Geodesic
Reflected Surfaces and Their Directing Cones
Journal for geometry and graphics, Tome 14 (2010) no. 1, pp. 69-8.

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

This article is devoted to the surface which arises after reflecting parallel rays along a planar section of a reflecting surface. The resulting "reflected rays surface" enables to decompose the congruence of the reflected rays into a one-parametric set of reflected rays surfaces. Three director curves of the reflected rays surfaces are determined: The given planar section, a double line and a directing cone. By the use of the directing cone as the third director curve of the reflected rays surface the law of reflection is realized. There is a connection between the direction of incident rays, the directing cone of the normal surface and the directing cone of the reflected rays surface. Proposed algorithms based on the directing cone give us the possibility to describe the reflected rays surfaces along planar sections of particular reflecting surfaces analytically and synthetically.
Classification : 51N05
Mots-clés : Ruled surface, directing cone, line congruence, reflected rays surface, normals surface 
@article{JGG_2010_14_1_JGG_2010_14_1_a5,
     author = {A. Dvoretsky },
     title = {Reflected {Surfaces} and {Their} {Directing} {Cones}},
     journal = {Journal for geometry and graphics},
     pages = {69--8},
     publisher = {mathdoc},
     volume = {14},
     number = {1},
     year = {2010},
     url = {http://geodesic.mathdoc.fr/item/JGG_2010_14_1_JGG_2010_14_1_a5/}
}
TY  - JOUR
AU  - A. Dvoretsky 
TI  - Reflected Surfaces and Their Directing Cones
JO  - Journal for geometry and graphics
PY  - 2010
SP  - 69
EP  - 8
VL  - 14
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/JGG_2010_14_1_JGG_2010_14_1_a5/
ID  - JGG_2010_14_1_JGG_2010_14_1_a5
ER  - 
%0 Journal Article
%A A. Dvoretsky 
%T Reflected Surfaces and Their Directing Cones
%J Journal for geometry and graphics
%D 2010
%P 69-8
%V 14
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/JGG_2010_14_1_JGG_2010_14_1_a5/
%F JGG_2010_14_1_JGG_2010_14_1_a5
A. Dvoretsky . Reflected Surfaces and Their Directing Cones. Journal for geometry and graphics, Tome 14 (2010) no. 1, pp. 69-8. http://geodesic.mathdoc.fr/item/JGG_2010_14_1_JGG_2010_14_1_a5/