1. We study the relationship between structure and function in inhibitory long-range interactions in visual cortex. The sharpening of orientation tuning with "cross-orientation inhibition" is used as an example to discuss anisotropies that are generated by long-range connections. 2. In this study, as opposed to the detailed cortex model described in a previous report, a model of the cortical orientation column structure is proposed in which cortical cells are described only by their orientation preference. 3. We present results using different geometric arrangements of orientation columns. In the simplest case, straight parallel orientation columns were used. We also utilized more realistic, curved columns generated by a simple algorithm. The results were confirmed by the study of a patch of real column structure, determined experimentally by Swindale et al. 4. A given cell receives functionally defined cross-orientation inhibition if the cell receives inhibitory input that is strongest along its nonpreferred orientation. On the other hand, a cell is said to receive structurally defined cross-orientation inhibition if the inhibition arises from source cells with an orientation preference orthogonal to that of the target cell. Even though those definitions seem to describe similar situations, we show that, in the general case, structurally defined cross-orientation inhibition does not efficiently sharpen orientation selectivity. In particular, for straight and parallel columns, structurally defined cross-orientation inhibition results in unequal amounts of inhibition for whole cell populations with different preferred orientations. 5. In more realistic column structures, we studied the question of whether structural cross-orientation inhibition could be implemented in a more efficient way. However, for the majority of cells, it is demonstrated that their nonpreferred stimulus will not preferably excite "cross-oriented" cells. Thus structural cross-orientation inhibition is not efficient in real cortical columns. 6. We propose a new mechanism called circular inhibition. In this connection scheme, a target cell receives inhibitory input from source cells that are located at a given distance (the same for all cells) from the target cell. Circular inhibition can be regarded as two-dimensional long-range lateral inhibition. As opposed to structural cross-orientation inhibition, this mechanism does not introduce unwanted anisotropies in the orientation tuning of the target cells. It is also conceptually much simpler and developmentally advantageous. It is shown that this connection scheme results in a net functional cross-orientation inhibition in all realistic column geometries. The inhibitory tuning strength obtained with circular inhibition is weak and similar to that measured in reality.(ABSTRACT TRUNCATED AT 400 WORDS)