A Streamline Selection Technique for Integrated Scalar and Vector
Visualization
Shiho Furuya∗

Takayuki Itoh†

Ochanomizu UniversityOchanomizu University

1 I NTRODUCTION
Scalar and vector field visualization techniques have evolved almost
independently. We think integration of scalar and vector visualization is still an interesting topic. For example, many researchersin fluid dynamics simulations still use 2D scalar and vector visualization techniques in one display, to demonstrate the coherency
between scalar (e.g., temperature and air pressure) and vector (e.g.,air flow) fields; however, it is not easy to understand three dimensional mechanism of fluid dynamics from the 2D visualization results. On the other hand, several visualization works integrate 3D
scalar and vector visualization techniques; for example, Treinish
et al. reported a visualization system for weather simulation results [1], as combination of 3D scalar and vector visualization techniques. Such integrated 3D visualization systems are useful to understand the three dimensional coherency between scalar and vector
fields. We think it is still a research issue to automatically obtain
optimal visualization results from such integrated 3D systems.
This poster presents a streamline selection technique for integrated scalar and vector field visualization. The technique visualizes a scalar field by multiple semitransparent isosurfaces, and avector field by multiple streamline, where the technique adequately
selects the streamline considering of reduction of cluttering among
the isosurfaces and streamlines.
The technique first selects and renders interesting isosurfaces. It
then temporarily generates a lot of streamlines from randomly selected seed points. It evaluates each of the streamlines according
to their visibility, and selects the specified number of highly evaluated streamlines. Consequently, the technique visualizes scalarand vector fields simultaneously, by isosurfaces selected from viewnondependent perspective, and streamlines selected from viewdependent perspective.
2 P RESENTED T ECHNIQUE
2.1 Isosurface Selection
First step of the presented technique selects interesting isosurfaces
by determining important isovalues in the scalar field. This problem has been well-discussed for transfer function definition for volume rendering [2, 3]. We suppose interesting isosurfaces can be extracted applying the important isovalues determined by such transfer function definition techniques.
Our current implementation generates predefined number of isosurfaces (1 to 3 in the examples of this poster), by automaticallydetermining the isovalues. Then it renders the isosurfaces as semitransparent surfaces, assigning independent colors (red, green, andblue in the examples of this poster) to each of isosurfaces.
2.2 Streamline Selection
Our technique then temporarily generates a lot of streamlines fromrandomly selected seed points, and evaluates them based on their∗ e-mail: shiho@itolab.is.ocha.ac.jp† e-mail:itot@is.ocha.ac.jp

information entropy. Information entropy has been already appliedin several works on optimal viewpoint selection [4]. Our idea isvery similar to these works: it calculates the information entropy Eof a streamline as follows:
E =−m DDj1
jlog2
∑log2 (m + 1) j=0 L
L(1)where m is the number of segments of a streamline, D j is the lengthof the j-th segment on the screen, and L is the total length of thestreamline in 3D space. Our technique applies the equation to all
the streamlines, and sort them according to E. It finally renders thepredefined number of streamlines in the sorted order.
Streamline selection is a recent active topic, and there have been
several novel works. For example, Li et al. reported an illustrativetechnique to select streamline on a screen space [5]. Comparing
with such existing techniques, our technique tends to render lessnumber of long and informative streamlines.
In addition to calculating the information entropy, our techniqueconsiders of following points:
Density control. Our technique often highly evaluates very closestreamlines, because they are usually very similar; however, it looks
very dense if it renders all such streamlines. Therefore, our technique calculates the minimum distances from several vertices ofcurrently rendering streamline to already rendered streamlines. If
at least one of the minimum distances is enough large, the techniquerenders the current streamline. Otherwise, it cancels to render thecurrent streamline.
Critical points. It is well-known that important phenomena in vector fields are often observed around critical points (e.g., center ofvortex), and therefore it is fruitful to generate streamline aroundthe critical points [6]. Our current implementation generates seedpoints which are enough close to at least one of the critical points,and sorts the streamlines starting from the seed points in the order of
E. This poster calls such streamlines as ”near-critical streamlines”.
It then preferentially renders predefined number of the near-criticalstreamlines, and finally renders non-near-critical streamlines. Ourcurrent implementation can distinguish the colors between nearcritical and non-near-critical streamlines. Examples in this poster
draw near-critical streamlines in red, and the others in black.
Figure 1 shows the effort of density control and critical point
extraction. We can observe that streamlines are effectively distributed, and vortex is certainly visualized by red streamlines, inFigure 1(right).
Cluttering with isosurfaces. Since it is not preferable that a lotof streamlines occluded by isosurfaces are rendered, our techniqueapplies a penalty to the occluded streamlines. It determines theocclusion by an isosurface for each segment of a streamline, andcalculates the new entropy E  by the following equation:
E  = (1 − m0 /m)E + (m0 /m)(1 − a)E(2)where mo is the number of occluded segments, and a is the opacityof an isosurface.
Extending the above idea, the technique calculates the new entropy, if a segment may be occluded by multiple isosurfaces. Suppose that the i-th segment of a streamline (1 ≤ i ≤ m) is occluded by

Figure 1: Comparison of streamline generation. (Left) Without density control and critical point extraction. (Right) With density control
and critical point extraction.

multiple isosurfaces, and let the opacities of occluding isosurfaces
a1 to ani , where ni is the number of isosurfaces occluding the i-thsegment, and the isosurfaces are sorted in the order of their depths.
We weight the length of Di as follows:
Di j = (1 − a j )Di( j−1)

Figure 2: Integrated visualization of air pressure and air flow.

(3)

where 1 ≤ j ≤ ni , and Di0 = Di . The technique calculates the entropy as follows:
E =−m DD jn j1jn j
log2∑log2 (m + 1) j=0 LL(4)2.3 GUIIn addition to focusing on automatic selection of isosurfaces andstreamlines, our current implementation provides GUI to adjust thefollowing parameters: isovalues and opacity of isosurfaces, andnumber of near-critical and non-near critical streamlines.
E XAMPLE : V ISUALIZATION OF W EATHER S IMULATIONR ESULTS
We applied the presented technique to visualization of weather simulation results, which contain scalar fields of temperature and airpressure, and a vector field of air flow. While visualizing such
weather simulation results, we often focus on high- or low- pressure
areas, and warm or cold air masses. Such phenomena can be visualized as isosurfaces around local maximum or minimum points ofthe scalar fields. Also, we often focus on air flow around such highor low- pressure areas, and warm or cold air masses. Such air flow
can be visualized by adequately generated streamlines.
Figure 2 shows an example of integrated visualization of air pressure and air flow obtained from a weather simulation result. The
simulation assumes the ground as XY-plane, and Z-coordinate denotes the altitude. In other words, Figure 2 draws the ground near,and the air far. Two isosurfaces denote specific air pressure values
which bring high- and low-pressure systems. The result denotesthat the air flow revolves around the high- and low-pressure systems. Here the technique randomly generated 500 streamlines andselected 22 of them.
Figure 3 shows a comparison of visualization results while theleft result does not consider of occlusion by an isosurface, while theright result considers of the occlusion. It proves that more numberof non-occluded streamlines and less number of occluded streamlines are generated in the right result.
34 C ONCLUSION AND F UTURE W ORKS
This poster presented a technique for automatic streamline selection technique for integration of scalar and vector field visualization, based on information entropy, density, critical points, and occlusion by isosurfaces. As future works, we would like to extend
the technique to time-varying volume data, implement on GPU environment, and carry out subjective evaluations.

Figure 3: Comparison of consideration of occlusion by isosurfaces.
(Left) A result without the consideration of the occlusion. (Right) Aresult considering of the occlusion.

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