%--------------------------
 % @Author: Jingqiao Hu
 % @Date: 2021-12-28 21:34:40
 % @LastEditTime: 2022-01-08 22:41:19

 % the mesh and MMCs are independent,
 %     which means the MMCs is moving and the mesh remains unchanged
 % c_interPolyMMC: the intersected polygon for each mmc
 % c_interPolySeed: the intersected polygon for each seed
%--------------------------
function [c_rho, c_phi] = projection_independent(nodes_cell, faces_cell, ...
    MMCs, epsilon, c_nnbEdgeIDX, c_interPolySeed)

    ncvt  = size(nodes_cell, 1);
    
    c_phi = init_phi(ncvt, nodes_cell);
    c_rho = cell(ncvt, 1);    
    
    for i = 1 : ncvt
        pid = c_interPolySeed{i};
        mid = c_nnbEdgeIDX{i}; 

        for j = 1 : length(mid)
            mmc = MMCs(mid(j), :);

            for k = 1 : length(pid)
                ele = pid(k); 
                nodes = nodes_cell{ele};

                phi = tPhi(mmc, nodes(:,1), nodes(:,2));
                c_phi{ele} = max(phi, c_phi{ele});
            end
        end
    end

    % Heaviside
%     figure; clf
    parfor ele = 1 : ncvt
        H = Heaviside_simply(c_phi{ele}, epsilon); 

        faces = faces_cell{ele};
        c_rho{ele} = sum(H(faces), 2) / 3;

%         nodes = nodes_cell{ele};
%         patch('Faces',faces,'Vertices',nodes,'FaceVertexCData',1 - H','FaceColor','interp','EdgeColor','interp'); hold on;
    end
%     colormap("gray"); axis equal; axis off; pause(1e-6);

    % % projection of signed distance
    % for i = 1 : nmmcs
    %     mmc = MMCs(i, :);
    %     r = c_interPolyMMC{i};
    %     % for all intersected cell
    %     for k = 1 : length(r)
    %         ele = r(k);
    %         nodes = nodes_cell{ele};

    %         phi = tPhi(mmc, nodes(:,1), nodes(:,2));
    %         c_phi{ele} = max(phi, c_phi{ele});
    %     end
    % end
end

function phi_cell = init_phi(ncvt, nodes_cell)
    phi_cell = cell(ncvt, 1);
    parfor ele = 1:ncvt
        phi_cell{ele} = repmat(-1e5, size(nodes_cell{ele}, 1), 1);
    end
end