%--------------------------
 % @Author: Jingqiao Hu
 % @Date: 2021-12-03 19:58:59
 % @LastEditTime: 2022-01-27 16:43:01
%--------------------------
function [valid_tets] = checkValid_tetmesh(node, tets)

    delta = 1e-3; 

    x = node(:,1); % n,1
    y = node(:,2);
    z = node(:,3);
    x = x(tets); % m,4
    y = y(tets);
    z = z(tets);

    vol = tet_volume(x,y,z);
    [idx, ~] = find(abs(vol) < delta);

    ntet = size(tets, 1);
    vaild_idx = setdiff(1:ntet, idx);
    valid_tets = tets(vaild_idx, :);
%     nonvalid_faces = tets(idx, :);

    if max(valid_tets(:)) ~= size(node, 1) || min(valid_tets(:)) ~= 1
        error("fixme!");
    end

%     valid_nodes = nodes;
%     test = unique(valid_tets(:));
%     figure; trimesh(valid_tets,nodes(:,1),nodes(:,2));
end

function [v] = tet_volume(x,y,z)
    
    x1 = x(:,1); x2 = x(:,2); x3 = x(:,3); x4 = x(:,4); 
    y1 = y(:,1); y2 = y(:,2); y3 = y(:,3); y4 = y(:,4); 
    z1 = z(:,1); z2 = z(:,2); z3 = z(:,3); z4 = z(:,4); 
    
    v = (x2-x1) .* ((y3-y1) .* (z4-z1) - (y4-y1) .* (z3-z1)) + ...
        (y2-y1) .* ((x4-x1) .* (z3-z1) - (x3-x1) .* (z4-z1)) + ...
        (z2-z1) .* ((x3-x1) .* (y4-y1) - (x4-x1) .* (y3-y1));
end