%--------------------------
 % @Author: Jingqiao Hu
 % @Date: 2021-12-07 09:13:42
 % @LastEditTime: 2022-01-29 20:35:31

 % sensitivity on align-CVT of MMC
 % dcdp = dcdH * dHdp
%--------------------------
function [c_dH, c_interEles] = sensitivity_mmc_align(c_nodes, c_tets, seeds0, step, T, ...
    epsilon, conn_list, c_rho, c_phi, c_interPolySeed, nelx, nely, nelz, microx,optDesign)

    npnts = size(seeds0, 1);    
    c_dH        = cell(npnts, 4);
    c_interEles = cell(npnts, 4);

    seeds = [seeds0, T];
    
    parfor i = 1 : npnts
        
        neighbor = conn_list{i};
        local_idx = int32([neighbor; i]);

        for j = 1:4
%             tic
            % minus
            seeds_minus = seeds;
            seeds_minus(i, j) = seeds_minus(i, j) - step;

            % only update the neighbor cells
            [~,~, edges, c_nnbEdgeIDX, c_nnbSeedIDX] = intersection_info(seeds_minus(:,1:3), ...
                local_idx, nelx, nely, nelz, microx ,optDesign);
            MMCs = update_MMCs(edges, seeds_minus(:,4), c_nnbSeedIDX);

            [rhoMinus, ~] = update_projection(c_nodes, c_tets, MMCs, ...
                epsilon, c_rho, c_phi, c_nnbEdgeIDX, c_interPolySeed, local_idx);
            
            % plus
            seeds_plus = seeds;
            seeds_plus(i, j) = seeds_plus(i, j) + step;

            [~,~, edges, c_nnbEdgeIDX, c_nnbSeedIDX] = intersection_info(seeds_plus(:,1:3), ...
                local_idx, nelx, nely, nelz, microx,optDesign);
            MMCs = update_MMCs(edges, seeds_plus(:,4), c_nnbSeedIDX);

            [rhoPlus, interEles] = update_projection(c_nodes, c_tets, MMCs, ...
                epsilon, c_rho, c_phi, c_nnbEdgeIDX, c_interPolySeed, local_idx);

            nnb = length(interEles);
            dH_ele = cell(nnb, 1); 
            for k = 1 : nnb
                ele = interEles(k);
                dH_ele{k} = (rhoPlus{ele} - rhoMinus{ele}) / 2 / step;
            end
            c_dH{i,j} = dH_ele;
            c_interEles{i,j} = interEles;
        end
    end
end