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Blind-spot problem for motor vehicles.

R Andrew Hicks1, Ronald K Perline

  • 1Department of Mathematics and Computer Science, Drexel University, 3141 Chestnut Street, Philadelphia, Pennsylvania 19104-2875, USA. ahicks@math.drexel.edu

Applied Optics
|July 12, 2005
PubMed
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Designing a blind-spot-free, distortion-free automobile passenger side mirror is challenging. Approximate solutions were found using nonlinear optimization, with one mirror solving the problem but not reversing the image.

Area of Science:

  • Automotive engineering
  • Applied mathematics
  • Optical design

Background:

  • Traditional passenger side mirrors often have blind spots and image distortion.
  • Designing mirrors with a complete field of view and accurate image representation is a significant challenge in automotive safety.

Purpose of the Study:

  • To design an automobile passenger side mirror that eliminates blind spots.
  • To achieve an undistorted image in the designed mirror.
  • To explore mathematical models and optimization techniques for mirror design.

Main Methods:

  • Formulated the design problem using a coupled pair of partial differential equations.
  • Employed a best mean-square-error functional to define solution quality.
  • Utilized nonlinear optimization techniques to find approximate solutions.

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Main Results:

  • Identified that the coupled partial differential equations do not possess a common exact solution.
  • Found an approximate solution using nonlinear optimization that eliminates the blind spot.
  • The resulting mirror design, while effective in eliminating blind spots, does not reverse the image.

Conclusions:

  • Achieving a blind-spot-free passenger side mirror is mathematically feasible through approximate solutions.
  • Image reversal is a separate consideration from blind-spot elimination in mirror design.
  • Nonlinear optimization provides a viable approach for complex optical design problems with no exact solutions.