Generate a 3D cone from directing vector and aperture angle

Hello,

I have a 3D vector, let's call it [Fx Fy Fz], an aperture angle theta and a set of coordinates for the vertex [Vx Vy Vz]. What I would like to do is generate a 3D cone [Cx Cy Cz] in order to append it in a 3D graph, so I would write mesh(Cx, Cy, Cz). [Fx Fy Fz] would be the "directing" vector, oriented from the vertex to the base disk center. I found this function and slighly modified it but I realized that it had a totally different approach :

function [X2,Y2,Z2] = cone_plot3(r,h,phi,theta,offset)
    m = h/r;
    [R,A] = meshgrid(linspace(0,r,50),linspace(0,2*pi,50));
    X = R.*cos(A);
    Y = R.*sin(A);
    Z = m*R;
    % Cone around the z-axis, point at the origin
    X1 = X*cos(phi) - Z*sin(phi);
    Y1 = Y;
    Z1 = X*sin(phi) + Z*cos(phi);
    % Previous cone, rotated by angle phi about the y-axis
    X2 = X1*cos(theta) + offset(1);
    Y2 = X1*sin(theta) + offset(2);
    Z2 = Z1 + offset(3);
    % Second cone rotated by angle theta about the z-axis
end

Thanks in advance for your help