Far-field reflector problem and intersection of paraboloids

DOI10.1007/s00211-015-0780-zzbMath1354.78003OpenAlexW2246456774MaRDI QIDQ315717

Boris Thibert, Quentin Mérigot, Pedro Machado Manhães de Castro

Publication date: 22 September 2016

Published in: Numerische Mathematik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00211-015-0780-z

zbMATH Keywords

inverse problemVoronoi diagramconcave maximization problemfar field reflector problem

Mathematics Subject Classification ID

PDEs in connection with optics and electromagnetic theory (35Q60) Computer graphics; computational geometry (digital and algorithmic aspects) (68U05) Convex functions and convex programs in convex geometry (52A41) Optimization problems in optics and electromagnetic theory (78M50) Geometric optics (78A05) Numerical methods for variational inequalities and related problems (65K15)

Related Items (12)

On the numerical solution of the far field refractor problem ⋮ Optimal transportation, modelling and numerical simulation ⋮ Point source regularization of the finite source reflector problem ⋮ Monotone discretization of the Monge–Ampère equation of optimal transport ⋮ Entropic optimal transport solutions of the semigeostrophic equations ⋮ The Sinkhorn algorithm, parabolic optimal transport and geometric Monge-Ampère equations ⋮ Optimal transport: discretization and algorithms ⋮ An Algorithm for Optimal Transport between a Simplex Soup and a Point Cloud ⋮ Aspherical Lens Design and Imaging ⋮ An overview of mathematical modeling of geometric optics problems involving refraction ⋮ An Iterative Least-Squares Method for Generated Jacobian Equations in Freeform Optical Design ⋮ A damped Newton algorithm for generated Jacobian equations

Uses Software

• CGAL

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• An iterative scheme for solving the optimal transportation problem
• Weak solutions of one inverse problem in geometric optics
• Dual coordinate step methods for linear network flow problems
• On a Monge-Ampère equation arising in geometric optics
• Minkowski-type theorems and least-squares clustering
• On the design of a reflector antenna. II
• On the regularity of reflector antennas
• Classroom examples of robustness problems in geometric computations
• A characterization of revolution quadrics by a system of partial differential equations
• Determination of reflector surfaces from near-field scattering data
• Power Diagrams: Properties, Algorithms and Applications
• On the design of a reflector antenna
• Interval arithmetic yields efficient dynamic filters for computational geometry

This page was built for publication: Far-field reflector problem and intersection of paraboloids