A new simulation method of field emission ion images is proposed. The method can be applied to any crystal shape, size and atomic structure (possibly with point defects and dislocations), without any trial-and-error adjustment of parameters. The algorithm is illustrated by three simple examples: spherical crystals of perfect FCC, BCC and HCP structures.

We present independent method to reduce the number of shadow ray tests. It can be used with standard acceleration ray tracing algorithms. Our method is conservative and produces the same results. We test just one shadow ray in modified scene insted of group of rays in original scene. If our ray is not obstructed in modified scene we know that all the rays in this group are not obstructed. The results give rise to many applications when there are many shadow rays e. g., in bidierectional path tracing or stochastically sampling area light sources. The formal proof of the method uses formalism of Minkowski operators and they can also be used in implementation details.

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