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Optics Letters

| RAPID, SHORT PUBLICATIONS ON THE LATEST IN OPTICAL DISCOVERIES

  • Editor: Alan E. Willner
  • Vol. 35, Iss. 2 — Jan. 15, 2010
  • pp: 100–102

On the reflection point where light reflects to a known destination on quadratic surfaces

Nuno Gonçalves  »View Author Affiliations


Optics Letters, Vol. 35, Issue 2, pp. 100-102 (2010)
http://dx.doi.org/10.1364/OL.35.000100


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Abstract

We address the problem of determining the reflection point on a specular surface where a light ray that travels from a source to a target is reflected. The specular surfaces considered are those expressed by a quadratic equation. So far, there is no closed form explicit equation for the general solution of this determination of the reflection point, and the usual approach is to use the Snell law or the Fermat principle whose equations are derived in multidimensional nonlinear minimizations. We prove in this Letter that one can impose a set of three restrictions to the reflection point that can impose a set of three restrictions that culminates in a very elegant formalism of searching the reflection point in a unidimensional curve in space. This curve is the intersection of two quadratic equations. Some applications of this framework are also discussed.

© 2010 Optical Society of America

OCIS Codes
(080.2720) Geometric optics : Mathematical methods (general)
(110.2990) Imaging systems : Image formation theory
(200.1130) Optics in computing : Algebraic optical processing
(150.0155) Machine vision : Machine vision optics
(150.1135) Machine vision : Algorithms
(080.1753) Geometric optics : Computation methods

History
Original Manuscript: June 5, 2009
Revised Manuscript: September 17, 2009
Manuscript Accepted: November 26, 2009
Published: January 11, 2010

Citation
Nuno Gonçalves, "On the reflection point where light reflects to a known destination on quadratic surfaces," Opt. Lett. 35, 100-102 (2010)
http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-35-2-100


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References

  1. M. Born and E. Wolf, Principles of Optics (Pergamon, 1965).
  2. E. Hecht, Optics (Addison-Wesley, 1987).
  3. L. Szirmay-Kalos, T. Umenhoffer, G. Patow, L. Szécsi, and M. Sbert, in Computer Graphics Forum (2009), pp. 1-31.
  4. K. Nielsen and N. Christensen, Journal of WSCG (2002), Vol. 10, pp. 91-98.
  5. P. Estalella, I. Martin, G. Drettakis, and D. Tost, in Eurographics Symposium on Rendering (2006), pp. 312-318.
  6. P. Estalella, I. Martin, G. Drettakis, D. Tost, O. Devillers, and F. Cazals, in Proceedings of Vision Modeling and Visualization (2005), pp. 471-478.
  7. D. Roger and N. Holzschuch, in Proceedings of Eurographics (2006), Vol. 25.
  8. J. Stolfi, Oriented Projective Geometry (Academic, 1991).
  9. J. Levin, Comput. Graph. Image Process. 11, 73 (1979). [CrossRef]
  10. L. Dupont, D. Lazard, S. Lazard, and S. Petitjean, J. Symb. Comput. 43, 168 (2008). [CrossRef]
  11. L. Dupont, D. Lazard, S. Lazard, and S. Petitjean, J. Symb. Comput. 43, 192 (2008). [CrossRef]
  12. L. Dupont, D. Lazard, S. Lazard, and S. Petitjean, J. Symb. Comput. 43, 216 (2008). [CrossRef]

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