Package for nonlinear plot coordinates

Question

Is there a package for plotting in nonlinear coordinates?

I mean that I provide coordinate transformation functions {xi(x,y), eta(x,y)}, for example {1/x,Log[y]}, and get plot in this coordinates with transformed grid and automatically set ticks to make 'em look equidistant

Solve[{xi(x,y)-xiIMinusOne==stepXi,eta(x,y)-etaIMinusOne==stepEta},{x,y}]

and mitigating all M. bugs in Plot function?

Answer 1

Not sure if I am interpreting your question correctly, but if you want to plot a function of the new coordinates, you can use ParametricPlot3D in this way (I am here using a working example from a very old notebook - it refers to polar coordinates - you might have to invert your transformations)

f[x_, y_] := 3Exp[-x^2 - y^2]

ParametricPlot3D[{
        x = r Cos[θ],
        y = r Sin[θ],
        f[x, y]},
    {r, 0, 4}, {θ, 0, 2Pi},
    PlotRange -> All,   BoxRatios -> {1, 1, .5},    PlotPoints -> {10, 40}]

Otherwise, if you want to plot the transformed grid in the the new coordinate system, I believe you can find the solution to your problem in Xah Lee's Transform2DPlot.m package. This is the man's website http://xahlee.info/. This is the math part of if http://xahlee.info/math_software/mathPrograms.html. Sadly, it appears he is not doing well lately.

EDIT: I see now the package is no longer free to download but requires the payment of a fee.