Geodesic
Light Ray Trajectories and Projective Correspondences
Journal for geometry and graphics, Tome 15 (2011) no. 2, pp. 181-193 Cet article a éte moissonné depuis la source Heldermann Verlag

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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 
@article{JGG_2011_15_2_JGG_2011_15_2_a5,
     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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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/