Local and Global Comparison of Continuous Functions

• Published in: 2004 IEEE Visualization Conference pp. 275 - 280
• Main Authors: Edelsbrunner, Herbert, Harer, John, Natarajan, Vijay, Pascucci, Valerio
• Format: Conference Proceeding
• Language: English
• Published: Washington, DC, USA IEEE Computer Society 10.10.2004; IEEE
• Series: ACM Conferences
• Subjects: Applied sciences; Artificial intelligence; Combustion; comparison measure; Computational modeling; Computer science; Computer science; control theory; systems; differential forms; Exact sciences and technology; Fires; Ignition; Level set; Mathematical analysis; Mathematics; Pattern recognition. Digital image processing. Computational geometry; Real functions; Riemannian manifolds; Sciences and techniques of general use; smooth functions; Software measurement; Software performance; Strips; time-varying data; Visualization; smooth functions; Visualization; Riemannian manifolds; differential forms; time-varying data; comparison measure; Software tool; Riemann manifold; Real function; Smooth function; Computer graphics; Contour line; piecewise function; Continuous function; Critical point; Piecewise linearization
• ISBN: 0780387880; 9780780387881
• DOI: 10.1109/VISUAL.2004.68

We introduce local and global comparison measures for a collection of k ≤ d real-valued smooth functions on a common d-dimensional Riemannian manifold. For k = d = 2 we relate the measures to the set of critical points of one function restricted to the level sets of the other. The definition of the measures extends to piecewise linear functions for which they are easy to compute. The computation of the measures forms the centerpiece of a software tool which we use to study scientific datasets.