Making Axes logarithmic in 3d plots

Question

I've been trying to get loglog plots in 3D, but to no avail. My initial approach was to take the logarithm inside the plot i.e

Plot3D[Log[10,function[a, b]],{a, 1, 100000},{b, 1, 1000000}]

but now I'm looking for a way to logarithm-ise the axes as well. Any help would be greatly appreciated!

Answer 1

Edit: The new package to install for this comes from the CustomTicks subpackage of the SciDraw package (formerly, LevelScheme).

You first have to install the SciDraw package, it's worth it if you produce a lot of figures. You can see how to do it on the SciDraw guide.

Load the package that you will be using

Get["CustomTicks`"]

Assign a function and do the 3D plot:

function = Log[10, a x + b /. a -> 1];
Plot3D[function, {x, 1, 3}, {b, -1, 3}, 
 PlotRange -> {{1, 3}, {-1, 3}, {-1, 1}}, 
 Ticks -> {LogTicks[10, 1, 3], LogTicks[10, -1, 3], LogTicks[10, -1, 1]}
]

This would produce this figure:

If you wanted to have the yy axis with linear ticks instead you could adapt the Ticks option above. Here, I also changed the PlotRange specification and added an AxesLabel so that it is easier to see.

Plot3D[function, {x, 1, 3}, {b, -1, 3}, 
 PlotRange -> {{1, 2}, {-1, 0}, {-1, 1}}, 
 Ticks -> {LogTicks[10, 1, 3], LinTicks[-1, 0, 0.25, 5], 
   LogTicks[10, -1, 3]}, AxesLabel -> {"x", "y", "z"}]

The SciDraw (and more specifically the CustomTicks) package is really nice to do these things!

Answer 2

LogTicks is really nice. However, if you might wish to avoid another package or have more control over the final output, here is a template. As mentioned in a comment above, I actually hope that ScalingFunctions will be fully implemented in the future.

function[a_, b_] := Log[10, a + b]

Plot3D[Log[10, function[#^10 &@a, #^10 &@b]], {a, Log10@1, 
  Log10@100000}, {b, Log10@1, Log10@100000}, 
 Ticks -> {Table[{y, ToString[Round[10^y, 0.001]]}, {y, Log[10, 1], 
     Log[10, 100000]}], 
   Table[{y, 
     ToString[
      Round[10^y, 0.001] // ScientificForm // TraditionalForm]}, {y, 
     Log[10, 0.001], Log[10, 100000]}], Automatic}]

Answer 3

You can simply use ScalingFunctions. (It appears red in version 10, but still works.)

function = Log[10, a x + b /. a -> 1];
Plot3D[function, {x, 1, 3}, {b, 1, 3}, PlotLabel -> "Normal"]
Plot3D[function, {x, 1, 3}, {b, 1, 3}, 
    ScalingFunctions -> {Identity, Identity, "Log"}, PlotLabel -> "Log"] 

Answer 4

Perhaps this is what you want:

Let say the function is describe as:

z=Log10[x]+Log10[y]

Where under normal plot, it will give you a curvy surface while on the log plot will give you a rectangular surface.

And you want to rescale the axes of x,y without changing the function of x and y.

Under normal circumstances, you will plot it like below to give you the curvy surface,

Plot3D[z, {x, 1, 1000}, {y, 1, 1000}]

In order to change it into a rectangular surface due to the change in the x and y axes scale, you can do the following

Plot3D[z/.{x->10^a,y->10^b},{a,0,3},{b,0,3}]

In order to change the axes from a and b to x and y again and keep the log scale, Since I know that if a = 1 then x = 10, then i can just rename the axes with ticks function.you can do the following

Plot3D[z /. {x -> 10^a, y -> 10^b}, {a, 0, 3}, {b, 0, 3}, Ticks -> {Table[{i,10^i},{i,0, 6}], Table[{i, 10^i}, {i, 0, 6}], Automatic}]

I hope this is what are you looking for.