Abstract

We describe an interactive visualization procedure for determining the optimal surface of a special automobile side mirror, thereby removing the blind spot, without the need for feedback from the error-prone manufacturing process. If the horizontally progressive curvature distributions are set to the semi-mathematical expression for a free-form surface, the surface point set can then be derived through numerical integration. This is then converted to a NURBS surface while retaining the surface curvature. Then, reflective scenes from the driving environment can be virtually realized using photorealistic ray tracing, in order to evaluate how these reflected images would appear to drivers.

© 2014 Optical Society of America

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References

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  1. J. F. Morgan and M. Blanco, “Synthesis study of light vehicle non-planar mirror research,” NHTSA DOT HS 811–328, 47 (2010).
  2. J. Luoma, M. J. Flannagan, and M. Sivak, “Effects of nonplanar driver-side mirrors on lane-change crashes,” Transp. Hum. Factors 2(3), 279–289 (2000).
    [Crossref]
  3. S. M. O'Day, “Binocular disparity in ashperical mirrors,” SAE Technical Paper 980918 (1998).
  4. R. A. Hicks, “Controlling a ray bundle with a free-form reflector,” Opt. Lett. 33(15), 1672–1674 (2008).
    [Crossref] [PubMed]
  5. J. Kuwana, M. Itoh, and T. Inagaki, “Dynamic side-view mirror: assisting situation awareness in blind spots,” in Proceedings of IEEE Conferences on Intelligent Vehicles Symposium (IV) (Gold Coast, Australia, 2013), pp. 455–460.
    [Crossref]
  6. T. Ehlgen, T. Pajdla, and D. Ammon, “Eliminating blind spot for assisted driving,” IEEE Trans. Intell. Transp. Syst. 9(4), 657–665 (2008).
    [Crossref]
  7. H. Lee, D. Kim, and S. Yi, “Horizontally progressive mirror for blind spot detection in automobiles,” Opt. Lett. 38(3), 317–319 (2013).
    [Crossref] [PubMed]
  8. C. Fowler, “Recent trends in progressive power lenses,” Ophthalmic Physiol. Opt. 18(2), 234–237 (1998).
    [Crossref] [PubMed]
  9. J. Loos, G. Greiner, and H. Seidel, “A variational approach to the progressive lens design,” Comput. Aided Des. 30(8), 595–602 (1998).
    [Crossref]
  10. J. Wang, R. Gulliver, and F. Santosa, “Analysis of a variational approach to progressive design,” SIAM J. Appl. Math. 64(1), 277–296 (2003).
    [Crossref]
  11. L. Qin, L. Qian, and J. Yu, “Simulation method for evaluating progressive addition lenses,” Appl. Opt. 52(18), 4273–4278 (2013).
    [Crossref] [PubMed]
  12. W. Jiang, W. Bao, Q. Tang, and H. Wang, “A variational-difference numerical method for designing progressive-addition lenses,” Comput. Aided Des. 48, 17–27 (2014).
    [Crossref]
  13. A. Selenow, E. A. Bauer, S. R. Ali, L. W. Spencer, and K. J. Ciuffreda, “Assessing visual performance with progressive addition lenses,” Optom. Vis. Sci. 79(8), 502–505 (2002).
    [Crossref] [PubMed]
  14. Y. Han, K. J. Ciuffreda, A. Selenow, and S. R. Ali, “Dynamic interactions of eye and head movements when reading with single-vision and progressive lenses in a simulated computer-based environment,” Invest. Ophthalmol. Vis. Sci. 44(4), 1534–1545 (2003).
    [Crossref] [PubMed]
  15. J. E. Sheedy, “Progressive addition lenses--matching the specific lens to patient needs,” Optometry 75(2), 83–102 (2004).
    [Crossref] [PubMed]
  16. H. Lee, G. Lee, S. Lee, and J. Kim, “Slumping process of the horizontally progressive type of automobile side mirror,” in Classical Optics 2014, OSA Technical Digest (online) (Optical Society of America, 2014), paperOW2B.2.
  17. Y. Chen and A. Y. Yi, “Design and fabrication of freeform glass concentrating mirrors using a high volume thermal slumping process,” Sol. Energy Mater. Sol. Cells 95(7), 1654–1664 (2011).
    [Crossref]
  18. A. S. Glassner, An Introduction to Ray Tracing (Morgan Kaufman, 1989).
  19. T. Ma, J. Yu, P. Liang, and C. Wang, “Design of a freeform varifocal panoramic optical system with specified annular center of field of view,” Opt. Express 19(5), 3843–3853 (2011).
    [Crossref] [PubMed]
  20. A. Davis, “Raytrace assisted analytical formulation of Fresnel lens transmission efficiency,” Proc. SPIE 7429, 74290D (2009).
    [Crossref]
  21. J. C. Halimeh, T. Ergin, J. Mueller, N. Stenger, and M. Wegener, “Photorealistic images of carpet cloaks,” Opt. Express 17(22), 19328–19336 (2009).
    [Crossref] [PubMed]
  22. J. C. Halimeh and M. Wegener, “Photorealistic rendering of unidirectional free-space invisibility cloaks,” Opt. Express 21(8), 9457–9472 (2013).
    [Crossref] [PubMed]
  23. A. J. Danner, “Visualizing invisibility: Metamaterials-based optical devices in natural environments,” Opt. Express 18(4), 3332–3337 (2010).
    [Crossref] [PubMed]
  24. F. Mauch, M. Gronle, W. Lyda, and W. Osten, “Open-source graphics processing unit–accelerated ray tracer for optical simulation,” Opt. Eng. 52(5), 053004 (2013).
    [Crossref]
  25. A. Brückner, J. Duparré, R. Leitel, P. Dannberg, A. Bräuer, and A. Tünnermann, “Thin wafer-level camera lenses inspired by insect compound eyes,” Opt. Express 18(24), 24379–24394 (2010).
    [Crossref] [PubMed]
  26. T. Nakamura, R. Horisaki, and J. Tanida, “Computational superposition compound eye imaging for extended depth-of-field and field-of-view,” Opt. Express 20(25), 27482–27495 (2012).
    [Crossref] [PubMed]
  27. C. Elster, J. Gerhardt, P. Thomsen-Schmidt, M. Schulz, and I. Weingärtner, “Reconstructing surface profiles from curvature measurements,” Optik (Stuttg.) 113(4), 154–158 (2002).
    [Crossref]
  28. D. W. Kim, B. C. Kim, C. Zhao, C. Oh, and J. H. Burge, “Algorithms for surface reconstruction from curvature data for freeform aspherics,” Proc. SPIE 8838, 88380B (2013).
    [Crossref]
  29. C. Zhao and J. H. Burge, “Orthonormal curvature polynomials over a unit circle: basis set derived from curvatures of Zernike polynomials,” Opt. Express 21(25), 31430–31443 (2013).
    [Crossref] [PubMed]
  30. http://www.plm.automation.siemens.com/products/nx/ .
  31. L. Piegl and W. Tiller, The NURBS Book (Springer, 1997), Chap. 4.

2014 (1)

W. Jiang, W. Bao, Q. Tang, and H. Wang, “A variational-difference numerical method for designing progressive-addition lenses,” Comput. Aided Des. 48, 17–27 (2014).
[Crossref]

2013 (6)

2012 (1)

2011 (2)

Y. Chen and A. Y. Yi, “Design and fabrication of freeform glass concentrating mirrors using a high volume thermal slumping process,” Sol. Energy Mater. Sol. Cells 95(7), 1654–1664 (2011).
[Crossref]

T. Ma, J. Yu, P. Liang, and C. Wang, “Design of a freeform varifocal panoramic optical system with specified annular center of field of view,” Opt. Express 19(5), 3843–3853 (2011).
[Crossref] [PubMed]

2010 (2)

2009 (2)

A. Davis, “Raytrace assisted analytical formulation of Fresnel lens transmission efficiency,” Proc. SPIE 7429, 74290D (2009).
[Crossref]

J. C. Halimeh, T. Ergin, J. Mueller, N. Stenger, and M. Wegener, “Photorealistic images of carpet cloaks,” Opt. Express 17(22), 19328–19336 (2009).
[Crossref] [PubMed]

2008 (2)

R. A. Hicks, “Controlling a ray bundle with a free-form reflector,” Opt. Lett. 33(15), 1672–1674 (2008).
[Crossref] [PubMed]

T. Ehlgen, T. Pajdla, and D. Ammon, “Eliminating blind spot for assisted driving,” IEEE Trans. Intell. Transp. Syst. 9(4), 657–665 (2008).
[Crossref]

2004 (1)

J. E. Sheedy, “Progressive addition lenses--matching the specific lens to patient needs,” Optometry 75(2), 83–102 (2004).
[Crossref] [PubMed]

2003 (2)

J. Wang, R. Gulliver, and F. Santosa, “Analysis of a variational approach to progressive design,” SIAM J. Appl. Math. 64(1), 277–296 (2003).
[Crossref]

Y. Han, K. J. Ciuffreda, A. Selenow, and S. R. Ali, “Dynamic interactions of eye and head movements when reading with single-vision and progressive lenses in a simulated computer-based environment,” Invest. Ophthalmol. Vis. Sci. 44(4), 1534–1545 (2003).
[Crossref] [PubMed]

2002 (2)

A. Selenow, E. A. Bauer, S. R. Ali, L. W. Spencer, and K. J. Ciuffreda, “Assessing visual performance with progressive addition lenses,” Optom. Vis. Sci. 79(8), 502–505 (2002).
[Crossref] [PubMed]

C. Elster, J. Gerhardt, P. Thomsen-Schmidt, M. Schulz, and I. Weingärtner, “Reconstructing surface profiles from curvature measurements,” Optik (Stuttg.) 113(4), 154–158 (2002).
[Crossref]

2000 (1)

J. Luoma, M. J. Flannagan, and M. Sivak, “Effects of nonplanar driver-side mirrors on lane-change crashes,” Transp. Hum. Factors 2(3), 279–289 (2000).
[Crossref]

1998 (2)

C. Fowler, “Recent trends in progressive power lenses,” Ophthalmic Physiol. Opt. 18(2), 234–237 (1998).
[Crossref] [PubMed]

J. Loos, G. Greiner, and H. Seidel, “A variational approach to the progressive lens design,” Comput. Aided Des. 30(8), 595–602 (1998).
[Crossref]

Ali, S. R.

Y. Han, K. J. Ciuffreda, A. Selenow, and S. R. Ali, “Dynamic interactions of eye and head movements when reading with single-vision and progressive lenses in a simulated computer-based environment,” Invest. Ophthalmol. Vis. Sci. 44(4), 1534–1545 (2003).
[Crossref] [PubMed]

A. Selenow, E. A. Bauer, S. R. Ali, L. W. Spencer, and K. J. Ciuffreda, “Assessing visual performance with progressive addition lenses,” Optom. Vis. Sci. 79(8), 502–505 (2002).
[Crossref] [PubMed]

Ammon, D.

T. Ehlgen, T. Pajdla, and D. Ammon, “Eliminating blind spot for assisted driving,” IEEE Trans. Intell. Transp. Syst. 9(4), 657–665 (2008).
[Crossref]

Bao, W.

W. Jiang, W. Bao, Q. Tang, and H. Wang, “A variational-difference numerical method for designing progressive-addition lenses,” Comput. Aided Des. 48, 17–27 (2014).
[Crossref]

Bauer, E. A.

A. Selenow, E. A. Bauer, S. R. Ali, L. W. Spencer, and K. J. Ciuffreda, “Assessing visual performance with progressive addition lenses,” Optom. Vis. Sci. 79(8), 502–505 (2002).
[Crossref] [PubMed]

Bräuer, A.

Brückner, A.

Burge, J. H.

D. W. Kim, B. C. Kim, C. Zhao, C. Oh, and J. H. Burge, “Algorithms for surface reconstruction from curvature data for freeform aspherics,” Proc. SPIE 8838, 88380B (2013).
[Crossref]

C. Zhao and J. H. Burge, “Orthonormal curvature polynomials over a unit circle: basis set derived from curvatures of Zernike polynomials,” Opt. Express 21(25), 31430–31443 (2013).
[Crossref] [PubMed]

Chen, Y.

Y. Chen and A. Y. Yi, “Design and fabrication of freeform glass concentrating mirrors using a high volume thermal slumping process,” Sol. Energy Mater. Sol. Cells 95(7), 1654–1664 (2011).
[Crossref]

Ciuffreda, K. J.

Y. Han, K. J. Ciuffreda, A. Selenow, and S. R. Ali, “Dynamic interactions of eye and head movements when reading with single-vision and progressive lenses in a simulated computer-based environment,” Invest. Ophthalmol. Vis. Sci. 44(4), 1534–1545 (2003).
[Crossref] [PubMed]

A. Selenow, E. A. Bauer, S. R. Ali, L. W. Spencer, and K. J. Ciuffreda, “Assessing visual performance with progressive addition lenses,” Optom. Vis. Sci. 79(8), 502–505 (2002).
[Crossref] [PubMed]

Dannberg, P.

Danner, A. J.

Davis, A.

A. Davis, “Raytrace assisted analytical formulation of Fresnel lens transmission efficiency,” Proc. SPIE 7429, 74290D (2009).
[Crossref]

Duparré, J.

Ehlgen, T.

T. Ehlgen, T. Pajdla, and D. Ammon, “Eliminating blind spot for assisted driving,” IEEE Trans. Intell. Transp. Syst. 9(4), 657–665 (2008).
[Crossref]

Elster, C.

C. Elster, J. Gerhardt, P. Thomsen-Schmidt, M. Schulz, and I. Weingärtner, “Reconstructing surface profiles from curvature measurements,” Optik (Stuttg.) 113(4), 154–158 (2002).
[Crossref]

Ergin, T.

Flannagan, M. J.

J. Luoma, M. J. Flannagan, and M. Sivak, “Effects of nonplanar driver-side mirrors on lane-change crashes,” Transp. Hum. Factors 2(3), 279–289 (2000).
[Crossref]

Fowler, C.

C. Fowler, “Recent trends in progressive power lenses,” Ophthalmic Physiol. Opt. 18(2), 234–237 (1998).
[Crossref] [PubMed]

Gerhardt, J.

C. Elster, J. Gerhardt, P. Thomsen-Schmidt, M. Schulz, and I. Weingärtner, “Reconstructing surface profiles from curvature measurements,” Optik (Stuttg.) 113(4), 154–158 (2002).
[Crossref]

Greiner, G.

J. Loos, G. Greiner, and H. Seidel, “A variational approach to the progressive lens design,” Comput. Aided Des. 30(8), 595–602 (1998).
[Crossref]

Gronle, M.

F. Mauch, M. Gronle, W. Lyda, and W. Osten, “Open-source graphics processing unit–accelerated ray tracer for optical simulation,” Opt. Eng. 52(5), 053004 (2013).
[Crossref]

Gulliver, R.

J. Wang, R. Gulliver, and F. Santosa, “Analysis of a variational approach to progressive design,” SIAM J. Appl. Math. 64(1), 277–296 (2003).
[Crossref]

Halimeh, J. C.

Han, Y.

Y. Han, K. J. Ciuffreda, A. Selenow, and S. R. Ali, “Dynamic interactions of eye and head movements when reading with single-vision and progressive lenses in a simulated computer-based environment,” Invest. Ophthalmol. Vis. Sci. 44(4), 1534–1545 (2003).
[Crossref] [PubMed]

Hicks, R. A.

Horisaki, R.

Jiang, W.

W. Jiang, W. Bao, Q. Tang, and H. Wang, “A variational-difference numerical method for designing progressive-addition lenses,” Comput. Aided Des. 48, 17–27 (2014).
[Crossref]

Kim, B. C.

D. W. Kim, B. C. Kim, C. Zhao, C. Oh, and J. H. Burge, “Algorithms for surface reconstruction from curvature data for freeform aspherics,” Proc. SPIE 8838, 88380B (2013).
[Crossref]

Kim, D.

Kim, D. W.

D. W. Kim, B. C. Kim, C. Zhao, C. Oh, and J. H. Burge, “Algorithms for surface reconstruction from curvature data for freeform aspherics,” Proc. SPIE 8838, 88380B (2013).
[Crossref]

Lee, H.

Leitel, R.

Liang, P.

Loos, J.

J. Loos, G. Greiner, and H. Seidel, “A variational approach to the progressive lens design,” Comput. Aided Des. 30(8), 595–602 (1998).
[Crossref]

Luoma, J.

J. Luoma, M. J. Flannagan, and M. Sivak, “Effects of nonplanar driver-side mirrors on lane-change crashes,” Transp. Hum. Factors 2(3), 279–289 (2000).
[Crossref]

Lyda, W.

F. Mauch, M. Gronle, W. Lyda, and W. Osten, “Open-source graphics processing unit–accelerated ray tracer for optical simulation,” Opt. Eng. 52(5), 053004 (2013).
[Crossref]

Ma, T.

Mauch, F.

F. Mauch, M. Gronle, W. Lyda, and W. Osten, “Open-source graphics processing unit–accelerated ray tracer for optical simulation,” Opt. Eng. 52(5), 053004 (2013).
[Crossref]

Mueller, J.

Nakamura, T.

Oh, C.

D. W. Kim, B. C. Kim, C. Zhao, C. Oh, and J. H. Burge, “Algorithms for surface reconstruction from curvature data for freeform aspherics,” Proc. SPIE 8838, 88380B (2013).
[Crossref]

Osten, W.

F. Mauch, M. Gronle, W. Lyda, and W. Osten, “Open-source graphics processing unit–accelerated ray tracer for optical simulation,” Opt. Eng. 52(5), 053004 (2013).
[Crossref]

Pajdla, T.

T. Ehlgen, T. Pajdla, and D. Ammon, “Eliminating blind spot for assisted driving,” IEEE Trans. Intell. Transp. Syst. 9(4), 657–665 (2008).
[Crossref]

Qian, L.

Qin, L.

Santosa, F.

J. Wang, R. Gulliver, and F. Santosa, “Analysis of a variational approach to progressive design,” SIAM J. Appl. Math. 64(1), 277–296 (2003).
[Crossref]

Schulz, M.

C. Elster, J. Gerhardt, P. Thomsen-Schmidt, M. Schulz, and I. Weingärtner, “Reconstructing surface profiles from curvature measurements,” Optik (Stuttg.) 113(4), 154–158 (2002).
[Crossref]

Seidel, H.

J. Loos, G. Greiner, and H. Seidel, “A variational approach to the progressive lens design,” Comput. Aided Des. 30(8), 595–602 (1998).
[Crossref]

Selenow, A.

Y. Han, K. J. Ciuffreda, A. Selenow, and S. R. Ali, “Dynamic interactions of eye and head movements when reading with single-vision and progressive lenses in a simulated computer-based environment,” Invest. Ophthalmol. Vis. Sci. 44(4), 1534–1545 (2003).
[Crossref] [PubMed]

A. Selenow, E. A. Bauer, S. R. Ali, L. W. Spencer, and K. J. Ciuffreda, “Assessing visual performance with progressive addition lenses,” Optom. Vis. Sci. 79(8), 502–505 (2002).
[Crossref] [PubMed]

Sheedy, J. E.

J. E. Sheedy, “Progressive addition lenses--matching the specific lens to patient needs,” Optometry 75(2), 83–102 (2004).
[Crossref] [PubMed]

Sivak, M.

J. Luoma, M. J. Flannagan, and M. Sivak, “Effects of nonplanar driver-side mirrors on lane-change crashes,” Transp. Hum. Factors 2(3), 279–289 (2000).
[Crossref]

Spencer, L. W.

A. Selenow, E. A. Bauer, S. R. Ali, L. W. Spencer, and K. J. Ciuffreda, “Assessing visual performance with progressive addition lenses,” Optom. Vis. Sci. 79(8), 502–505 (2002).
[Crossref] [PubMed]

Stenger, N.

Tang, Q.

W. Jiang, W. Bao, Q. Tang, and H. Wang, “A variational-difference numerical method for designing progressive-addition lenses,” Comput. Aided Des. 48, 17–27 (2014).
[Crossref]

Tanida, J.

Thomsen-Schmidt, P.

C. Elster, J. Gerhardt, P. Thomsen-Schmidt, M. Schulz, and I. Weingärtner, “Reconstructing surface profiles from curvature measurements,” Optik (Stuttg.) 113(4), 154–158 (2002).
[Crossref]

Tünnermann, A.

Wang, C.

Wang, H.

W. Jiang, W. Bao, Q. Tang, and H. Wang, “A variational-difference numerical method for designing progressive-addition lenses,” Comput. Aided Des. 48, 17–27 (2014).
[Crossref]

Wang, J.

J. Wang, R. Gulliver, and F. Santosa, “Analysis of a variational approach to progressive design,” SIAM J. Appl. Math. 64(1), 277–296 (2003).
[Crossref]

Wegener, M.

Weingärtner, I.

C. Elster, J. Gerhardt, P. Thomsen-Schmidt, M. Schulz, and I. Weingärtner, “Reconstructing surface profiles from curvature measurements,” Optik (Stuttg.) 113(4), 154–158 (2002).
[Crossref]

Yi, A. Y.

Y. Chen and A. Y. Yi, “Design and fabrication of freeform glass concentrating mirrors using a high volume thermal slumping process,” Sol. Energy Mater. Sol. Cells 95(7), 1654–1664 (2011).
[Crossref]

Yi, S.

Yu, J.

Zhao, C.

D. W. Kim, B. C. Kim, C. Zhao, C. Oh, and J. H. Burge, “Algorithms for surface reconstruction from curvature data for freeform aspherics,” Proc. SPIE 8838, 88380B (2013).
[Crossref]

C. Zhao and J. H. Burge, “Orthonormal curvature polynomials over a unit circle: basis set derived from curvatures of Zernike polynomials,” Opt. Express 21(25), 31430–31443 (2013).
[Crossref] [PubMed]

Appl. Opt. (1)

Comput. Aided Des. (2)

W. Jiang, W. Bao, Q. Tang, and H. Wang, “A variational-difference numerical method for designing progressive-addition lenses,” Comput. Aided Des. 48, 17–27 (2014).
[Crossref]

J. Loos, G. Greiner, and H. Seidel, “A variational approach to the progressive lens design,” Comput. Aided Des. 30(8), 595–602 (1998).
[Crossref]

IEEE Trans. Intell. Transp. Syst. (1)

T. Ehlgen, T. Pajdla, and D. Ammon, “Eliminating blind spot for assisted driving,” IEEE Trans. Intell. Transp. Syst. 9(4), 657–665 (2008).
[Crossref]

Invest. Ophthalmol. Vis. Sci. (1)

Y. Han, K. J. Ciuffreda, A. Selenow, and S. R. Ali, “Dynamic interactions of eye and head movements when reading with single-vision and progressive lenses in a simulated computer-based environment,” Invest. Ophthalmol. Vis. Sci. 44(4), 1534–1545 (2003).
[Crossref] [PubMed]

Ophthalmic Physiol. Opt. (1)

C. Fowler, “Recent trends in progressive power lenses,” Ophthalmic Physiol. Opt. 18(2), 234–237 (1998).
[Crossref] [PubMed]

Opt. Eng. (1)

F. Mauch, M. Gronle, W. Lyda, and W. Osten, “Open-source graphics processing unit–accelerated ray tracer for optical simulation,” Opt. Eng. 52(5), 053004 (2013).
[Crossref]

Opt. Express (7)

Opt. Lett. (2)

Optik (Stuttg.) (1)

C. Elster, J. Gerhardt, P. Thomsen-Schmidt, M. Schulz, and I. Weingärtner, “Reconstructing surface profiles from curvature measurements,” Optik (Stuttg.) 113(4), 154–158 (2002).
[Crossref]

Optom. Vis. Sci. (1)

A. Selenow, E. A. Bauer, S. R. Ali, L. W. Spencer, and K. J. Ciuffreda, “Assessing visual performance with progressive addition lenses,” Optom. Vis. Sci. 79(8), 502–505 (2002).
[Crossref] [PubMed]

Optometry (1)

J. E. Sheedy, “Progressive addition lenses--matching the specific lens to patient needs,” Optometry 75(2), 83–102 (2004).
[Crossref] [PubMed]

Proc. SPIE (2)

D. W. Kim, B. C. Kim, C. Zhao, C. Oh, and J. H. Burge, “Algorithms for surface reconstruction from curvature data for freeform aspherics,” Proc. SPIE 8838, 88380B (2013).
[Crossref]

A. Davis, “Raytrace assisted analytical formulation of Fresnel lens transmission efficiency,” Proc. SPIE 7429, 74290D (2009).
[Crossref]

SIAM J. Appl. Math. (1)

J. Wang, R. Gulliver, and F. Santosa, “Analysis of a variational approach to progressive design,” SIAM J. Appl. Math. 64(1), 277–296 (2003).
[Crossref]

Sol. Energy Mater. Sol. Cells (1)

Y. Chen and A. Y. Yi, “Design and fabrication of freeform glass concentrating mirrors using a high volume thermal slumping process,” Sol. Energy Mater. Sol. Cells 95(7), 1654–1664 (2011).
[Crossref]

Transp. Hum. Factors (1)

J. Luoma, M. J. Flannagan, and M. Sivak, “Effects of nonplanar driver-side mirrors on lane-change crashes,” Transp. Hum. Factors 2(3), 279–289 (2000).
[Crossref]

Other (7)

S. M. O'Day, “Binocular disparity in ashperical mirrors,” SAE Technical Paper 980918 (1998).

J. Kuwana, M. Itoh, and T. Inagaki, “Dynamic side-view mirror: assisting situation awareness in blind spots,” in Proceedings of IEEE Conferences on Intelligent Vehicles Symposium (IV) (Gold Coast, Australia, 2013), pp. 455–460.
[Crossref]

J. F. Morgan and M. Blanco, “Synthesis study of light vehicle non-planar mirror research,” NHTSA DOT HS 811–328, 47 (2010).

A. S. Glassner, An Introduction to Ray Tracing (Morgan Kaufman, 1989).

H. Lee, G. Lee, S. Lee, and J. Kim, “Slumping process of the horizontally progressive type of automobile side mirror,” in Classical Optics 2014, OSA Technical Digest (online) (Optical Society of America, 2014), paperOW2B.2.

http://www.plm.automation.siemens.com/products/nx/ .

L. Piegl and W. Tiller, The NURBS Book (Springer, 1997), Chap. 4.

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Figures (6)

Fig. 1
Fig. 1 Two principal components of the radii of curvature of the mirror surface. Rx varies along the horizontal direction only. (a) Rx. (b) Ry.
Fig. 2
Fig. 2 NURBS surface acquisition from the point set. The number of degrees and patches are adjusted until the desired conversion accuracy and curvature deviation is obtained.
Fig. 3
Fig. 3 Reference image source.
Fig. 4
Fig. 4 Schematic diagram of the ray-traced rendering method used to obtain the reflected images on the mirror surface from the reference image.
Fig. 5
Fig. 5 Virtual reflection images from three spherical convex surface mirrors on the driver’s side. Radius of curvature of (a) 1,250 mm, (b) 1,050 mm, and (c) 950 mm.
Fig. 6
Fig. 6 Virtual view of horizontally progressive mirrors on the driver’s side. The three Rx distributions are identical and decrease continuously from 1,250 mm on the right side to 400 mm on the left side. The three Ry distributions all differ. (a) Ry is 1,150 mm on the right side and 1,050 mm on the left side. (b) Ry is 1250 mm on the right side and 1,150 mm on the left side. (c) Ry is 1,250 mm on the right side and 1,350 mm on the left side.

Tables (2)

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Table 1 Performance evaluation with the visualized scenes for blind spot area control

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Table 2 The comparison of the proposed work with the latest research progress of referenced papers

Equations (8)

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K m = ( K m a x + K m i n ) 2 = 1 2 ( 1 R x + 1 R y ) ; K a = ( K m a x K m i n ) = | 1 R x 1 R y | .
R ( x ) = [ 1 + ( d z d x ) 2 ] 3 2 | d 2 z d x 2 | .
R ( x i , y j ) = [ R x R y ] = [ R 1 ( x i ) R 2 ( x i , y j ) ] , i = 1 , ... , m ; j = 1 , ... , n .
z ¨ ( x i , y c ) = g ˙ ( x i , y c ) , = | 1 R 1 ( x i ) [ 1 + { g ( x i , y c ) } 2 ] 3 2 | , = f ( x i , g ( x i , y c ) ) .
g ( x i + 1 , y c ) = g ( x i , y c ) + f ( x i , g ( x i , y c ) ) h , z ( x i + 1 , y c ) = z ( x i , y c ) + g ( x i , y c ) h .
z ¨ ( x m , y j ) = p ˙ ( x m , y j ) , = | 1 R 2 ( x m , y j ) [ 1 + { p ( x m , y j ) } 2 ] 3 2 | , = q ( x m , p ( x m , y j ) ) .
S ( u , v ) = i = 0 n j = 0 m N i , p ( u ) N j , q ( v ) w i , j P i , j i = 0 n j = 0 m N i , p ( u ) N j , q ( v ) w i , j , 0 u , v 1 ,
U = { 0 , ... , 0 p + 1 , u p + 1 , ... , u r p 1 , 1 , ... , 1 q + 1 } ; V = { 0 , ... , 0 q + 1 , v q + 1 , ... , v s q 1 , 1 , ... , 1 q + 1 } ,

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