I can beat your solution and get a score of 0.433....
Gnxr gur pbirevat funcr gb or gur jubyr fdhner naq pbzcyrgryl snvy gb pbire gur gevnatyr.
:-P
EDIT: Va snpg, jul abg trg n ernyyl tbbq fpber ol gnxvat n pbzcyrgryl tvtnagvp funcr gung qbrfa'g pbire nalguvat.
Yes, well ... If the shape is gigantic and therefore doesn't cover anything ... this is a cunning solution, but in a sense trivial.
A non-trivial solution would be (even) better. ;)
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