Multi-resolution representation of topology

The Contour Tree of a scalar field is the graph obtained by contracting, all the connected components of the level sets of the field into points. This is a powerful abstraction for representing the structure of the field with explicit description of the topolocrical changes of its level sets. It has proven effective as a data-structure for fast extraction of isosurfaces and its application has been advocated as a user interface component guiding interactive data exploration sessions. We propose a new metaphor for visualizing the Contour Tree borrowed from the classical design of a mechanical orrery - see Figure I (a) - reproducing a hierarchy of orbits of the planets around the sun or moons around a planet. In the toporrery - see Figure 1(b) - the hierarchy of stars, planets and moons is replaced with a hierarchy of maxima, minima and saddles that can be interactively filtered, both uniformly and adaptively, by importance with respect to a given metric.