color surface according to absolut value of the gradient

• To: mathgroup at smc.vnet.net
• Subject: [mg131452] color surface according to absolut value of the gradient
• Date: Mon, 8 Jul 2013 04:23:02 -0400 (EDT)
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```I have a set of data, let's say

data = Flatten[
Table[{i, j,
Sin[i] Cos[
j]}, {i, -\[Pi], \[Pi], .25}, {j, -\[Pi], \[Pi], .25}], 1];

If I plot this, everything is fine. To get the derivatives I interpolated the set of data

f = Interpolation[data];

If I then plot the absolute value of the gradient in the same range it also looks correct.

ListPlot3D[
Flatten[Table[{i, j,
Sqrt[D[f[x, y], x]^2 + D[f[x, y], y]^2] /. {x -> i,
y -> j}}, {i, -\[Pi], \[Pi], .25}, {j, -\[Pi], \[Pi], .25}], 1]]

Now I want to plot the original data with the surface colored according to the values of the last plot. I tried

ListPlot3D[data,
ColorFunction -> (ColorData["Rainbow"][
Sqrt[D[f[x, #2], x]^2 + D[f[#1, y], y]^2] /. {x -> #1,
y -> #2}] &)]

but the result is definitely off. What am I making wrong?