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If you picture a kidney shaped swimming pool or a lima bean, its boundary is
not a circle, but a circle with one side pushed in. In the X & Y coordinates
I wrote earlier the pushed in area are the coordinates:
X  Y

Maybe this is the "re-entrant" portion you mentioned. Describing problems
like this verbally is difficult. I don't suppose there is a way to post an
image of my graph here? 

More efficient is good, but simpler might be better here. 

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