merging voronoi

Here we are playing again with the Voronoi diagram (VD). We wanted to see what happen when sites are merged together (MVD, merged VD).

VD partitions the plane in cells where each of these cell represents the closest part of the plane to a particular site. So, if you have sites on a map of various fast food restaurants, the Voronoi diagram tells you which one is physically the closest to your location.

But imagine that we want to consider all restaurant from a particular chain as one entity. We want to know the influence or the domination of a particular chain.

The following images are in pair. The first one is the influence of a chain of restaurant and the second is the actual VD that everyone knows. Cells with the same color represents a chain of restaurant.

In the images, you can see some brighter points (particularly in the first two images), this is the actual location of the site (or restaurant for in our example).

And just like the VD is well known for its role in texture synthesis, we hope to find a way to use the MVD to create some interesting results.

As for the diagram itself, we don't really know what to do with it or how to interpret it. VD has a dual graph called the Delaunay Triangulation. But what would be the dual graph of MVD ? Where do we put the edges ? That's an open question.

More texture synthesis

In this post, I present some new result that we really like. Again, it's a variation of the Voronoi diagram. You can observe the Voronoi cells interacting with each other. The colors help to see clearly the cells. And because of the few number of color, some cells might share the same color but are not related at all.

Here's some of the results:

This method, if it produces the result we're expecting, can be used to create texture by simply specifying some parameters or an artist can use a program with that method implemented to place some control points and control other parameters.

Again, all these images can be computed with CUDA because each pixel is unique.

More textures

In my research, I'm still working on my textures. Here's some results I produced today that I really like.

Those effects might be implemented in a next version of my live-wallpaper. I haven't decided yet. For the first two images, I put the orientation of the points right on the plane. Plus I tried a new function to compute the distance. This one allows some distance pixels to actually have a distance of zero when it's perfectly aligned with another points.

Next, I will try to use images as a source of points and orientations. To see if with this method it's possible to create mosaic from an image. Creating mosaic with the normal Voronoi diagram is something well known in the literature. But with this method of oriented points that creates cells that are not convex polygons might allow us to do something very unique.

Let me know what you think of these images.

Yin Yang Texture

Here's a post on texture.

Previously, we were using a method to control images with points and normals. Alone, a point and a normal split the plane in two, a positive and negative part. But combined with other points and normals, we can actually control curve shapes. To visualize it, we assign white to the positive part and black for the other.

The textures proposed here are made by first splitting the plane in two parts. The two parts must be symmetrical just like the Yin Yang symbol.

We then distribute points and normals inside one of the part. We then reflect the point into the second part, but not the normal.

The method create a contrast and a perfect symmetry. Here's some results:

I won't describe the method to render those images because it's very complex. Also, the process is very slow. Unlike the live-wallpaper I'm working on, or the previous images I showed, we cannot compute those in real-time.

Unfortunately, we haven't implement this with CUDA. With CUDA, it wouldn't be in real-time, but it would be much faster. Specially the per-pixel rendering part. Let me know what you think about these Yin-Yang images.