%--------------------------
 % @Author: Jingqiao Hu
 % @Date: 2022-01-06 11:30:36
 % @LastEditTime: 2022-05-09 21:01:13

 % cvt energy
%--------------------------
function [E, dE] = cvt_energy(seeds, cenP)

    npnts   = size(seeds, 1);

    E0  = sum((seeds - cenP) .^ 2, 2); % [n,1]
    dE0 = 2 * (seeds - cenP);          % [n,2]
    
    E  = sum(E0);
    dE0(:, 4) = 0;
    dE = reshape(dE0', [], 1);
end

function [E, dE] = cvt_energy_rho(seeds, cpnts, rho, cenP)

    npnts   = size(seeds, 1);
    rhoP    = zeros(npnts, 1);

    % compute centroid & its rho 
%     figure;
    parfor i = 1 : npnts
        % find the nearest point of current seed
        pi = seeds(i, :);
        dist = vecnorm(cpnts - pi, 2, 2);
        [~, idx] = min(dist);
        rhoP(i) = rho(idx);
    end

    E0  = sum((seeds - cenP) .^ 2, 2); % [n,1]
    dE0 = 2 * (seeds - cenP);          % [n,2]
    
    E  = sum(E0 .* rhoP);
    dE = dE0 .* rhoP;
    dE(:, 4) = 0;
    dE = reshape(dE', [], 1);
end