Jan. 12, 2001

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Publications by Wu Shin-Ting et al. (State University of Campinas, Brasil) :

• On Improving the Search for Critical Points of Implicit Functions, 1999.

BibTeX references.

Recently, there is a trend to develop efficient polygonization techniques for implicit surfaces, aiming at interactive modeling and animation. One of the most challenging issues for such techniques is to ensure the matching between the topology of the surface and the topology of its polygonal approximation. Therefore, it is important to accurately extract the topological information from a given implicit function. This can be done using Morse theory, which says that the critical points of a real function are intimately related to the topology of its level sets. Previous efforts to locate critical points consist of either employing interval search over the domain of the implicit function or trying to find them incrementally in the neighborhood of selected vertices. In this paper we propose an alternative procedure for a specific skeleton-based model. We use the spatial coherence of the skeleton elements to give a good first guess for the locations of the critical points. Newton's method is then applied to improve the accuracy of these predictions.

Uses the critical set of implicit functions in R^3 defined as spherical shape functions which decay over distance. Details an algorithms which first estimates a critical point locus of index 0 (maximum), and then proceeds to match maxima together to form a cycle, and estimate critical points of index 1 (2-saddles) as their barycenters. This position is refined via a Newton iterative search. The same loop is iterated for critical points of index 2 (1-saddles), and, finally, index 3 (minima).

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Page created & maintained by Frederic Leymarie, 2001
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