Reflection: The angle that a reflected ray makes with the interior
normal of the surface of relection.
In three dimension, the angle of incidence, the angle of reflection and the normal are co-planar.
Illuminated Region: Let G be a connected and bounded region. G is illuminated from a point p if for every point q that belong to G, there is a ray containing both p and q.
Directly Illuminated Region: Let G be a connected and bounded smooth region. G is directly illuminated from a point p if for every point q that belong to G, there the line segment pq lies in G.
ray: Given a region G c R2. A ray is a piecewise linear path with corners lying on a point p at the boundary of G respecting the usual law of reflection with the tangent line at p. Given a region H c R3, the ray behaves as in R2 with the tangent plane. Further, the incident and reflected portion of a ray are coplanar with the surface normal at p.
Smooth Region: We define a smooth bounded region G c R2 such that the partial derivative of G has continuously turning tangent and G lies on one side of its boudary.