Curvature Blindness from Polarity Breaks and Orientation Channel Fragmentation in V1

We present a mathematical model of the curvature blindness illusion in which sinusoids appear as angular zigzags when drawn with alternating contrast polarity against a gray background. The model identifies two complementary mechanisms, both operating in V1. First, polarity channel separation: simple cells are selective for contrast polarity, and lateral connections link only same polarity neurons; where the line switches from darker than background to lighter than background at each peak and trough, the encoding population changes and the lateral chain is broken, segmenting the contour into half-wavelength pieces. Second, orientation channel fragmentation: at moderate contrast, the active orientation window is narrow, and within each half-wavelength segment no single orientation channel spans the full range of edge normals; the inflection point at the center of each segment anchors a locally straight percept. Together, the two mechanisms produce a zigzag: polarity breaks supply the corners, and fragmentation straightens the segments between them.