Continuous Representation of Projected Attribute Spaces of Multifields over Any Spatial Sampling

Abstract

For the visual analysis of multidimensional data, dimension reduction methods are commonly used to project to a lower-dimensional visual space. In the context of multifields, i.e., volume data with a multidimensional attribute space, the spatial arrangement of the samples in the volumetric domain can be exploited to generate a Continuous Representation of the Projected Attribute Space (CoRPAS). Here, the sample locations in the volumetric domain may be arranged in a structured or unstructured way and may or may not be connected by a grid or a mesh. We propose an approach to generate CoRPAS for any sample arrangement using an isotropic density function. An interactive visual exploration system with three coordinated views of volume visualization, CoRPAS, and an interaction widget based on star coordinates is presented. The star-coordinates widget provides an intuitive means for the user to change the projection matrix. The coordinated views allow for feature selection in form of brushing and linking. The approach is applied to both synthetic data and data resulting from numerical simulations of physical phenomena. In particular, simulations based on Smoothed Particle Hydrodynamics are addressed, where the simulation kernel can be used to produce a CoRPAS that is consistent with the simulation. We also show how a logarithmic scaling of attribute values in CoRPAS is supported, which is of high practical relevance.