function flag = IsCrossingWindow(A,R)

%  Checks if the given conic crosses the given window
%    (the square of size 2*R centered at the origin)

%      Nikolai Chernov,  March 2012

flag = 0;

RR = R*R;

F0 = (A(1) + 2*A(2) + A(3))*RR + 2*(A(4) + A(5))*R + A(6);
if ((A(1) - 2*A(2) + A(3))*RR + 2*(A(4) - A(5))*R + A(6))*F0 <= 0
    flag = 1;
    return;
end
if ((A(1) - 2*A(2) + A(3))*RR - 2*(A(4) - A(5))*R + A(6))*F0 <= 0
    flag = 1;
    return;
end
if ((A(1) + 2*A(2) + A(3))*RR - 2*(A(4) + A(5))*R + A(6))*F0 <= 0
    flag = 1;
    return;
end

y = (-A(2)*R-A(5))/A(3);
if abs(y) < R
    if (A(1)*RR + 2*A(2)*R*y + A(3)*y*y + 2*A(4)*R + 2*A(5)*y + A(6))*F0 <= 0
        flag = 1;
        return;
    end
end

y = (A(2)*R-A(5))/A(3);
if abs(y) < R
    if (A(1)*RR - 2*A(2)*R*y + A(3)*y*y - 2*A(4)*R + 2*A(5)*y + A(6))*F0 <= 0
        flag = 1;
        return;
    end
end

x = (-A(2)*R-A(4))/A(1);
if abs(x) < R
    if (A(1)*x*x + 2*A(2)*R*x + A(3)*RR + 2*A(4)*x + 2*A(5)*R + A(6))*F0 <= 0
        flag = 1;
        return;
    end
end

x = (A(2)*R-A(4))/A(1);
if abs(x) < R
    if (A(1)*x*x - 2*A(2)*R*x + A(3)*RR + 2*A(4)*x - 2*A(5)*R + A(6))*F0 <= 0
        flag = 1;
        return;
    end
end

XY = -[A(1) A(2); A(2) A(3)]\[A(4); A(5)];
if max(abs(XY(1)),abs(XY(2))) < R
    if (A(1)*XY(1)^2 + 2*A(2)*XY(1)*XY(2) + A(3)*XY(2)^2 + 2*A(4)*XY(1) + 2*A(5)*XY(2) + A(6))*F0 <= 0
        flag = 1;
        return;
    end
end

end