%--------------------------
 % @Author: Jingqiao Hu
 % @Date: 2021-02-26 13:51:19
 % @LastEditTime: 2021-03-04 21:38:32

 % the order is sorted as noedenrs, from small to big
%--------------------------
function [iK, jK, edofMat] = assemble_bezier(nelx, nely, nelz, num_b)

    % STEP.1 construct global surface nodes
    new_nelx = nelx * (num_b + 1);
    new_nely = nely * (num_b + 1);
    new_nelz = nelz * (num_b + 1);
    Num_node = (1+new_nelx) * (new_nely+1) * (new_nelz+1);
    nodenrs = reshape(1:Num_node, 1+new_nely, 1+new_nelx, 1+new_nelz);
    
    [up, front, down, back, left, right, dofs_num] = surface_dofs_id(num_b+1);
    surface_nodes = zeros(nelx, nely, nelz, dofs_num/3);
    
    parfor i = 1 : nelx
        for j = 1 : nely
            for k = 1 : nelz
                nodes_ele = nodenrs((j-1)*(num_b+1)+1 : j*(num_b+1)+1, ...
                                    (i-1)*(num_b+1)+1 : i*(num_b+1)+1, ...
                                    (k-1)*(num_b+1)+1 : k*(num_b+1)+1);
                inner = nodes_ele(2:end-1, 2:end-1, 2:end-1);
                surface_nodes(i,j,k,:) = setdiff(nodes_ele(:), inner(:));
            end
        end
    end
    global_nodes = unique(surface_nodes(:)); % remove interior nodes of every macro-ele

    % STEP.2 using local surface_id to get global surface dofs    
    edofMat = zeros(nelx*nely*nelz, dofs_num);
    
    for i = 1 : nelx
        for j = 1 : nely
            for k = 1 : nelz                
                sn  = squeeze(surface_nodes(i,j,k,:));

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

                % remove dofs on duplicated edges
                % NOTE: there is a sorting
                nid1 = unique([up_id, front_id, down_id, back_id, left_id, right_id]);
                dofs_id = [3*nid1(:)-2, 3*nid1(:)-1, 3*nid1(:)]';
                dofs_id = dofs_id(:);

                ele = (k-1)*nelx*nely + (i-1)*nely + j;
                edofMat(ele, :) = dofs_id;
            end
        end
    end

    iK = reshape(kron(edofMat,ones(dofs_num,1)).', dofs_num^2*nelx*nely*nelz, 1);
    jK = reshape(kron(edofMat,ones(1,dofs_num)).', dofs_num^2*nelx*nely*nelz, 1);

    EleNodesID = edofMat(:, 3:3:end)./3; 

    % test
%     tmp = ref_nodes';
%     tmp = tmp(:);
%     figure;
%     for ele = 1: nelx*nely*nelz
%         edof = edofMat(ele, :);
%         nodes_e = reshape(tmp(edof), 3, [])';
%         scatter3(nodes_e(:,1), nodes_e(:,2), nodes_e(:,3),'filled'); axis equal; hold on;
%     end
end

function nid1 = get_dofs_id(global_nodes, surface_nodes, local_dofs_id)
    local_nodes_id = local_dofs_id(3:3:end)/3;
    nodes = surface_nodes(local_nodes_id);
    [nid1,~] = find(global_nodes(:)==nodes(:)'); % global nodes id

%     dofs_id = [3*nid1(:)-2, 3*nid1(:)-1, 3*nid1(:)]';
%     dofs_id = dofs_id(:);
end