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## -*- texinfo -*-
## @deftypefn {} {[@var{faces}, @var{vertices}, @var{J}] =} __unite_shared_vertices__ (@var{faces}, @var{vertices})
##
## Detect and unite shared vertices in patches.
##
## Vertices of neighboring faces are detected and united to shared vertices.
## For this, the mutual squared distances between all vertices are
## calculated.  If all coordinates are closer than
## @code{2 * eps (max (abs (vertices(:))))}, the vertices are united to one.
##
## @var{J} holds the indices of the remaining vertices.
##
## @seealso{isosurface, reducepatch}
## @end deftypefn

function [faces, vertices, J] = __unite_shared_vertices__ (faces, vertices)

  nan_vertices = any (isnan (vertices), 2);
  lut = (1:rows (vertices))';
  J = lut;
  for di = 1:3
    [v, idx] = sortrows (vertices, 1 + mod ((0:2)+di, 3));
    Js = [true;
          any(abs (diff (v, 1, 1)) > eps * abs (v(2:end,:)+v(1:end-1,:)), 2)];
    vertices = v(Js,:);
    J = J(idx(Js));
    l(idx) = cumsum (Js);
    lut = l(lut);
  endfor
  [J, idx] = sort (J);
  j(idx) = 1:length (idx);
  vertices = vertices(idx,:);
  if any (nan_vertices)
    j(end+1) = length (idx) + 1;
    vertices(end+1,:) = NaN;
    lut(nan_vertices) = rows (vertices);
  endif
  faces = j(lut(faces));

  ## Eliminate faces with zero area
  faces = faces(all (faces - faces(:, [2 3 1]) != 0, 2), :);

endfunction