%--------------------------
 % @Author: Jingqiao Hu
 % @Date: 2021-02-26 13:52:54
 % @LastEditTime: 2021-02-26 14:01:46

 % find the indices of its 48-macro-dofs distributed on the surface in this macro-ele
 % don't care about duplicated pnts on neighbor edges, just cover them when assigning
 %   4-----3
 %  /|    /|
 % 8-----7 2   
 % |     |/
 % 5-----6
 % RETURN:    back(1234),up(3478),front(5678),down(1256),left(1485),right(2376)
 % PARAMETER: this macro-ele is divided into microx^3 elements
%--------------------------
function [up_id, front_id, down_id, back_id, left_id, right_id, dofs_num] = surface_dofs_id(microx)
    
    Num_node = (1+microx)^3;
    nodenrs = reshape(1:Num_node, 1+microx, 1+microx, 1+microx);
    
    % extract surface nodes
    inner = nodenrs(2:end-1, 2:end-1, 2:end-1);
    surface_nodes = setdiff(nodenrs(:), inner(:));
    
    dofs_num = length(surface_nodes)*3;

    % faces
    back  = reshape(squeeze(nodenrs(1:end, 1:end, 1)), 1, []);
    front = reshape(squeeze(nodenrs(1:end, 1:end, end)), 1, []);
    up    = reshape(squeeze(nodenrs(1, 1:end, 1:end)), 1, []);
    down  = reshape(squeeze(nodenrs(end, 1:end, 1:end)), 1, []);
    left  = reshape(squeeze(nodenrs(1:end, 1, 1:end)), 1, []);
    right = reshape(squeeze(nodenrs(1:end, end, 1:end)), 1, []);

    back_id  = get_dofs_id(surface_nodes, back);
    front_id = get_dofs_id(surface_nodes, front);
    up_id    = get_dofs_id(surface_nodes, up);
    down_id  = get_dofs_id(surface_nodes, down);
    left_id  = get_dofs_id(surface_nodes, left);
    right_id = get_dofs_id(surface_nodes, right);
end

function dofs_id = get_dofs_id(all_nodes, nid)
    [nid1, ~] = find(all_nodes==nid);
    dofs_id = [3*nid1(:)-2, 3*nid1(:)-1, 3*nid1(:)]';
    dofs_id = dofs_id(:);
end