Topology preserving data simplification with error bounds

Many approaches to simpliication of triangulated terrains and surfaces have been proposed which permit bounds on the error introduced. A few algorithms additionally bound errors in auxiliary functions deened over the triangulation. We present an approach to simpliication of scalar elds over unstructured grids which preserves the topology of functions deened over the triangulation, in addition to bounding of the errors. The topology of a 2D scalar eld is deened by critical points (local maxima, local minima, saddle points), in addition to integral curves between them, which together segment the eld into regions which vary monotonically. By preserving this shape description, we guarantee that isocontours of the scalar function maintain the correct topology in the simpliied model. Methods for topology preserving simpliication by both point-insertion (reenement) and point-deletion (coarsening) are presented and compared.