Kinetic volume-based persistence for 1D terrains

Persistence is the method of choice to simplify terrains by removing insignificant features while retaining topologically important ones. Motivated by applications in geomorphology, we study volume-persistence, a variant of persistence which is based on the volume underneath the terrain (instead of the usual vertex heights). Specifically, we want to kinetically maintain a volume-simplified time-varying terrain. In this paper we describe a kinetic data structure (KDS) that maintains the pruned split tree of an area-persistent 1D terrain under linear vertex motion. The main ingredient of this KDS is an algorithm that detects those combinatorial events when a pruned part of the terrain attains a certain threshold volume.