Listen to your better angles: Horizontality, verticality, and cardinality in visual scanning and foraging

During visual search and foraging tasks, an observer freely scans a display looking for one or more targets of interest among distractors. One strategy for studying the scan patterns uses the angles between consecutive saccades. The methods used to study scan directions range from descriptive angle analysis to "binning" the direction in discrete spatial categories. Here we present some trigonometry-based indicators to quantitatively account for horizontality and verticality. Furthermore, we propose an indicator to assess the combined trend to scan either horizontally or vertically (as opposed to oblique directions). We demonstrate its usefulness with both horizontal and directional angles, reanalyzing data from a visual foraging task. We also detect a cardinality effect in horizontal angles which would not have been detected by analyzing the angles directly. Furthermore, we show a not-going-forward effect on directional angles, which is more detectable using simple trigonometric functions.