voronoi based NERF training isn't going incredibly well... 😂20k iterations with 80k voronoi sites takes about 10 hours to train. And it still looks dog water.

Definitely need more sites and some better approach to accelerating sampling....

Voronoi implicit but this time in 3d. It's not fully NERF mode yet, as I'm not doing any kind of sampling along rays, this is just trying to learn volumetric data.

30,000 Voronoi sites. Probably not enough for the pighead, but it's just a fun first test.

Lebronsketball 2

Lebronsketball 1

*morphs your cat*

Gaboronoi (top) vs Anisotropic Voronoi (bottom), with 5000 Sites. I feel like the anisotropic voronoi's artifacts are more aesthetically pleasing. Gaboronoi is faster to train by a lot!

I've compiled all of my recent voronoi experiments into a collab:
colab.research.google.com/github/jaker...

Assuming uniform weights and frequencies, and random colors and anisotropy directions, this is what an example gaboronoi diagram would look like.

I'm once again making neural implicits of my cats. This time we're back to the voronoi. Gabor noise style.

We weight the result of the softmax at any site i by sin(F_i*(x_i-x_j)•u_i) where F_i is learned frequency and u_i is a learned anisotropy direction. I call it Gaboroni

These are the noise layers that are all summed up to get the predicted image. each noise layer is colored with two colors, and each layer has a circular mask associated with it as well.

I scaled the values here by a factor of ten so that they're easier to see.

Wanted to make a neural implicit that's just layers of anisotropic simplex noise. Turns out it works pretty well. With 24 layers of simplex noise each with a 96x96 texture of anisotropy data we can get this kind of result!

It's not at all a good compression method but it's fun and cool :)

They like to hug now that they're older

Here's the aforementioned paper: sphericalvoronoi.github.io

All credit to Lucky Lyinbor for the idea to apply this to euclidean voronoi.

Also here's the ground truth image

I had the idea to incorporate anisotropy into the recent Spherical Voronoi paper. And when we apply their ideas to euclidean problems (not Spherical) the results are pretty great when anisotropy is used. This is 3000 anisotropic sites vs 3000 isotropic sites. Same learning rates for both

For the snow on the hedge maze in Zootopia 2, we cast rays upwards from each leaf and if it didn't collide with anything we instanced a snow chunk onto it. We made a few variants of the snow chunks to add extra variation.

The least obvious part of all of this is how to construct that metric tensor G from a given vector, but it turns out it's super straight forward. The attached example shows how to do so for a 3D metric tensor. In our paper we outline specific bounds for the sizing of this metric.

Just to elucidate the idea a bit more, on the left we have the original perlin noise algorithm, and on the right we have the steerable version, with the changes underlined in red. We simply add a second set of weights, and incorporate our metric into the original dot product step

New at #SIGGRAPH2025:

Can we make Perlin Noise stretch along some underlying vector field? Well it turns out it's possible with two simple additions to the original method! No need for advection or convolutions.

Find the paper and implementations here:
github.com/jakericedesi...

Distances to LP Voronoi Edges :)

shadertoy.com/view/MXVyz1

Distances to the boundary of voronoi in L4.

shadertoy.com/view/lfKfWV

Hopefully it doesn't crash webgl on your device! :)