We consider a problem of geometric tomography whith a strip-based model of projections: the projections are the areas of the intersection between the shape and some strips. We investigate some elementary algorithms that allow to construct a shape with prescribed projections. We start with an exact algorithm based on Linear Programming which leads to practical difficulties. Then we investigate three practical heuristics based on a cell decomposition of the domain of interest: GA is a greedy algorithm, GAME its multiresolution derivative and MPH a multiresolution heuristic close to a parallel Simulated Annealing.