function F = calculate_F_vertex(these_plane_angles,these_fold_angles) %#codegen
assert(isa(these_plane_angles, 'double'));
assert(isa(these_fold_angles, 'double'));

assert (all(size(these_plane_angles)<=[1 100]));
assert (all(size(these_fold_angles)<=[100 1]));


% Compute F at a possibly open vertex using plane angles and fold angles
valence = length(these_fold_angles);

% go through and construct edges,normals and matrices

ej = [1 0 0];% First edge lies along x axis, second edge lies in x y plane
njp1 = [0 0 1]; %normal_2 = e1 x e2 lies along z axis
Bj = axis_angle(ej,these_fold_angles(1)); 
Cjp1 = axis_angle(njp1,these_plane_angles(1)); 
ej = (Cjp1*ej')'; 

F = Cjp1*Bj;

for j = 2:valence  % runs over edges
    Bj = axis_angle(ej,these_fold_angles(j)); % rotate about next edge with fold angle    

    njp1 = (Bj*njp1')';    
    Cjp1 = axis_angle(njp1,these_plane_angles(j));
    
    ej = (Cjp1*ej')'; 
    F=Cjp1*Bj*F;
end

end

function R = axis_angle(n, theta)

    % let's try this faster code from vrrotvec2mat.m    
    s = sin(theta);
    c = cos(theta);
    t = 1 - c;

    x = n(1);
    y = n(2);
    z = n(3);
    R = [ ...
     t*x*x + c,    t*x*y - s*z,  t*x*z + s*y; ...
     t*x*y + s*z,  t*y*y + c,    t*y*z - s*x; ...
     t*x*z - s*y,  t*y*z + s*x,  t*z*z + c ...
    ];

end