IMHASO, (...And Sober...)

I wouldn't get worried about the fact that intersect operates on more than one Line. So does 'equals' - you just take another member of the class as an arg and its all quite natural.

As I suspect you think too, the Helpers idea is barbaric. Why use objects at all in that case?

So one OO way to do it (in pseudo-code definitions) would be:

Polygon:
->new( Point p1, Point p2, ... );
->has_inside( Point p );  # return true/false
->get_outside_point();    # return Point outside the polygon
->first_line();           # return 'line 1' - reset counter
->next_line();            # return next_line, incr counter
                          # undef if no more

Line:
->new( Point x, Point y );
->intersects( Line l );   # return true/false
# Is this what you mean by 'same_line'?
->equals( Line l );       # return true/false
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Lastly, I like to name 'private' methods with a leading underscore. So if ->same_line or ->equals is really only needed by ->intersects you might want to rename it to ->_equals.

(This is just documentation obviously. Anyone with the MilliClue (or KiloClue) who wishes to violate the published API is free to. This is perl, after all.)

However, in this particular case it seems like a sensible function to have as part of the object's "published" API and so I probably wouldn't do it.