Issues on Displaying 3D Data for Scientific Visualization Thomas Theußl theussl@cg.tuwien.ac.at Institute of Computer Graphics Vienna University of Technology Vienna, Austria

Volume Line Integral Convolution

Line Integral Convolution (LIC) is an elegant algorithm for visualizing vector fields. Very good results are achieved for 2D vector fields, but extending it to 3D arises some problems. The pictures get confusing, too many details obscure the flow topology. Some modifications to the original algorithm have been proposed by Interrante and Grosch [7] to achieve better results in three dimensions.
The texture used with 2D LIC would normally be an opaque, uncorrelated white noise. This has the drawback that the orientation of the vector field cannot be perceived. Wegenkittl et al. [16] developed a method, Oriented Line Integral Convolution (OLIC), where they use a low frequency input texture and a ramp like convolution kernel to depict both direction and orientation of the flow. This, further, inspired Interrante and Grosch to enhance 3D LIC by using a sparsely opaque input texture and to use LIC to correlate both color and opacity values in the direction of the flow. They also proposed that the input spots in the volume should be randomly situated according to an approximate Poisson-disk distribution, rather than laid out purely randomly. See Figure 3 for an example.

  
Figure 3: Volume Line Integral Convolution from an input texture of evenly-distributed random point samples. Shading is computed as described in Section 2.1.

If the stream lines are shaded as described in Section 2.1, the local orientation of the flow can be clearly depicted but streamlines that are separated in depth but which flow in a similar direction cannot effectively be distinguished. The following techniques have proven useful for clarifying the display of volume textures generated via 3D LIC:

• By assigning each of the different input texture elements one of a small number of harmonious yet readily distinguishable different hues, the differentiating of the distinct lines is facilitated. Colors can be randomly distributed among the input points or may alternatively be assigned on the basis of a function computed either over the streamline or its point of origin. Care must be taken with the second approach to prevent the perceptual clumping of elements in homogeneously-valued regions, for example by assigning random luminance variations.
• Artists and illustrators often use gaps to indicate the depth relation if a line crosses behind another. To depict such gaps, a second input texture, identical to the first except that it contains slightly larger spots at the same location as the smaller spots in the original texture, is used during volume rendering to decrease the contribution to the final image of any voxel encountered after a halo, that is the margin that surrounds every line in the second input texture, has been entered and subsequently exited, emphasizing the depth discontinuities in such a way.
• Another approach to facilitate local depth order judgements would be to use stereo, or to animate the lines so that they follow the flow.