eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2015-06-12
796
811
10.4230/LIPIcs.SOCG.2015.796
article
Maintaining Contour Trees of Dynamic Terrains
Agarwal, Pankaj K.
Mølhave, Thomas
Revsbæk, Morten
Safa, Issam
Wang, Yusu
Yang, Jungwoo
We study the problem of maintaining the contour tree T of a terrain Sigma, represented as a triangulated xy-monotone surface, as the heights of its vertices vary continuously with time. We characterize the combinatorial changes in T and how they relate to topological changes in Sigma. We present a kinetic data structure (KDS) for maintaining T efficiently. It maintains certificates that fail, i.e., an event occurs, only when the heights of two adjacent vertices become equal or two saddle vertices appear on the same contour. Assuming that the heights of two vertices of Sigma become equal only O(1) times and these instances can be computed in O(1) time, the KDS processes O(kappa + n) events, where n is the number of vertices in Sigma and kappa is the number of events at which the combinatorial structure of T changes, and processes each event in O(log n) time. The KDS can be extended to maintain an augmented contour tree and a join/split tree.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol034-socg2015/LIPIcs.SOCG.2015.796/LIPIcs.SOCG.2015.796.pdf
Contour tree
dynamic terrain
kinetic data structure