%--------------------------
 % @Author: Jingqiao Hu
 % @Date: 2021-12-28 21:34:40
 % @LastEditTime: 2022-05-09 21:09:42

 % the mesh and MMCs are independent,
 %     which means the MMCs is moving and the mesh remains unchanged
 % c_interPolySeed: the intersected polytope for each seed
%--------------------------
function [c_rho, c_phi] = projection_independent_hex(c_nodes, c_tets, ...
    MMCs, epsilon, c_nnbEdgeIDX, c_interPolySeed)

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

        for j = 1 : length(mid)
            mmc = MMCs(mid(j), :);
            t  = mmc(1);
            sp = mmc(2:4);
            ep = mmc(5:7);

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

                phi = signed_distance(nodes, sp, ep, t);
                c_phi{ele} = max(phi, c_phi{ele});
            end
        end
    end

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

        faces = c_tets{ele};
        c_rho{ele} = sum(H(faces), 2) / length(faces);
    end
end

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