An algorithm for reconstructing convex bodies from their projections (Q1118817)

The authors describe an iterative procedure for constructing a plane convex body whose projections in a finite number of directions are given. The output of the algorithm is a finite number of approximative solutions of the problem or the information that there is no convex body having the prescribed projections. A priori and a posteriori estimates measuring the difference between the exact and the approximative solutions are presented. It is also proved that a suitable modification of the method can be applied to the reconstruction of a plane convex body from discrete projectional data.