Vector Field Visualization - Project Webpage


The purpose of this project is to visualize vector fields in a new way. Existing techniques often make use of the standard LIC approach that visualizes the whole vector field by creating a pattern of lines. These lines follow the streamlines of the vector field, which is a good way to display the direction of the flow. However, to improve the perception of both direction and magnitude of flow, this project proposes a new way to visualize the vector field. The basic idea of this approach is to incorporate LIC lines as well, but rotate them by 90 degrees, so that they are perpendicular to the flow at all times. The goal of the project is to visualize tangential flow on three dimensional surfaces and to use advanced computer graphics methods for the final rendering part.


A huge amount of work has been done in the area of vector field visualization. A detailed summary of that work can be found e.g. in [Hauser et al, 2002] or [Sanna et al, 2000]. The work of this project adds another way of visualizing the flow of a vector field - using a method that has not been published so far. In this project, the approach of [Cabral and Leedom, 1993], the so-called LIC method, is adopted and modified to generate a new kind of vector field visualization. Original LIC generates long lines along the streamlines of a vector field in order to give an impression of the direction of the flow. However, the velocity of the flow cannot be visualized easily using this technique. To overcome this issue, a new approach is taken so that the direction and magnitude of the flow can be perceived at the same time.


This project benefits from existing unpublished work, which is used as a base to build on. The already existing software is able to create LIC lines that are perpendicular to the flow at all times, but this software is limited to two dimensions (the image plane in this case). By extending this software, this project will make it possible to display the flow on arbitrary three dimensional surfaces (which is a so-called 2.5D approach). To accomplish this, the idea of [Weiskopf and Ertl, 2004] is used to perform particle tracing for the creation of the space-time coherent noise. Major parts of the project are working only in image space, following the basic concept of [Laramee et al, 2003] and [Wijk, 2003].
In order to improve the visual perception of the flow, bump mapping will be used to create an artificial surface structure. To achieve this, the perpendicular LIC lines are interpreted as a height field that perturbs the normals, which will result in a rough looking surface. To illuminate the surface, standard Phong shading will be implemented first, cool/warm shading [Gooch et al, 1998] can be added as well.
After implementing these techniques, it is planned to evaluate the image quality by using for example fourier analysis.


The software that will be written for this project makes heavy use of vertex and pixel shaders to produce intermediate results as well as the final image. The software consists of three major parts, each of them producing intermediate results. The process can be seen as a pipeline, which means the result of one part (or stage as it is called) is needed as input for the following part. Below you can see the processing through the three stages until the final output is created:

algorithm for orthogonal LIC Bump mapping the surface of the objects in the scene will be used to improve the quality of the result of the three stages. In detail, the resulting LIC pattern is interpreted as a height field which is used to perturb the normals of the surface accordingly. The expected result of this operation portrays a better perception of the flow, since the bumpy surface gives the impression of a structure on top of the object (and therefore a better contrast between lit and "shadowed" regions).


Expected Results

Since the approach works partly in image space, the known image space problems may arise here as well. One of these issues could be overlapping surfaces - overlapping in this case means, that two different surfaces overlap in image space, but in object space they are just at different depths relative to the image plane. The LIC will just integrate over the overlapping boundary, giving an incorrect result in these regions. For the sake of brevity, this issue is just ignored.

Results - Screenshots

uniform flow on a torus- orthogonal LIC This screenshot shows uniform flow on a torus, which is visualized with the proposed technique. Click on the image to see a large version of that screenshot!

CFD simulation for a car - orthogonal LIC This screenshot shows a the result of a CFD simulation for a car, which is visualized with the proposed method. Click on the image to see a large version of that screenshot! (Car geometry and vector field by courtesy of the BMW group)

Results - Videos

There are two videos available for download, which show the animated version of the above screenshots. Both videos are approx. 5 MB large. The first video shows the torus with an uniform vector field. The second video shows the animated vector field on a car. (Car geometry and vector field by courtesy of the BMW group)


The concept of orthogonal vector field representation is introduced for visualization purposes. A filtering process is proposed to obtain a consistent and temporally coherent animation of the orthogonal vector field visualization. A fast GPU implementation of the proposed algorithm is presented.


[Blinn, 1978]
J. Blinn: Simulation of Wrinkled Surfaces, Proceedings SIGGRAPH, p. 286 - 292, Aug. 1978.

[Cabral and Leedom, 1993]
B. Cabral and L. Leedom: Imaging Vector Fields Using Line Integral Convolution, Proceedings of ACM SIGGRAPH, Annual Conference Series, p. 263 - 272, 1993.

[Gooch et al, 1998]
A. Gooch, B. Gooch, P. Shirley, E. Cohen: A non-photorealistic lighting model for automatic technical illustration, SIGGRAPH 1998 Conference Proceedings, p. 101 - 108, 1998.

[Hauser et al, 2002]
H. Hauser, R. S. Laramee and H. Doleisch: State-of-the-art report 2002 in flow visualization, TR-VRVis 2002 - 2003, VRVis 2002.

[Laramee et al, 2003]
R. S. Laramee, B. Jobard and H. Hauser : Image space based visualization of unsteady flow on surfaces, IEEE Visualization 2003, p. 131 - 138, 2003.

[Sanna et al, 2000]
A. Sanna, B. Montrucchio and P. Montuschi: A survey on visualization of vector fields by texture-based methods, Recent Research Development in Pattern Recognition 1, p. 13 - 27, 2000.

[Weiskopf and Ertl, 2004]
D. Weiskopf and T. Ertl: A Hybrid Physical/Device-Space Approach for Spatio-Temporally Coherent Interactive Texture Advection on Curved Surfaces, Proceedings of Graphics Interface, p. 263 - 270, 2004.

[Wijk, 2003]
J. van Wijk: Image Based Flow Visualization for Curved Surfaces, Proceedings of the 14th IEEE Visualization Conference (VIS 03), p. 123 - 130, 2003.

Last modified: Jan. 17th, 2007
by Sven Bachthaler