This seems to approximate what I believe you want:
[x,y] = meshgrid(-80:80, -80:80);
z = -(cosd(x).^2 + cosd(y).^2).^2;
mesh(x,y,z)
grid
[xx,yy] = meshgrid(-80:10:80, -80:10:80);
zz = -(cosd(xx).^2 + cosd(yy).^2).^2;
[U,V] = gradient(zz);
hold on
h = quiver3(xx,yy,ones(size(zz))*min(zlim),U,V,zeros(size(zz)));
hold off
grid on
view(-30,30)
producing:
To plot it along the surface itself:
[x,y] = meshgrid(-80:80, -80:80);
z = -(cosd(x).^2 + cosd(y).^2).^2;
mesh(x,y,z)
grid
[xx,yy] = meshgrid(-80:10:80, -80:10:80);
zz = -(cosd(xx).^2 + cosd(yy).^2).^2;
[U,V,W] = surfnorm(xx,yy,zz);
dW = gradient(W);
hold on
h = quiver3(xx,yy,zz,U,V,dW);
hold off
grid on
view(-30,60)
(There may be better mathematical expressions for the same idea.)
producing:
Best Answer