Surfaces

Implementation

Needs["Graphics`Colors`"]

Needs["SURFS`"]

Needs["CSPROGS`"]

dip[ins_][g_]:=$DisplayFunction[Insert[g,ins,{1,1}]]

Monkey Saddle

Here is the standard parametrization of the monkey saddle:

monkeysaddle[u,v]

Let us calculate its mean curvature

mcurvature[monkeysaddle][u,v]

We can also plot the mean curvature.

Plot3D[mcurvature[monkeysaddle][u,v]//Evaluate,
{u,-1.5,1.5},{v,-1.5,1.5}];

Finally we plot the monkey saddle and use the mean curvature
to color it.

ParametricPlot3D[
Append[monkeysaddle[r Cos[theta],r Sin[theta]],
Hue[(mcurvature[
monkeysaddle][r Cos[theta],r Sin[theta]]+0.88)/
1.76]]//Evaluate,
{r,0,1},{theta,0,2Pi},
Boxed->False,Axes->None,
Lighting->False,
PlotPoints->{20,40},
PlotRange->All];