On the topology of the level sets of a scalar field

This paper introduces a new simple algorithm for the construction of the Contour Tree of a 3D scalar field augmented with the Betti numbers of each contour component. The algorithm has {Omicron}(n log n) time complexity and {Omicron}(n) auxiliary storage. where n is the number of vertices in the domain of the field. The algorithm can be applied to fields of any dimension in which case it computes the Contour Tree augmented, with the Euler characteristic of each contour. The complexity in any dimension remains {Omicron}(n logn). This is the same complexity as in [4] but with correct computation of the tree for fields with bounded domains.

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