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%                            Michael Pokojovy                             % 
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set(gcf, 'PaperUnits', 'centimeters');
xSize = 14; ySize = 12;
xLeft = (21 - xSize)/2; yTop = (30 - ySize)/2;
set(gcf,'PaperPosition', [xLeft yTop xSize ySize]);
set(gcf,'Position',[0 0 xSize*50 ySize*50]);

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figure(1);
hold on;
t = title('Das Vektorfeld $v(x) = (x_{3}^2 - x_{2} \sin(x_{1}), \cos(x_{1}) - 2 x_{3}, 2 x_{1} x_{3} - 2 x_{2} + x_{3})^{T}$', 'interpreter', 'latex');
set(t, 'FontSize', 16);

[X, Y, Z] = meshgrid(-1:0.2:1);

U = zeros(size(X));
V = zeros(size(Y));
W = zeros(size(Z)); 

for i = 1:size(X, 1)
for j = 1:size(X, 2)
for k = 1:size(X, 3)
    x = X(i, j, k);
    y = Y(i, j, k);
    z = Z(i, j, k);
    
    U(i, j, k) = z^2 - y*sin(x);
    V(i, j, k) = cos(x) - 2*z;
    W(i, j, k) = 2*x*z - 2*y + z;
end
end
end

quiver3(X, Y, Z, U, V, W);
grid on;
axis([-1 1 -1 1 -1 1]);

view([125 42]);

xlabel('x_{1}');
ylabel('x_{2}');
zlabel('x_{3}');