How to match value coloring in Plot3d to value coloring of legend

Question

In a Plot3D I want to change the displayed value range, see the following example. The function generates the values {-1,1}, they are displayed correctly on the z-axis within {-2, 2}, but the color coding is not correct, because it still runs from {-1,1} instead of {-2,2}.

Plot3D[ Sin[x*y], {x, -Pi, Pi}, {y, -Pi, Pi},
ColorFunction -> "Rainbow", PlotRange -> {-2, 2},
PlotLegends -> {Placed[BarLegend[{"Rainbow", {-2, 2}}, None,
LegendLabel -> Placed["Val", Above]], Right]}]

How do I match the value and color ranges in the plot and the legend to {-2, 2}?

Answer 1

Creating a ColorFunction that runs through the Rainbow colors over the range (-2,2):

cf = Function[x, ColorData["Rainbow"]@Rescale[x, {-2, 2}]];
legend = BarLegend[{cf, {-2, 2}}, None, LegendLabel -> Placed["Val", Above]];

Plot3D[Sin[x*y], {x, -Pi, Pi}, {y, -Pi, Pi},
 PlotRange -> {-2, 2},
 ColorFunction -> Function[{x, y, z}, cf[z]],
 ColorFunctionScaling -> False,
 PlotLegends -> legend
 ]