Visualizing and analyzing 3D unsteady flow fields is a very challenging task. We approach this problem by leveraging the mathematical foundations of 3D observer fields to explore and analyze 3D flows in reference frames that are more suitable to visual analysis than the input reference frame. We design novel interactive tools for determining, filtering, and combining reference frames for observer-aware 3D unsteady flow visualization. We represent the space of reference frame motions in a 3D spatial domain via a 6D parameter space, in which every observer is a time-dependent curve. Our framework supports operations in this 6D observer space by separately focusing on two 3D subspaces, for 3D translations, and 3D rotations, respectively. We show that this approach facilitates a variety of interactions with 3D flow fields. Building on the interactive selection of observers, we furthermore introduce novel techniques such as observer-aware streamline- and pathline-filtering as well as observer-aware isosurface animations of scalar fluid properties for the enhanced visualization and analysis of 3D unsteady flows. We discuss the theoretical underpinnings as well as practical implementation considerations of our approach, and demonstrate the benefits of its 6+1D observer-based methodology on several 3D unsteady flow datasets.

Large-scale scientific data, such as weather and climate simulations, often comprise a large number of attributes for each data sample, like temperature, pressure, humidity, and many more. Interactive visualization and analysis require filtering according to any desired combination of attributes, in particular logical AND operations, which is challenging for large data and many attributes. Many general data structures for this problem are built for and scale with a fixed number of attributes, and scalability of joint queries with arbitrary attribute subsets remains a significant problem. We propose a flexible probabilistic framework for multivariate range queries that decouples all attribute dimensions via projection, allowing any subset of attributes to be queried with full efficiency. Moreover, our approach is output-sensitive, mainly scaling with the cardinality of the query result rather than with the input data size. This is particularly important for joint attribute queries, where the query output is usually much smaller than the whole data set. Additionally, our approach can split query evaluation between user interaction and rendering, achieving much better scalability for interactive visualization than the previous state of the art. Furthermore, even when a multi-resolution strategy is used for visualization, queries are jointly evaluated at the finest data granularity, because our framework does not limit query accuracy to a fixed spatial subdivision.

The rapidly growing size and complexity of 3D geological models has increased the need for level-of-detail techniques and compact encodings to facilitate interactive visualization. For large-scale hexahedral meshes, state-of-the-art approaches often employ wavelet schemes for level of detail as well as for data compression. Here, wavelet transforms serve two purposes: (1) they achieve substantial compression for data reduction; and (2) the multiresolution encoding provides levels of detail for visualization. However, in coarser detail levels, important geometric features, such as geological faults, often get too smoothed out or lost, due to linear translation-invariant filtering. The same is true for attribute features, such as discontinuities in porosity or permeability. We present a novel, integrated approach addressing both purposes above, while preserving critical data features of both model geometry and its attributes. Our first major contribution is that we completely decouple the computation of levels of detail from data compression, and perform nonlinear filtering in a high-dimensional data space jointly representing the geological model geometry with its attributes. Computing detail levels in this space enables us to jointly preserve features in both geometry and attributes. While designed in a general way, our framework specifically employs joint bilateral filters, computed efficiently on a high-dimensional permutohedral grid. For data compression, after the computation of all detail levels, each level is separately encoded with a standard wavelet transform. Our second major contribution is a compact GPU data structure for the encoded mesh and attributes that enables direct real-time GPU visualization without prior decoding.