Data sets resulting from physical simulations typically contain a multitude of physical variables. It is, therefore, desirable that visualization methods take into account the entire multi-field volume data rather than concentrating on one variable. We present a visualization approach based on surface extraction from multi-field particle volume data. The surfaces segment the data with respect to the underlying multi-variate function. Decisions on segmentation properties are based on the analysis of the multi-dimensional feature space. The feature space exploration is performed by an automated multi-dimensional hierarchical clustering method, whose resulting density clusters are shown in the form of density level sets in a 3D star coordinate layout. In the star coordinate layout, the user can select clusters of interest. A selected cluster in feature space corresponds to a segmenting surface in object space. Based on the segmentation property induced by the cluster membership, we extract a surface from the volume data. Our driving applications are smoothed particle hydrodynamics (SPH) simulations, where each particle carries multiple properties. The data sets are given in the form of unstructured point-based volume data. We directly extract our surfaces from such data without prior resampling or grid generation. The surface extraction computes individual points on the surface, which is supported by an efficient neighborhood computation. The extracted surface points are rendered using point-based rendering operations. Our approach combines methods in scientific visualization for object-space operations with methods in information visualization for feature-space operations.

The application of parallel axes for the interactive visual analysis of multidimensional data is a widely used concept. While multidimensional data sets are commonly heterogeneous in nature, i.e. data items contain both numerical and categorical (including ordinal) attribute values, the use of parallel axes often assumes either numerical or categorical attributes. While Parallel Coordinates and their large variety of extensions focus on numerical data, Parallel Sets and related methods focus on categorical attributes. While both concepts allow for displaying heterogeneous data, no clear strategies have been defined for representing categories in Parallel Coordinates or discretization of continuous ranges in Parallel Sets. In practice, type conversion as a pre‐processing step can be used as well as coordinated views of numerical and categorical data visualizations. We evaluate traditional and state‐of‐the‐art approaches with respect to the interplay of categorical and numerical dimensions for querying probability‐based events. We also compare against a heterogeneous Parallel Coordinates/Parallel Set approach with a novel interface between categorical and numerical axes . We show that approaches for mapping categorical data to numerical axis representations can lead to lower accuracy in answering probability‐based questions and higher response times than hybrid approaches in multiple‐event scenarios.