Ronald Peikert

Over Two Decades of Integration‐Based, Geometric Flow Visualization

With ever increasing computing power, it is possible to process ever more complex fluid simulations. However, a gap between data set sizes and our ability to visualize them remains. This is especially true for the field of flow visualization, which deals with large, time‐dependent, multivariate simulation data sets. In this paper, geometry‐based flow visualization techniques form the focus of discussion. Geometric flow visualization methods place discrete objects in the velocity field whose characteristics reflect the underlying properties of the flow. A great amount of progress has been made in this field over the last two decades. However, a number of challenges remain, including placement, speed of computation and perception. In this survey, we review and classify geometric flow visualization literature according to the most important challenges when considering such a visualization, a central theme being the seeding algorithm upon which they are based. This paper details our investigation into these techniques with discussions on their applicability and their relative merits and drawbacks. The result is an up‐to‐date overview of the current state‐of‐the‐art that highlights both solved and unsolved problems in this rapidly evolving branch of research. It also serves as a concise introduction to the field of flow visualization research.

The “parallel vectors” operator: a vector field visualization primitive

We propose an elementary operation on a pair of vector fields as a building block for defining and computing global line-type features of vector or scalar fields. While usual feature definitions often are procedural and therefore implicit, our operator allows precise mathematical definitions. It can serve as a basis for comparing feature definitions and for reuse of algorithms and implementations. Applications focus on vortex core methods.

Efficient Visualization of Lagrangian Coherent Structures by Filtered AMR Ridge Extraction

This paper presents a method for filtered ridge extraction based on adaptive mesh refinement. It is applicable in situations where the underlying scalar field can be refined during ridge extraction. This requirement is met by the concept of Lagrangian coherent structures which is based on trajectories started at arbitrary sampling grids that are independent of the underlying vector field. The Lagrangian coherent structures are extracted as ridges in finite Lyapunov exponent fields computed from these grids of trajectories. The method is applied to several variants of finite Lyapunov exponents, one of which is newly introduced. High computation time due to the high number of required trajectories is a main drawback when computing Lyapunov exponents of 3-dimensional vector fields. The presented method allows a substantial speed-up by avoiding the seeding of trajectories in regions where no ridges are present or do not satisfy the prescribed filter criteria such as a minimum finite Lyapunov exponent.

A higher-order method for finding vortex core lines

This paper presents a novel method to extract vortical structures from 3D CFD (computational fluid dynamics) vector fields automatically. It discusses the underlying theory and some aspects of the implementation. Making use of higher-order derivatives, the method is able to locate bent vortices. In order to structure the recognition procedure, we distinguish locating the core line from calculating attributes of strength and quality. Results are presented on several flow fields from the field of turbomachinery.

Signed distance transform using graphics hardware

This paper presents a signed distance transform algorithm using graphics hardware, which computes the scalar valued function of the Euclidean distance to a given manifold of co-dimension one. If the manifold is closed and orientable, the distance has a negative sign on one side of the manifold and a positive sign on the other. Triangle meshes are considered for the representation of a two-dimensional manifold and the distance function is sampled on a regular Cartesian grid. In order to achieve linear complexity in the number of grid points, to each primitive we assign a simple polyhedron enclosing its Voronoi cell. Voronoi cells are known to contain exactly all points that lay closest to its corresponding primitive. Thus, the distance to the primitive only has to be computed for grid points inside its polyhedron. Although Voronoi cells partition space, the polyhedrons enclosing these cells do overlap. In regions where these overlaps occur, the minimum of all computed distances is assigned to a grid point. In order to speed up computations, points inside each polyhedron are determined by scan conversion of grid slices using graphics hardware. For this task, a fragment program is used to perform the nonlinear interpolation and minimization of distance values.

Vortex tracking in scale-space

Scale-space techniques have become popular in computer vision for their capability to access the multiscale information inherently contained in images. We show that the field of flow visualization can benefit from these techniques, too, yielding more coherent features and sorting out numerical artifacts as well as irrelevant large-scale features. We describe an implementation of scale-space computation using finite elements and show that performance is sufficient for computing a scale-space of time-dependent CFD data. Feature tracking, if available, allows to process the information provided by scale-space not just visually but also algorithmically. We present a technique for extending a class of feature extraction schemes by an additional dimension, resulting in an efficient solution of the tracking problem.

A practical structured light acquisition system for point-based geometry and texture

We present a simple and high-quality 3D scanning system based on structured light. It uses the common setup of a video projector, a computer-controlled turntable and a single camera. Geometry is acquired using a combination of gray code and phase-shift projections, and it is stored and processed in a point-based representation. We achieve high accuracy by careful calibration of camera, projector, and turntable axis. In addition, we make use of the projectors calibration and extend it to a calibrated light source, allowing for a simple reconstruction of material properties for each surface point. We alternatively use a Lambertian reflectance model, or fit a Phong reflectance model to the samples under different turntable orientations. The acquisition pipeline is entirely point-based, avoiding the need of triangulation during all processing stages.

The State of the Art in Topology-Based Visualization of Unsteady Flow

Vector fields are a common concept for the representation of many different kinds of flow phenomena in science and engineering. Methods based on vector field topology are known for their convenience for visualizing and analysing steady flows, but a counterpart for unsteady flows is still missing. However, a lot of good and relevant work aiming at such a solution is available. We give an overview of previous research leading towards topology‐based and topology‐inspired visualization of unsteady flow, pointing out the different approaches and methodologies involved as well as their relation to each other, taking classical (i.e. steady) vector field topology as our starting point. Particularly, we focus on Lagrangian methods, space–time domain approaches, local methods and stochastic and multifield approaches. Furthermore, we illustrate our review with practical examples for the different approaches.

Illustrative Flow Visualization: State of the Art, Trends and Challenges

Flow visualization is a well established branch of scientific visualization and it currently represents an invaluable resource to many fields, like automotive design, meteorology and medical imaging. Thanks to the capabilities of modern hardware, flow datasets are increasing in size and complexity, and traditional flow visualization techniques need to be updated and improved in order to deal with the upcoming challenges. A fairly recent trend to enhance the expressiveness of scientific visualization is to produce depictions of physical phenomena taking inspiration from traditional handcrafted illustrations: this approach is known as illustrative visualization, and it is getting a foothold in flow visualization as well. In this state of the art report we give an overview of the existing illustrative techniques for flow visualization, we highlight which problems have been solved and which issues still need further investigation, and, finally, we provide remarks and insights on the current trends in illustrative flow visualization.

Illuminated lines revisited

For the rendering of vector and tensor fields, several texture-based volumetric rendering methods were presented in recent years. While they have indisputable merits, the classical vertex-based rendering of integral curves has the advantage of better zooming capabilities as it is not bound to a fixed resolution. It has been shown that lighting can improve spatial perception of lines significantly, especially if lines appear in bundles. Although OpenGL does not directly support lighting of lines, fast rendering of illuminated lines can be achieved by using basic texture mapping. This existing technique is based on a maximum principle which gives a good approximation of specular reflection. Diffuse reflection however is essentially limited to bidirectional lights at infinity. We show how the realism can be further increased by improving diffuse reflection. We present simplified expressions for the Phong/Blinn lighting of infinitesimally thin cylindrical tubes. Based on these, we propose a fast rendering technique with diffuse and specular reflection for orthographic and perspective views and for multiple local and infinite lights. The method requires commonly available programmable vertex and fragment shaders and only two-dimensional lookup textures.