Dense texture-based visualization of unsteady and multi-variate vector fields
Introduction
The analysis and the visualization of time-dependent vector fields, in general unsteady fields, are fundamental topics in scientific visualization and computer graphics. Relevant fields of application are in fluid- and aerodynamics, electromagnetism, meteorology, physics, etc. Despite intensive research efforts and many interesting methods that have been developed, the representation of complex flow fields and multi-variate vector fields remains challenging, and the need for a general and adaptive method still exists.
In this paper, we propose a novel flexible approach. Our method uses a simple algorithm to generate a smooth and continuous visualization with correlation in the spatial and temporal domains.
The paper is organized as follows: in the next section we discuss relevant previous and related work, then we explain our motivation and the main contributions of this research. Successively, we describe our approach and algorithm and we illustrate the application showing some results. We discuss features and limitations of our technique, presenting solutions for optimization. Finally, we conclude addressing possible extensions and future work.
Section snippets
Previous work
Vector fields visualization is a very productive area of research and, consequently, numerous techniques exist. For this reason, a complete review of the field is beyond the scope of this paper, and we remand to [1] for a good survey and state of the art on vector fields and flow visualization. Here, we just provide a general classification and refer to some recent techniques, which are at most related to our approach. Direct visualization is an intuitive technique, which consists in drawing
Our motivation and contribution
The cited methods provide good visualization, but do not always result to be general: direct visualization is intuitive but may miss density and accuracy, geometric visualization directly communicates information but is sometimes too simplified, feature-based visualization may be too specialistic for inexperienced users. Our technique has the target to combine the advantages of the various methods in a general way, resulting in a visualization that is intuitive and easy to perceive for the user
Approach
We generate a dense visualization of variable vector fields getting as input a given array of vector values or an arbitrary functional expression of the field. In this visualization every point in the output is appropriately colored. Such color value represents the combined information of scalar values, direction, orientation, carried by the field at that specific point and time. The user may choose sample patterns to control the appearance and certain properties of the vector field. In this
Algorithm
Let be a time-dependent vector field in d dimensions over : . We aim at visualizing its variation over time. In our algorithm, each 2D (in space) vector defines an example texture image , i.e. , with for gray level and for colored textures. To generate a visualization of each frame, one defines the pixel counts of the output, which in turn define the sampling of the vector field. The pixel at and at time step t is computed using
Results and discussion
The results in Fig. 4 show some frames extracted from longer generated sequences. Different patterns are used as seed to generate unsteady fields evolution. Fig. 5 represents two sets of successive frames, showing underlying time-dependent vector field structure together with color coding, which maps the varying intensity of the velocity field. The visualization of variable vector fields is a multi-variate visualization, hence we use multiple information mapping. Fig. 5 (left) shows an
Conclusion and future work
This paper outlines a novel technique for generating continuous visualizations of unsteady and multi-variate fields. The presented algorithm automatically generates a set of frames, which in turn represent the structure of the flow field at several time steps. Besides providing a methodology for precise smooth visualization of dense flow fields, one of our main targets was to allow user intervention for local and global control in the visualization process. Our method combines the intuitivism
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