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

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Diaa 2021-6-21

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/861835-find-the-normal-vector-at-a-specific-point-on-a-3d-surface-defined-by-an-equation

编辑： Diaa 2021-6-21

Consider the following code:

rng('default')
[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'} ...
    ,'coefficients',{'a','b','c'}...
    );
[XOut, YOut, ZOut] = prepareSurfaceData(xdata, ydata, zdata);
SurFit = fit( [XOut, YOut] , ZOut , ft  );
plot(SurFit)

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.