Iterative Scheme for Solving Optimal Transportation Problems Arising in Reflector Design

Figure 4

Sketch of the reflectors 𝑅₁ and 𝑅₂. 𝑅₁ is the boundary of an ellipsoid whose foci are the points 𝑂 and 𝐚. 𝑅₂ is the boundary of a paraboloid whose focus is 𝐚. The sketch shows a two-dimensional cross section. A ray given by the direction 𝐦∈𝑆² will be reflected by 𝑅₁ and then by 𝑅₂ to a ray in the direction of the negative 𝑧-axis.