Find the normal vector at a specific point on a 3D surface defined by an equation

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Diaa on 21 Jun 2021
Edited: Diaa on 21 Jun 2021
Consider the following code:
[Xs,Ys,Zs] = sphere;
X = (0.99+0.01*rand(size(Xs))).*Xs;
Y = (0.99+0.01*rand(size(Ys))).*Ys;
Z = (0.99+0.01*rand(size(Zs))).*Zs;
noVertcs = 5;
xdata = X(1:noVertcs,1:noVertcs);
ydata = Y(1:noVertcs,1:noVertcs);
zdata = Z(1:noVertcs,1:noVertcs);
ft = fittype(...
'a*x^3 + b*y^3 + c' ...
,'independent', {'x','y'} ...
,'dependent',{'z'} ...
[XOut, YOut, ZOut] = prepareSurfaceData(xdata, ydata, zdata);
SurFit = fit( [XOut, YOut] , ZOut , ft );
I need to make a code that takes x, y, z coordinates of some certain point on the surface created by SurFit, then it returns the components and the direction cosines of the normal vector at this specific point.

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