Memorandum for Record

DEPARTMENT OF THE ARMY
UNITED STATES MILITARY ACADEMY
WEST POINT, NEW YORK 10996

1. Many people in the general population are affected by imperfect vision. Several emerging techniques in optometry allow for the reshaping of the eye through surgical procedures. However, before doctors may reshape the eye, they need to know the eye’s original shape.

2. By reflecting light from a known source pattern onto film through a camera lens, we are able to use a theoretical differential equation to approximate where several points on the eye are located.

3. Various numerical methods were implemented in this project in order to observe which method yielded the best results. While implementations of both Forward Euler’s and Backward Euler’s methods were successful, the implementation of the Runge-Kutta method was by far the most successful method, as it allowed for the most accuracy with relatively few, simple calculations.

4. Included in the supporting attachments are a detailed analysis of the situation, C++ code implementing the various numerical methods, a detailed analysis of the results, and suggestions for future improvements.

5. The person of contact for this memo is the undersigned at (914) 515-5353 or by email at x24346@usma.edu.