I do not know what it is that makes people think that cambered rigs need extra lines that were not present in "flat" sails. Nor do I know why so many people think that traditional junk sail are flat. If you look at photos of junks, those sails are mostly anything but flat. The shape maybe there by happy accident but it is there. Even the sails belonging to my good friend and flat earther Kurt Jon Ulmer (sorry I mean flat sailor) show shape in them. A fact that he probably would rather not have pointed out. Sorry Kurt :-) but tis true

The extra line that some are making a fuss about is what is called in the west a Hong Kong parrel. Hasler mentions them in PJR (page 47 in the second Ed.) but he did not know what they were for. An understandable mistake since he also thought that junk sails are flat and since he used modern sail cloth which has tremendous diagonal stiffness he would never have see any reason for them.

Hong Kong parrels are used when the cloth does not have enough diagonal stiffness to keep intact the parallelogram that makes up the shape of each panel. When the cloth lacks diagonal stiffness, you get diagonal creases in each panel that is complaining. The Hong Kong parrel is then rigged diagonally from the top batten to the lower one. The angle should be 45 deg or more, generally the more acute the angle (within reason) the better as less acute angles have more of a tendency to pull the battens together. The parrel is normally rigged in the luff area but I can see no reason why they could not be rigged in the leach area where they would have less effect on the shape of the sail.

The parrels do appear in so called flat sails for the above reasons. If you look at the photos of Donald Riddlers Eric the Red (flat sails) you will see Hong Kong parrels. Donald needed them because his sails were made from cotton bed sheets and so he had many of the issues that traditional junks had to deal with. They also appear in many photos of traditional junks (that supposedly have flat sails).

In the west, our cloth is of better quality that most junkmen could afford so as long as we persisted in making flat sails, we never saw the need for the "extra line". However once we put camber into our sails, you very quickly see the need for Hong Kong parrels. The parrels do not mean that the sail is weaker, it just means that the sail does not have diagonal stiffness. A natural consequence of giving the panels shape.

A well made junk sail whether cambered or not is tremendously strong by virtue of the batten structure and the manner by which the loads are transferred from the sail to the hull. I do not see that camber in any way weakens the sail but it does introduce a little more complexity to the construction of the sail and in the setting up. Once the sail is set up, there is no operational difference between a flat sail and a shaped one. Except that you will sail rather more efficiently to the windward if your sail has some shape. This is not to run down flat sails, everything in boats is a compromise. You must just make the one that suits your temperament and type of sailing. One is not better than the other, just different.

If the old Chinese junk sails held together even when their weak-to-begin-with panels were partly shredded to bits, the perimeter ropes must have been good enough. And if they developed camber naturally, their fabric must have been baggy. So the idea of coming 'round full circle to old ways, is fitting. 

A shrewd and pertinent comment.  I guess only time will tell, but it's something worth considering.  At least one can always take the camber out of an existing sail if it does seem to be an issue.