The aim of this work was to elucidate several characteristic phenomena associated with rapid curved-line detection in multi-element arrays and to provide a unified account of the underlying curvature-sensitive mechanisms. To this end, a parametric experiment was performed in which the detectability of a curved-line target in a briefly presented planar array of curved-line distractors was measured for a range of target and distractor curvatures and distractor numbers. For both vertically oriented and randomly oriented curved lines, it was found that (1) the dependence of target detectability on target curvature was independent of distractor number for small distractor curvatures but not for medium-to-large distractor curvatures; (2) an asymmetry in target detectability with respect to interchange of target and distractor curvatures occurred only with large distractor numbers; and (3) with small distractor numbers, target detectability depended only on the difference between target and distractor curvatures. These properties of spatial parallelism, asymmetry, and uniformity were explained quantitatively by a minimal model of rapid curved-line detection in which contour curvature was coded in terms of just two or three curvature categories, depending on curved-line orientation.