Robust epsilon visibility

Analytic visibility algorithms, for example methods which compute a subdivided mesh to represent shadows, are notoriously unrobust and hard to use in practice. We present a new method based on a generalized definition of extremal stabbing lines, which are the extremities of shadow boundaries. We treat scenes containing multiple edges or vertices in degenerate configurations, (e.g., collinear or coplanar). We introduce a robust ε method to determine whether each generalized extremal stabbing line is blocked, or is touched by these scene elements, and thus added to the line's generators. We develop robust blocker predicates for polygons which are smaller than ε. For larger ε values, small shadow features merge and eventually disappear. We can thus robustly connect generalized extremal stabbing lines in degenerate scenes to form shadow boundaries. We show that our approach is consistent, and that shadow boundary connectivity is preserved when features merge. We have implemented our algorithm, and show that we can robustly compute analytic shadow boundaries to the precision of our chosen ε threshold for non-trivial models, containing numerous degeneracies.