Abstraction

Abstract

This chapter describes examples of reference algorithms for the efficient and robust computation of topological abstractions, for the purpose of data abstraction in scientific visualization. First, we present a combinatorial technique for the topological simplification of scalar data, given some user-defined or application-driven constraints. The algorithm slightly perturbs the input data such that only a constrained sub-set of critical points remains. Thus, this technique can serve in practice as a pre-processing step that significantly speeds up the subsequent computation of topological abstractions. Second, we present an efficient algorithm for the computation of Reeb graphs of PL scalar fields defined on PL 3-manifolds in $\mathbb {R}^3$. This approach described the first practical algorithm for volumetric meshes, with virtually linear scalability in practice and up to three orders of magnitude speedups with regard to previous work. Such an algorithm enabled for the first time the generalization of contour-tree based interactive techniques to non simply-connected domains.