From continuum model to a detailed discrete theory of median shifts

This paper presents a new discrete theory of median shifts. It relates the theory to the older continuum model, predicts angular variations, and also gives an accurate figure for the active area of any discrete neighbourhood, thereby making the continuum model more accurate. The work shows that at low curvature values a quadratic law applies, this being followed by the previously known linear variation. It also explains why the observed linear behaviour is significantly larger than indicated by the continuum model. Overall, there is now very good agreement between the new discrete theory, the continuum model and the observed results.