New visualization tools unlock insights hidden in complex data sets

<p>The problem of visualising multivariate data and tensor fields inherits its complexity from the data it targets. By definition, complex data is "hard to separate, analyse, or solve"¹. This becomes evident through the fact that methods for "simple" data such as scalars and vectors do not trivially extend to multivariate data and tensors. In the light of increasing number of output variables from simulation models and measurements, this lack of methods leads to a limited choice in the analysis and to a lower fidelity of the analysis. In addition, split application of established methods to a subset of the data, for example the separate rendering of isosurfaces for the different scalar fields contained in multivariate data, brings about a number of challenges and pitfalls.</p><p>In this work I present several approaches to extending existing methods for scalar field visualisation and analysis to multivariate data and, in some cases by extension, tensor fields. Specifically, I have investigated the extraction of isosurfaces from multivariate data, the topological analysis of multivariate data and tensor fields, and the design of transfer functions for tensor fields.</p><p>Isosurfaces (contours) are a widely used visualisation modality. They can be used to intuitively highlight regions of interest and are the goto choice for taking snapshots during large-scale in-situ simulations to verify results. In domains such as meteorology where simulations yield a number of output variables for pressure, temperature, precipitation, etc., methods for visualising multivariate isosurfaces are needed. Feature level sets offer such a method by interpreting an isosurface as the result of an intersection of the isovalue with the data in the domain. From this, we expand the notion of isovalues, in this context called traits, and isosurfaces to arbitrary dimensionality.</p><p>An intermediate product of the calculation of feature level sets is the distance field defining every data point’s distance towards the trait. Given this distance field, we compute the merge tree for it and thereby enable topological analysis of multivariate data. The choice of merge trees comes naturally as minima in the distance field correspond to regions closest to the trait.</p><p>The concept of derived fields as input is also used in our approach to topological analysis of tensor fields. Special attention needs to be paid to the non-linear behaviour of derived vector and scalar fields. We use the field of eigenvectors derived from the tensor field to determine cells containing degenerate points in tensor fields and insert zero-valued points in the corresponding anisotropy field. This process yields a scalar field which can subsequently be used as input for further topological analysis.Another challenge when it comes to the visualisation of tensor fields is the design of transfer functions in the context of volume rendering. This is because of the high dimensional entity that is a tensor and its non-linear derivatives. We span a shape space which is populated by representatives which visually encode the tensor. This allows the user to steer the rendering by selecting the desired "shape" of the tensor rather than adjusting a slider for a derived scalar value.</p><p></p><p>¹ Merriam-Webster. Complex. In Merriam-Webster dictionary (Merriam-Webster.com). Retrieved December 1st, 2024, from https://www.merriam-webster.com/dictionary/complex </p>