27 research outputs found
Maintaining Contour Trees of Dynamic Terrains
We consider maintaining the contour tree of a piecewise-linear
triangulation that is the graph of a time varying height function
. We carefully describe the
combinatorial change in that happen as varies over time and
how these changes relate to topological changes in . We present a
kinetic data structure that maintains the contour tree of over time. Our
data structure maintains certificates that fail only when for two
adjacent vertices and in , or when two saddle vertices lie
on the same contour of . A certificate failure is handled in
time. We also show how our data structure can be extended to
handle a set of general update operations on and how it can be
applied to maintain topological persistence pairs of time varying functions