The analytical calculation of absorption in multifaceted crystals

The exact analytic method of evaluating the absorption during scattering in multifaceted convex crystals is developed in a way that permits efficient computation. A fast and accurate algorithm is given for finding the Howells polyhedra whose determination is fundamental to the analytic method. The algorithm allows for the evaluation of cases when the sample is only partly illuminated, can be adapted to more general situations and can be used to generate an estimate of the error in the computation. In most cases this is to 1 part in 1014. Results of standard tests are given to greater accuracy than previously available and results for multifaceted approximations to a cylinder and a sphere are given to illustrate the power of the method.