Segment-based methods explicitly describe a boundary. This means that a boundary in two- or three-dimensional space is usually represented as line segmentation [38,52] or as triangulation [12,31,59,68,105,131], respectively. The time evolution of the boundary is computed by advancing all nodes in the normal direction according to the given surface velocities at every time step. Since the surface normal is not defined at the nodes, it must be obtained by averaging the normals of neighboring segments.

The drawback of segment-based methods is that accumulation or rarefaction of nodes can occur, especially at regions with high curvature or large differences in surface velocities. Therefore, nodes must be deleted or inserted to keep their density, and consequently the surface resolution, appropriate. A further problem is the proper treatment of self-intersections, which can occur if, for example, two different parts of the boundary merge. Hence, much effort is necessary to obtain an efficient and, more importantly, a robust boundary tracking algorithm, especially in three dimensions.

Otmar Ertl: Numerical Methods for Topography Simulation