%--------------------------
 % @Author: Jingqiao Hu
 % @Date: 2021-11-30 11:16:16
 % @LastEditTime: 2022-01-08 22:36:10
%--------------------------
function [edofMat, nvar, nodes] = assembleInfo_cvt(c_vedges, nbridge_each, nbnodes_cell)

    ncvt = size(c_vedges, 1);

    nodes0 = [];
    cbns_cell = cell(ncvt, 1);

    % step.1 transverse all nodes, generate unique nodes
    % generate bezier control nodes for the following step
    for ele = 1 : ncvt
        vedges = c_vedges{ele};
        cbns = [];

        nbele = nbnodes_cell{ele} - 1; % for those three situations

        for i = 1 : size(vedges, 1)
            n1 = vedges(i, 1:2);
            n2 = vedges(i, 3:4);
            step = (n2 - n1) / (nbridge_each + 1);

            if i == 1
                cbns = [cbns; n1];
            end

            nb_edge = nbele(i);
            % 1. nb_edge = 1, without additional nodes
            % 2. nb_edge = 2, add one control node
            if nb_edge == 2
                n11 = (n1+n2) / 2;
                cbns = [cbns; n11];
                
            elseif nb_edge > 2
                % 3. nb_edge = 3, add control nodes as usual
                % TODO: update in the future
                assert(nbridge_each + 1 <= nb_edge); 
            
                for j = 1 : nbridge_each + 1 % the segment num of one edge
                    % the two control pnts
                    n11 = step * 1/3 + n1 + step * (j-1);
                    n12 = step * 2/3 + n1 + step * (j-1);
    
                    % additional bridge nodes
                    if j==nbridge_each+1
                        nbnode = [];
                    else
                        nbnode = j * step + n1;
                    end
    
                    % add these nodes
                    cbns = [cbns; n11; n12; nbnode];
                end
            end            
            if i < size(vedges, 1)
                cbns = [cbns; n2];
            end
        end
        cbns_cell{ele} = cbns;
        nodes0 = [nodes0; cbns];

%         figure; scatter(cbns(:,1), cbns(:,2));
    end 
    nodes = unique(nodes0, 'rows'); % NOTE: the order changed
    nvar = size(nodes,1) * 2;
%     figure; hold on; scatter(nodes(:,1), nodes(:,2));
%     figure;

    % step.2 each cvt-i, check each nodes on global
    edofMat = cell(ncvt, 1);
    for ele = 1 : ncvt
        cbns_local = cbns_cell{ele};
        [~, idx] = ismember(cbns_local, nodes, 'rows'); 
        
        % NOTE: the sequence must conforms to Ke
        edof0 = [2*idx-1, 2*idx]';
        edofMat{ele} = edof0(:);
    end    
end