TuckAngles.m

function [tuckangle] = TuckAngles(r, n, phi, theta, split)
% Calculates the angle that needs to be fold away for the hidden part of
% the elbow fitting. The inputs are the same as the elbow fitting, the out
% put is an array of angles with the same size as "lengths".
% Last edited 8/26/2021 by Wei-Hsi Chen

[lengths, ls] = Origami_Elbow_Parameters(r, n, phi, theta, split);
tuckangle = zeros(n, 1);
w = [cos(phi); sin(phi);0];
lengthsTemp = [lengths(n);lengths];
% the size of lengthsTemp is (n+2), its index is (n, 1, 2, ..., n, 1)

for k = 2:n+1
    % First find the angle around i vertex in the 2D crease pattern
    i = k;
    vfih = [-ls;lengthsTemp(i-1)-lengthsTemp(i);0];
    vfij = [ls;lengthsTemp(i+1)-lengthsTemp(i);0];
    thetafi = mod(SignedAngle(vfij, vfih, [0;0;1]),2*pi);
    
    % Then find the angle around i vertex on the truncated surface in 3D
    i = k-1;
    Ph = [r*cos(pi*(2*(i-1)-1)/n);r*sin(pi*(2*(i-1)-1)/n);0];
    Pi = [r*cos(pi*(2*i-1)/n);r*sin(pi*(2*i-1)/n);0];
    Pj = [r*cos(pi*(2*(i+1)-1)/n);r*sin(pi*(2*(i+1)-1)/n);0];
    v3dih = [Ph(1)-Pi(1);Ph(2)-Pi(2);vfih(2)];
    v3dij = [Pj(1)-Pi(1);Pj(2)-Pi(2);vfij(2)];
    an = RotationalMatrix(w,theta/2)*[0;0;1];
    theta3di = SignedAngle(v3dij, v3dih, an);
    
    tuckangle(i) = (thetafi-theta3di)/2;
end

% Outputs a size n+1 array of angles
tuckangle = [tuckangle;tuckangle(1)];

end