DensityPlot3D with clear division negative/positive value but also value dependent

Question

It is easy to obtain a clear positive/negative boundary, with, exemplary

ColorFunction -> Function[{f}, If[f > 0, Red, Blue]]

Do you have an idea how I can define a color function to get a clear division negative/positive value but also some info about the value?

Answer 1

When posting a question, provide a concrete example and the code used to demonstrate the issue.

One approach to clearly delineate the boundary is to use ContourPlot3D for the boundary

Show[
 DensityPlot3D[x y z,
  {x, -1, 1}, {y, -1, 1}, {z, -1, 1},
  PlotLegends -> Automatic],
 ContourPlot3D[x y z == 0,
  {x, -1, 1}, {y, -1, 1}, {z, -1, 1},
  ContourStyle -> Red]]

Answer 2

Whether one of the pictures satisfied you requirement?

fig1 = DensityPlot3D[x*y*z, {x, -1, 1}, {y, -1, 1}, {z, -1, 1}, 
   ColorFunction -> Function[{f}, ColorData["TemperatureMap"][f]], 
   ColorFunctionScaling -> True];
fig2 = DensityPlot3D[x*y*z, {x, -1, 1}, {y, -1, 1}, {z, -1, 1}, 
   ColorFunction -> Function[{f}, If[f > 0, Red, Blue]], 
   ColorFunctionScaling -> False];
fig3 = DensityPlot3D[x*y*z, {x, -1, 1}, {y, -1, 1}, {z, -1, 1}, 
   ColorFunction -> Function[{f}, Blend[{Blue, Red}, f]], 
   ColorFunctionScaling -> False];

Answer 3

Making a custom plotting function based on Bob Hanlon's method combining DensityPlot3D and ContourPlot3D:

ClearAll[densityPlot3DwithContours]

SetAttributes[densityPlot3DwContours, HoldAll]

densityPlot3DwContours[f_, r1:{_,_,_}, r2:{_,_,_}, r3:{_,_,_}, o:OptionsPattern[]] :=
 Show[DensityPlot3D[f, r1, r2, r3, 
   Evaluate@FilterRules[{o}, Options[DensityPlot3D]]], 
  ContourPlot3D[f, r1, r2, r3, 
   PlotLegends -> Automatic, 
   Evaluate @ FilterRules[DeleteCases[ColorFunction -> _]@{o}, 
     Options[ContourPlot3D]], 
   Contours -> {{0., Opacity[.3, Red]}}, 
   ContourStyle -> Automatic,
   Mesh -> None, 
   BoundaryStyle -> None, 
   PlotPoints -> 70]]

Examples:

densityPlot3DwContours[x y z, {x, -1, 1}, {y, -1, 1}, {z, -1, 1}, 
 PlotLegends -> BarLegend[Automatic, "StyledContours" -> {{0, Red}}]]

densityPlot3DwContours[x y z, {x, -1, 1}, {y, -1, 1}, {z, -1, 1}, 
 ColorFunction -> "Rainbow", 
 Contours -> Thread[{{-.2, .1}, Opacity[.3, #] & /@ {Red, Green}}], 
 PlotLegends -> 
   BarLegend[Automatic, "StyledContours" -> Thread[{{-.2, .1}, {Red, Green}}]]]

Answer 4

I would prefer Bob Hanlon's approach as it is both simple and flexible. As an alternative approach we can also use a custom OpacityFunction to modify default opacity at function values close to 0:

ClearAll[customOpacity]
customOpacity[op1_: Automatic, op2_: .5] := If[.75 - .001 <= # <= .75 + .001, op2, 
  If[9/22 <= -1. + 2.*#1 < 7/11, .01, op1 /. Automatic -> .3, 0] ]& @
    Rescale[#1, {0, 1}, {0.5, 1}] &

Examples:

DensityPlot3D[x y z, {x, -1, 1}, {y, -1, 1}, {z, -1, 1}, 
 PlotLegends -> Automatic, OpacityFunction -> customOpacity[]]

Use OpacityFunction -> customOpacity[Automatic, 1] to get

OpacityFunction -> customOpacity[.5] to get

Add the option ColorFunction -> "Rainbow" to get

We can also use a custom ColorFunction:

defaultColorFunction = "DefaultColorFunction" /. (Method /. 
     Charting`ResolvePlotTheme[Automatic, DensityPlot3D]);

ClearAll[customColor]
customColor[cf1_: Automatic, cf2_: Red] :=
    If[.5 - .0001 <= # <= .5 + .0001, cf2, 
      (cf1 /. Automatic -> defaultColorFunction) @ # ] &  ;


DensityPlot3D[x y z, {x, -1, 1}, {y, -1, 1}, {z, -1, 1}, 
 PlotLegends -> Automatic, 
 ColorFunction -> customColor[], 
 OpacityFunction -> customOpacity[]]

Use ColorFunction -> customColor[ColorData["Rainbow"]] to get