EuroVisShort2014

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Extracting Jacobi Structures in Reeb Spaces
(The Eurographics Association, 2014) Chattopadhyay, Amit; Carr, Hamish; Duke, David; Geng, Zhao; N. Elmqvist and M. Hlawitschka and J. Kennedy
Jacobi sets have been identified as significant in multi-field topological analysis, but are defined in the domain ofthe data rather than in the Reeb Space. This distinction is significant, as exploiting multi-field topology actuallydepends on the projection of the Jacobi set into the Reeb Space, and the details of its internal structure. Wetherefore introduce the Jacobi Structure of a Reeb Space which describes this, explain its relationships with boththe Jacobi Set and Fiber Analysis in mathematical topology, give an algorithm for computing the Jacobi Structurerecursively using a Multi-Dimensional Reeb Graph and illustrate it using an early implementation in VTK.