A line of curvature is a curve on a surface whose tangent at every point is aligned along a principal curvature direction. We have studied the basics of lines of curvature in Sect. 3.4 and will study them further in Chap. 9. The principal directions at a given point are those directions for which the normal curvature takes on minimum and maximum values. A line of curvature indicates a directional flow for the maximum or the minimum curvature across the surface [22]. Curvature lines provide some useful information about the surface. For example, when a plate is going to be shaped by rolling it is fed into the rolls using a principal direction and the forming rolls are adjusted according to the principal curvature [279]. The network of curvature lines may also be useful in idealization, meshing and structural analysis of shells with free-form surfaces as boundaries, because of their orthogonality property.