Point Distribution

News from my research. Right now, we have a very good tool to create textures. But because we are not artists, we have to develop algorithms that use that tool to create textures automatically. To create textures with our tool, we have to place points and orientations on the plane, therefore, the main purpose of our algorithms is to place these points.

To create interesting textures, we have to find methods to place the points. One of the most popular method consists of selecting a minimal distance d and then, for each new potential point, test with the previous point if the minimal distance is at least d. If it is, the point is added to the set, otherwise, it's rejected. To determine how this process terminates, you can either put a maximal number of points or a maximal number of consecutive failure. For more information, you can take a look at Poisson Disk Sampling for more information and for the description of a more efficient algorithm to produce the point set.

But, while investigating those process, we noticed that our tool, with the points and orientations, can be used to determined the distance between two points. We use the orientation to create different distance functions and the minimal distance is considered according to these functions. So, we end up sometimes with pair of points closer than the minimal distance, but not according to the distance function.

Here's some point distribution with the orientation parallel to the z-axis. In this case, it creates a point distribution similar to the Poisson Disk Sampling described above.

But, if we start changing the orientations randomly, we have point distributions that are much less regular:

With this method, we can see that creating a random night sky is not that difficult.

It's also possible to manage point distribution with clusters. A basic method to do clusters is first to place clusters centers, just like distributing points (by choosing an orientation and a distance function), but without any minimal distance (but it's possible to have one). Then, for each point that you want to add to the point set, you first look for the closest center. Just like before, you test that new point with all the previous points already in the point set. If the point can be added, you assign a minimal distance to that point using the distance between that point and its center. The minimal distance can be the distance itself, but for better result, you can use the square or the square root of that distance.

Here's some result of cluster point distribution:

So now that we have methods to distribute points that also use our tool, we are now able to generate textures. We plan to first use these point distribution to create textures such as caustics, clouds and random abstract images.