Sets of Globally Optimal Stream Surfaces for Flow Visualization

Abstract

Stream surfaces are a well‐studied and widely used tool for the visualization of 3D flow fields. Usually, stream surface seeding is carried out manually in time‐consuming trial and error procedures. Only recently automatic selection methods were proposed. Local methods support the selection of a set of stream surfaces, but, contrary to global selection methods, they evaluate only the quality of the seeding lines but not the quality of the whole stream surfaces. Global methods, on the other hand, only support the selection of a single optimal stream surface until now. However, for certain flow fields a single stream surface is not sufficient to represent all flow features. In our work, we overcome this limitation by introducing a global selection technique for a set of stream surfaces. All selected surfaces optimize global stream surface quality measures and are guaranteed to be mutually distant, such that they can convey different flow features. Our approach is an efficient extension of the most recent global selection method for single stream surfaces. We illustrate its effectiveness on a number of analytical and simulated flow fields and analyze the quality of the results in a user study.

Fourier Opacity Optimization for Scalable Exploration

“…Martinez Esturo et al [39] searched for a single best stream surface, such that principal surface curvature directions align with the underlying flow. The method was extended by Schulze et al [51] to find multiple best surfaces. Other optimization criteria include the stretch-minimization by Barton et al [3] and the flow alignment or orthogonality by Martinez Esturo et al [40].…”

Towards optimal advection using stretch-maximizing stream surfaces

“…Visualization of vector fields is a very active area; see [5,21,9,10], and the survey paper [24] and the references cited therein. Among flow visualization techniques, stream surfaces play an important role [31,29,27,23,11,8].…”

Stretch-minimising stream surfaces

“…Stream surfaces, used as a tool for visualising characteristic features of vector fields, have been extensively studied in the visualisation literature; see Bauer and Peikert (2002);Martinez Esturo et al (2013); Edmunds et al (2012b); Schulze et al (2014); Edmunds et al (2012c), the survey paper McLoughlin et al (2010) and the references cited therein. Classical methods Hultquist (1992) are usually based on trial-and-error approaches: the user inserts seed curves (typically straight lines), stream surfaces are computed, and, if they do not capture desired features well, the initial seed curves are modified, and the whole process is repeated.…”