write code that determines the normal vector in matlab

main.m
% Define the surface points
[X, Y] = meshgrid(-1:0.1:1);
Z = X.^2 + Y.^2;

% Convert the surface to a triangular mesh
[F, V] = surf2patch(X, Y, Z);

% Calculate the normal vectors of the triangles
N = patchnormals(F, V);

% Plot the surface with the normal vectors
figure;
patch('Faces', F, 'Vertices', V, 'FaceColor', 'red', 'FaceAlpha', 0.5);
hold on;
quiver3(V(:,1), V(:,2), V(:,3), N(:,1), N(:,2), N(:,3), 0.5, 'b');
hold off;

% Example usage: Get the normal vector at a specific point (x,y,z)
x = 0;
y = 0;
z = x^2 + y^2;
index = dsearchn(V, [x, y, z]);
normal_vector = N(index, :)
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