To examine how local velocities from different regions of the visual field combine to form a coherent motion percept, we subjected a sinusoidal line stimulus to translational motion. Horizontal movement of a sinewave line along its axial direction is perceived as nonrigid if the angle at the zero crossing is smaller than a critical angle of about 15 deg. This angle is independent of spatial scale and the number of sinusoidal cycles. To extend the applicability of this concept of angle, we developed a mathematical model to predict an observer's sensitivity to small changes in motion direction based on two assumptions: (1) the computed velocity signal is obtained from the intersection of constraint lines defined by local velocity components, (2) local velocity components are contaminated by noise. Measurement of directional discrimination thresholds of moving targets confirmed our expectations. Thresholds varied as a function of the angle of the local contour independent of spatial scale and in quantitative accord with our assumptions.