5, (2-z)/4])): plot(f)

and this is what we get