Topological considerations in isosurface generation extended abstract

An emerging technique for extracting isosurfaces fro m sampled data is to consider cells with sample points as corners and approximate the isosurface in each cell b y polygons whose vertices lie between sample points wit h values on opposite sides of the threshold . When a cell face has an intersection point in each of its four edges, the correc t connection among intersection points becomes ambiguous . An incorrect connection can lead to erroneous topology i n the rendered surface, and possible discontinuities . This paper studies the problems of disambiguation , reports on some solutions, and presents some statistics o n the occurrence of ambiguities . We show that disambiguation methods, to be at all accurate, need to consider sampl e values in the neighborhood outside the cell . We introduc e two gradient-consistency heuristics that disambiguate a t reasonable computational cost and give correct topology o n several examples that caused problems for other method s we examined . The full version of this extended abstract i s available as a Technical Report [WVG90], which should be consulted for many additional details .