fluids halftoning

Line Integral Convolution

Line integral convolution, or LIC, is a nice way to get a sense of the directions of a flow field. By averaging a noisy image along sections of streamlines, you get some nice streaks. Look at this example, applied to the flow around a spinning cylinder:

Noise image on the left, LIC on the right.

There are a couple main parameters to tweak: the noise scale, and the integration length. In the example above, the integration length varies (left to right) from zero to ten times the noise scale. Increasing the length scale results in smoother streaks, and larger noise gives wider streaks.

One way to take advantage of the parameters is by using the streak length to indicate speed! Think in terms of blurred images of falling snow. Faster snowflakes have longer streaks, and slower ones have short streaks. How does this look?

Uniform length on the left, velocity-scaled length on the right.

It does give a sense of where the flow is slower, but at the price of weakening the sense of the flow direction. The easier answer is to scale the LIC image by the flow velocity:


And since it’s a nice pattern, let’s apply it to halftoning. Once the LIC image is histogram-equalized, it’s a handy halftone screen:


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