You said the above illustration is kind of rough, so maybe I'm just confused by that....  But aren't two points of equal distance from a third point on a curve?  A circle is the set of all points of equal distance from a central point.  Uh.  Right?  Does this affect the premise which starts from points 1 and 4 being of equal distance, or am I fixating on the illustration?

Well, darn it... I have code to gather all the information, but it slows everything down again!  So back to the drawing board for the umpteenth time....

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Cage can be an opinionated jerk who posts without thinking.  He apologizes for this.  He's honestly not trying to be a turkeyhead.

Cage had some freebies, compatible with Poser 11 and below.  His Python scripts were saved at archive.org, along with the rest of the Morphography site, where they were hosted.