by "antipodal visibility" of planar, simple polygons I mean the following property:
if two points $p$ and $q$ on the polygon's boundary divide the polygon's boundary into two polylines of equal length, then the line-segment between $p$ and $q$ doesn't intersect the polygon's boundary, except in $p$ and in $q$.
Questions:
- do non-convex polygons with antipodal visibility exist?
- if yes, is anything known about their algorithmic construction (esp. of random instances)?