Using custom ticks with RegionPlot3D

Question

I'm trying to change to plot a sphere using RegionPlot3D and look at how the shape of the sphere changes when you use a logarithmic scale (or any nonlinear scale) for the x, y, and z axes. The code to produce a sphere on linear axes is:

RegionPlot3D[x^2 + y^2 + z^2 < 1, {x, -1, 1}, {y, -1, 1}, {z, -1, 1}, 
  Mesh -> False, PlotPoints -> 90]

This works fine, but I cannot seem to change the axes to a nonlinear scale. The CustomTicks package seems to be a good start, but I cannot seem to make it work for RegionPlot3D.

Answer 1

Logarithmic transformation is not a good idea, since the coordinates are varying partially in the negative domain, as I mentioned above. One can do this with the positive part of the sphere, if you like:

 RegionPlot3D[
 x^2 + Exp[y]^2 + z^2 < 4, {x, 1, 2}, {y, 0, Log[2]}, {z, 1, 2}, 
 Mesh -> False, PlotPoints -> 90, 
 PlotRange -> {{0, 2}, {0, 2}, {0, 2}}, PlotStyle -> Opacity[0.3], 
 AxesLabel -> {"x", "y", "z"}]

where I only transformed the coordinate y. It should look as follows:

Have fun!