%--------------------------
 % @Author: Jingqiao Hu
 % @Date: 2021-12-28 21:34:40
 % @LastEditTime: 2022-05-09 21:13:55

 % 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(c_nodes, c_tets, ...
    MMCs, epsilon, c_nnbEdgeIDX, c_interPolySeed, microx)

    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

%     figure; camlight;lighting gouraud

    % Heaviside
    parfor ele = 1 : ncvt
        H = Heaviside_simply(c_phi{ele}, epsilon);  
        
%         FF = reshape(c_phi{ele}, microx+1, microx+1, microx+1);
%         x = c_nodes{ele}(:,1);
%         y = c_nodes{ele}(:,2);
%         z = c_nodes{ele}(:,3);
%         x = reshape(x, microx+1,microx+1, microx+1);
%         y = reshape(y, microx+1,microx+1, microx+1);
%         z = reshape(z, microx+1,microx+1, microx+1);
% %         [faces,verts] = isosurface(x,y,z,phi,0); 
%             
%     p=patch(isosurface(x,y,z,FF,0));
%     set(p,'facecolor','[0.8 0.4 0.4]','edgecolor','none');
%     p=patch(isocaps(x,y,z,FF,0,'FaceColor','red'));
%     set(p,'facecolor','[0.8 0.4 0.4]','edgecolor','none');
%     view([10 25])
%     axis equal; axis tight;
%     xlabel('x axis');
%     ylabel('y axis');
%     zlabel('z axis');
%     hold on;

        
%         sum(c_rho{ele} > 0.1)

        faces = c_tets{ele};
        c_rho{ele} = sum(H(faces), 2) / size(faces,2);
        
%         sum(c_rho{ele} > 0.5)
    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