Many experimental approaches to the control of steering rely on the tangent point (TP) as major source of information. The TP is a good candidate to control self-motion. It corresponds to a singular and salient point in the subject's visual field, and its location depends on the road geometry, the direction of self-motion relative to the road and the position of the driver on the road. However, the particular status of the TP in the optical flow, as a local minimum of flow speed, has often been left aside. We therefore assume that the TP is actually an optimal location in the dynamic optical array to perceive a change in the trajectory curvature. In this study, we evaluated the ability of human observers to detect variations in their path curvature from optical flow patterns, as a function of their gaze direction in a virtual environment. We simulated curvilinear self-motion parallel to a ground plane. Using random-dot optic flow stimuli of brief duration and a two-alternative forced-choice adaptive procedure, we determined path curvature discrimination thresholds, as a function of gaze direction. The discrimination thresholds are minimal for a gaze directed toward a local minimum of optical flow speed. A model based on Weber fraction of the foveal velocities (DV =V) correctly predicts the relationship between experimental thresholds and local flow velocities. This model was also tested for an optical flow computation integrating larger circular areas in central vision. Averaging the flow over five degrees leads to an even better fit of the model to experimental thresholds. We also found that the minimal optical flow speed direction corresponds to a maximal sensitivity of the visual system, as predicted by our model. The spontaneous gazing strategies observed during driving might thus correspond to an optimal selection of relevant information in the optical flow field.