The authors study the problem of recovering a surface slice from the shadows it casts on itself when lighted by the sun at various times of the day. The problem is formulated and solved in a Hilbert space setting. The spine algorithm interpolating the data that result from the shadows is constructed. This algorithm is optimal in terms of the approximation error and has low cost. The authors implement the optimal error algorithm and show a series of test runs. Another modified version of the algorithm that improves the cost considerably is also shown. This version is suited for parallel computation with further reductions in the cost of the solution.>