Two-dimensional representations of molecular structure may be generated from the three-dimensional coordinates by nonlinear mapping. These representations not only retain the look of familiar structural formulas but also incorporate the distance geometry information available in three-dimensional structures. The technique is shown to be trivial so long as the molecular structure is not essentially spherical and an objective test as to whether this is true is introduced, together with extensions for coping with such cases. The two-dimensional diagrams have great promise in handling molecular similarity and data searching with very large numbers of compounds since they permit the use of two-dimensional pattern recognition techniques.