Crater depths, often obtained from shadow measurements, have long been used for several purposes in planetary science. However, the usual method for obtaining depth from shadow length suffers from several drawbacks and limitations. Chappelow and Sharpton (2002) introduced a much improved shadow method, which has the advantages of giving some shape information (as well as depth), and is not limited to shadows that cross the crater bottom. However, it is not general, in that it only gives very approximate crater shape information, in terms of three special cases (parabolic, conical, or flat-floored). Here, I present a completely generalized method, valid for any conic section shaped crater, and give a proof of concept and demonstration of its use, using Linne crater as a test case. In the process, I find that Linne is neither parabolic nor conical, and that it contains approximately 20 m of bottom fill, which forms a flat floor. I also conclude that the long-used parabolic paradigm for the shapes of simple craters may need to be revised.