%--------------------------
 % @Author: Jingqiao Hu
 % @Date: 2021-12-29 10:34:40
 % @LastEditTime: 2022-01-29 20:38:20

 % only update the projection of the neighbor cell of curr_idx, for efficiency
%--------------------------
function [c_rho1, interEles] = update_projection(c_nodes, c_tets, MMCs, ...
    epsilon, c_rho, c_phi, c_nnbEdgeIDX, c_interPolySeed, local_idx)

    npnts = length(local_idx);

    [c_phi, interEles] = init_phi(local_idx, c_interPolySeed, c_phi); % important

    for i = 1 : npnts
        sid = local_idx(i);         % seed-id
        pid = c_interPolySeed{sid}; % pgon-id intersected with this seed
        mid = c_nnbEdgeIDX{i};         % MMCs-id corresponding this seed        

        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

    c_rho1 = c_rho;

    % Heaviside
    for i = 1 : length(interEles)
        ele = interEles(i);

        H = Heaviside_simply(c_phi{ele}, epsilon); 

        faces = c_tets{ele};
        c_rho1{ele} = sum(H(faces), 2) / 4;
    end
end

function [phi_cell, interEles] = init_phi(local_idx, c_interPolySeed, phi_cell)

    interEles = [];
    for i = 1:length(local_idx)
        sid = local_idx(i);
        pid = c_interPolySeed{sid}; % pgon-id intersected with this seed

        for j = 1 : length(pid)
            ele = pid(j);
            phi_cell{ele}(:) = -1e5;
        end
        interEles = [interEles; pid];
    end
    interEles = unique(interEles);
end