Speaker: Mary H. Avery
Candidate for Bachelor of Science in Mathematics
Time: 2:45 PM
Place: Trustee Hall 203
Supervisor: David Naples
Title: Reconstructing Convex Polyhedra from a Single Directed X-ray

Abstract: This talk deals with the subject of geometric tomography, in particular, the theory and methods of reconstruction of convex polyhedra from single directed X-rays. A directed X-ray is the set of all X-rays from a single point source. This project proved that most convex polyhedra can be uniquely determined by a single directed X-ray. The authors then developed reconstruction techniques which use discrete X-ray data from certain configurations of seven or eight X-rays through each wedge of a convex polyhedron. The reconstruction algorithm is based on D. Lam and D.C. Solomon's work on reconstructing convex polygons in the plane. Whether or not six rays could be sufficient for reconstruction remains an open question.