Light in Power: A General and Parameter-free Algorithm for Caustic Design

Quentin Mérigot 1 Jocelyn Meyron 2, 3, * Boris Thibert 3
* Auteur correspondant
2 GIPSA-AGPIG - AGPIG
GIPSA-DIS - Département Images et Signal
3 CVGI - Calcul des Variations, Géométrie, Image
LJK - Laboratoire Jean Kuntzmann
Abstract : We present in this paper a generic and parameter-free algorithm to efficiently build a wide variety of optical components, such as mirrors or lenses, that satisfy some light energy constraints. In all of our problems, one is given a collimated or point light source and a desired illumination after reflection or refraction and the goal is to design the geometry of a mirror or lens which transports exactly the light emitted by the source onto the target. We first propose a general framework and show that eight different optical component design problems amount to solving a Light Energy Conservation equation that involves the computation of Visibility diagrams. We show that these diagrams all have the same structure and can be obtained by intersecting a 3D Power Diagram with a planar or spherical domain. This allows us to propose an efficient and fully generic algorithm capable to solve the eight optical component design problems. Our solutions can satisfy design constraints such as convexity or concavity and are always graphs over the plane or the sphere. We show the effectiveness of our algorithm on numerous simulated examples.
Type de document :
Pré-publication, Document de travail
2017
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https://hal.archives-ouvertes.fr/hal-01570739
Contributeur : Jocelyn Meyron <>
Soumis le : lundi 31 juillet 2017 - 15:53:03
Dernière modification le : jeudi 17 mai 2018 - 10:26:04

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lenses-mirrors.pdf
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  • HAL Id : hal-01570739, version 1

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Quentin Mérigot, Jocelyn Meyron, Boris Thibert. Light in Power: A General and Parameter-free Algorithm for Caustic Design. 2017. 〈hal-01570739〉

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