What are the "lines" in a constellation or asterism called?
My understanding is that the stick-figure lines (in terms of applying them to every constellation) are a fairly modern invention - before that the individual stars were not (generally speaking) linked together directly but were instead highlighting important areas of each constellation figure. The constellation figures were fully 2D and potentially quite detailed, and there was not always a one to one correspondence between stars and details. In this sense one is free to modify the existing stick figure patterns to suit one's needs. Many of the stars visible to the naked eye have individual names (sometimes more than one name in fact) and these names usually mean/meant something about the constellation figure they are/were in. It's not always possible to follow these names when redrawing the figures (the constellations we use today are not all ancient and star names remain from figures we no longer use), but usually you can accommodate most of them. This is one of my main problems with H.A.Rey's versions - they often pay no attention at all to what the star names mean and you end up with a star named for a tail now marking the figure's mouth. :)