Splitting a 3D inequality into 3 2-D inequalities

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Cédric Cavents
Cédric Cavents 2016-5-19
Hello! Given triplets
(s,k,w)
that satisfy the following inequalities:
s<0 & k>3+11.1282s^2 &
(1/32)(27-3*sqrt(6)+sqrt(111+46*sqrt(6))[(k-3)^2/s]+10s > w >[(k-3)^2/s] + 10s
The following code creates a 3D scatter plot
s = linspace(-20,0,200);
k = linspace(3,200,600);
w = linspace(-500,0,1000);
[S,K,W] = meshgrid(s,k,w);
I = (K>3+1.12577*S.^2) & (W < ((K-3).^2)./S + 10*S) & ( W > (((K-3).^2)./(32*S))*(27+sqrt(111+46*sqrt(6))-3*sqrt(6))+10*S);
scatter3(S(I),K(I),W(I),2)
xlabel('skewness')
ylabel('kurtosis')
zlabel('hyper skewness')
This is great, however It would be better to have an interpolated 3D-surface. Is this possible? I have taken a look into Matlab functions such as 'interp3' and 'griddata' ... However, those kind of Matlab functions require a function that matches the three variables, which I don't have here. Is there a way to interpolate this 3D inequality?
If not, I can also make 3 separated scatter 2D-plots, for instance:
scatter(S(I),K(I),2)
xlabel('Skewness','interpreter','latex');
ylabel('Kurtosis','interpreter','latex');
Same question, how to interpolate the above 2D plot?
Many thanks! Cheers, Cédric

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