algorithm - probabilty of a point inside a non-convex polygon such that all rays coming from that point combinedly hit all sides of the polygon -

like in image rays coming point p cannot hit side ae directly point p not satisfy condition probability of point inside non-convex polygon such rays coming point combinedly hits sides of polygon.

if polygon convex think rays coming point inside polygon combinedly hit sides . interested in knowing concave polygon case. we given coordinates of vertex of polygon.

the set of points reach edges of polygon called visibility kernel.

the kernel intersection of half planes on left of edges. simple polygon, can computed in linear time o(n).

if points drawn uniformly inside polygon, probability ratio of area of kernel of polygon. kernel can empty, hence probability zero. convex polygons one.