Geodesic
Light Ray Trajectories and Projective Correspondences
Journal for geometry and graphics, Tome 15 (2011) no. 2, pp. 181-193

Voir la notice de l'article provenant de la source Heldermann Verlag

This paper considers trajectories of light rays from the position of projective geometry. On the basis of the well-known Law of Reflection the trajectory of a light ray between two intersecting planes is examined. A process of construction leads to a spatial polygon made up from repeatedly reflected rays. It demonstrates that there are projective fields of points involved. We examine the construction of trajectory of a light ray in a diamond. The process of light reflection creates a collineation between two diamond facets. Double points of this collineation indicate the presence of closed light contours inside the diamond. A computer program, developed by the authors, enables users to compare various forms of diamonds and search for the best with respect to light reflection properties.
Classification : 51N05
Mots-clés : Reflected and refracted rays, collineation, double points, graphical interface 
M. Manevich; E. Itskovich. Light Ray Trajectories and Projective Correspondences. Journal for geometry and graphics, Tome 15 (2011) no. 2, pp. 181-193. http://geodesic.mathdoc.fr/item/JGG_2011_15_2_JGG_2011_15_2_a5/
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     author = {M. Manevich and E. Itskovich},
     title = {Light {Ray} {Trajectories} and {Projective} {Correspondences}},
     journal = {Journal for geometry and graphics},
     pages = {181--193},
     year = {2011},
     volume = {15},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/JGG_2011_15_2_JGG_2011_15_2_a5/}
}
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