As scientific data sets increase in size and complexity, scientific visualization increasingly depends on formal analysis of the data. One of the most successful forms of analysis uses computational topology to analyse properties such as minima, maxima, thresholds, ridges and flow. To date, however, these methods have been applied to univariate (scalar) fields and to vector fields, but not to the more general case of multivariate fields.
In particular, Contour Trees and Reeb Graphs are often used for analysing univariate (scalar) fields. We generalize this analysis to multivariate fields with a data structure called the Joint Contour Net that quantizes the variation of multiple variables simultaneously. We report the first algorithm for constructing the Joint Contour Net, and demonstrate some of its fundamental properties. Based on this, we also show some preliminary results on its use for visualization by applying it to a problem from nuclear fission analysis, in which the topological insight provided aided scientists in understanding a physical phenomenon.