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Journal for Geometry and Graphics 14 (2010), No. 1, 069--080
Copyright Heldermann Verlag 2010

Reflected Surfaces and Their Directing Cones

Alexander Dvoretsky
The National Academy of Nature Protection and Resort Construction, Kievskay Steet 181, Simferopol 95493, Ukraine

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.

Keywords: Ruled surface, directing cone, line congruence, reflected rays surface, normals surface.

MSC: 51N05

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