Chattopadhyay, AmitCarr, HamishDuke, DavidGeng, ZhaoN. Elmqvist and M. Hlawitschka and J. Kennedy2014-12-162014-12-162014978-3-905674-69-9https://doi.org/10.2312/eurovisshort.20141156Jacobi 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.KeywordsTopological analysisMultiFieldReeb spaceJacobi setMultiDimensional Reeb GraphJCNI.3.6 [Computer Graphics]Methodology andTechniquesGraphics data structures and data types