Extracting Jacobi Structures in Reeb Spaces
نویسندگان
چکیده
Jacobi sets have been identified as significant in multi-field topological analysis, but are defined in the domain of the data rather than in the Reeb Space. This distinction is significant, as exploiting multi-field topology actually depends on the projection of the Jacobi set into the Reeb Space, and the details of its internal structure. We therefore introduce the Jacobi Structure of a Reeb Space which describes this, explain its relationships with both the Jacobi Set and Fiber Analysis in mathematical topology, give an algorithm for computing the Jacobi Structure recursively using a Multi-Dimensional Reeb Graph and illustrate it using an early implementation in VTK.
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