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added 66 characters in body

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edited Jan 24, 2017 at 14:32

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BarLegend["Rainbow"] gives a generic bar over a range of [0, 1].

BarLegend["Rainbow"]

It appears that for RegionPlot3D you will need to specify the range manually:.

Update: adjusted to match your target plot from your own solution.

f[x_, y_, z_] := x^2 + y^2 - z^2;

RegionPlot3D[x^2color += y^2ColorData[{"Rainbow", {-1, z^21}}];

RegionPlot3D[f[x, y, z] <= 1 && 0 <= z <= 1, {x, -2, 2}, {y, -2, 2}, {z, 0, 1},
   
 Axes -> True, AxesLabel -> {x, y, z}, 
 ColorFunction -> Function[{x,(color y,@ z}f[#, ColorData["Rainbow"][f[x#2, y,#3] z]]]&), 
 ColorFunctionScaling -> False, MeshFunctionsMesh -> Function[{x, y, z}, f[x, y, z]]False, 
 BoxRatios -> {1, 1, 1}, PlotPoints -> 75, 
 PlotLegends -> BarLegend[{"Rainbow"color, {-1, 1}}]]

BarLegend["Rainbow"] gives a generic bar over a range of [0, 1].

BarLegend["Rainbow"]

It appears that for RegionPlot3D you will need to specify the range manually:

f[x_, y_, z_] := x^2 + y^2 - z^2;

RegionPlot3D[x^2 + y^2 - z^2 <= 1 && 0 <= z <= 1, {x, -2, 2}, {y, -2, 2}, {z, 0, 1},
   Axes -> True, AxesLabel -> {x, y, z}, 
 ColorFunction -> Function[{x, y, z}, ColorData["Rainbow"][f[x, y, z]]], 
 ColorFunctionScaling -> False, MeshFunctions -> Function[{x, y, z}, f[x, y, z]], 
 BoxRatios -> {1, 1, 1}, PlotPoints -> 75, 
 PlotLegends -> BarLegend[{"Rainbow", {-1, 1}}]]

BarLegend["Rainbow"] gives a generic bar over a range of [0, 1].

BarLegend["Rainbow"]

It appears that for RegionPlot3D you will need to specify the range manually.

Update: adjusted to match your target plot from your own solution.

f[x_, y_, z_] := x^2 + y^2 - z^2;

color = ColorData[{"Rainbow", {-1, 1}}];

RegionPlot3D[f[x, y, z] <= 1 && 0 <= z <= 1, {x, -2, 2}, {y, -2, 2}, {z, 0, 1},  
 Axes -> True, AxesLabel -> {x, y, z}, ColorFunction -> (color @ f[#, #2, #3] &), 
 ColorFunctionScaling -> False, Mesh -> False, 
 BoxRatios -> {1, 1, 1}, PlotPoints -> 75, PlotLegends -> BarLegend[{color, {-1, 1}}]]

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created Jan 24, 2017 at 11:51

Mr.Wizard

273.1k
34
595
1.4k

BarLegend["Rainbow"] gives a generic bar over a range of [0, 1].

BarLegend["Rainbow"]

It appears that for RegionPlot3D you will need to specify the range manually:

f[x_, y_, z_] := x^2 + y^2 - z^2;

RegionPlot3D[x^2 + y^2 - z^2 <= 1 && 0 <= z <= 1, {x, -2, 2}, {y, -2, 2}, {z, 0, 1},
  Axes -> True, AxesLabel -> {x, y, z}, 
 ColorFunction -> Function[{x, y, z}, ColorData["Rainbow"][f[x, y, z]]], 
 ColorFunctionScaling -> False, MeshFunctions -> Function[{x, y, z}, f[x, y, z]], 
 BoxRatios -> {1, 1, 1}, PlotPoints -> 75, 
 PlotLegends -> BarLegend[{"Rainbow", {-1, 1}}]]