# 3D plots of negative points with mixed log and linear scale

Is it possible somehow to generalize the symlog function proposed here 'symlog'-like Plot with a mixed log-linear-log scale to a 3D plot, as ListPointPlot3D or Plot3D, so that it would be possible to use it in ScalinFunction as: ScalingFunctions -> {"Log", None, "symlog"} or maybe as ScalingFunctions -> {"Log", None, Function[z, Sign[z] (Exp[Abs[z]] - 1)]} to plot negative data points. I would like to have the possibility to choose one axis in log scale, one in normal scale and another using this symlog option, for example. Also because my version does not seem to have the embeded scaling function SignedLog.

ScalingFunctions seem to require a function and its inverse to work. Therefore you need one of these two:

symlog = {Function[x, Sign[x]*Log[Abs[x] + 1]],
Function[y, Sign[y]*(Exp[Abs[y]] - 1)]};

(* Same functionality as "SignedLog" *)
symlog10 = {Function[x, Sign[x]*(Log10[Abs[x] + 1])],
Function[y, Sign[y]*(10^Abs[y] - 1)]};


Then you can use exactly what you suggested:

Plot3D[x^3 y^2, {x, -3, 3}, {y, -3, 3},
ScalingFunctions -> {None, None, symlog}, BoxRatios -> {1, 1, 1}] • However, this seems to distort the data. For example if you do: data={{1, 5}, {2, 4}, {3, 3}, {4, 2}, {5, 0}, {6, -2}, {7, -8}, {8, -14}, {9, -22}, {10, -30}} and ListPlot[data + 40, Frame -> True, ScalingFunctions -> {None, "Log"}] or ListPlot[data, Frame -> True, ScalingFunctions -> {None, symlog}] you get two different plots. Apr 13, 2022 at 9:27
• Why would you expect them to be the same? Note that adding data + 40, adds it to everything, both x and y. Secondly, if you think about what is happening, since you are using a log axis, you are essentially using log(y), and note that log(f(x)+40) is not the same as shifting the data, i.e. log(f(x))+c. Thirdly, SignedLog is actually defined as sign(y)*log(|y|+1), so you can't just compare it directly with the log scale - for large values of y they will look the similar, but for smaller they will not. Apr 15, 2022 at 0:43