Visualizing the transformation from surface to contour plot in Windows

Question

According to my understanding, this transformation from a surface in $\mathbb{R}^3$ to contour lines in $\mathbb{R}^3$ to a contour plot in $\mathbb{R}^2$ was made in Grapher, a program exclusive to Apple. Is there a way to view this type of transformation for a desired multivariable function in MATLAB, Python, or some free tool online or compatible with Windows? Is there also a way to view the inverse transformation from a contour plot in $\mathbb{R}^2$ to contour lines in $\mathbb{R}^3$ to a surface in $\mathbb{R}^3$ for such a user supplied function?

Answer 1

In Mathematica (which certainly has Windows-compatible versions):

surface = 
 Plot3D[2.5 + Sin[x^2 y], 
 {x, -2, 2}, {y, -2, 2},
 MeshFunctions -> {#3 &},
 Mesh -> 10,
 MeshStyle -> Directive[Blue, Thickness[0.009]],
 PlotStyle -> Opacity[0.7]];

slice = 
 SliceContourPlot3D[2.5+Sin[x^2 y], 
 {"ZStackedPlanes", 1},
 {x, -2, 2}, {y, -2, 2}, {z, -2, 2},
 ContourStyle -> Directive[Blue, Thickness[0.009]]];

Show[surface,slice]

I think you may want to get access to more powerful tools than freeware.

The only way you can go from a contour plot up to a three-dimensional plot is to first infer the function.