Reconstruction of convex bodies of revolution from the areas of their shadows
The paper shows how to reconstruct a three-dimensional convex body \(K\) of revolution when we know the areas of all its projections. It can be done with the help of two formulas. The first formula presents the curvature function \(f(K)\) of \(K\) as a function of the areas of the projections of \(K\). The second formula is an explicit expression for the support function of \(K\) in terms of \(f(K)\). It is proved under the assumptions that \(\partial K\) is of class \(C^ 5\) and that the Gauss curvature of \(K\) at each point is positive.
scientific article; zbMATH DE number 2138526