Maintaining Contour Trees of Dynamic Terrains
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.
Contour tree
dynamic terrain
kinetic data structure
796-811
Regular Paper
Pankaj K.
Agarwal
Pankaj K. Agarwal
Thomas
Mølhave
Thomas Mølhave
Morten
Revsbæk
Morten Revsbæk
Issam
Safa
Issam Safa
Yusu
Wang
Yusu Wang
Jungwoo
Yang
Jungwoo Yang
10.4230/LIPIcs.SOCG.2015.796
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