Stochastic Texturing

May 30, 2023

One of the significant challenges associated with creating a planet-sized world is the issue of texture repetition. Monotonous textures not only degrade the aesthetic quality of the environment but also disrupt the immersive experience. Therefore, in order to create convincingly vast open worlds, it is vital to discover methods to overcome this repetitive pattern.

So, what exactly is stochastic texturing? The term 'stochastic' refers to randomness, thus, stochastic texturing implies the application of randomness in texturing. Essentially, this technique involves infusing randomness into the uniform placement of textures.

This methodology incorporates the generation of multiple masks and subsequently adjusting the placement of textures for each of these masks. Once this process is complete, the various textures are blended together. This technique should effectively mitigate, if not completely eradicate, repetition across expansive landscapes.

Author: Djanco Dewus
Shader / Technical artist

Repetitive texture tilling

Step 1 - Generating mask

One of the essential components of stochastic texturing is generating high-quality masks. these masks are used to blend between differently transformed (rotated, scaled, and moved) versions of the textures. There are numerous types of masks that can be used.

Hexagon grid

One way to break texture repetition is to generate an RGB hexagon map. For every color of the hexagon grid, you can have a different transformed texture placement. After that blend the textures together.

Soft Hexagon Grid

We now have something resembling some type of grid, but the hexagon grid is not yet visible and appears to be a blurry mess.

Fortunately, we can easily address this by first powering the hexagon grid by a chosen number and then dividing it by the sum of the three colors

Hexagon grid

By adjusting the 'l_hex_sharpness' variable we can control the sharpness of the hexagons. A transition is needed between the hexagons. This will be used for blending the textures together.

Single Noise

We can also generate some noise (like Perlin or simplex noise), then make sure the noise values go from
[0 - 1]. We can then split the noise into 3 RGB bands.

Here is the code to transform a greyscale 0-1 value to 3 RGB bands. You can increase the contrast with the 'contrast' variable.

One issue with the method used here is that the red and blue masks become islands and the green fills everything inside. This will cause the green mask to be more continuous than we want.

Tripple noise

We could also create three noises and then blend them. Each noise is its separate mask. This would be heavier because we have to generate multiple noises instead of one but, you don't have to convert a greyscale noise to an RGB noise.

We can do the same as we did with the Hex grid to bring contrast to the mask. You power all the masks by some value. Then you divide them by the sum of the 3.

Triple noise with changing contrast

Checkerboard grid

If you are more focused on performance here is another option that also works great. Instead of random noise, we generate a checkerboard pattern. While the mask is less random than a hex grid or some noise. One thing we can do when we have a predictable mask is for every square of the grid we can generate a random value and use that for rotation and offset. So instead that of every color of the mask has the same offset and rotation, every checker has a different transform.

The reason this mask is more performant is that we can do this with only 2 texture samples instead of 3.

First, we generate a square grid where every square taper to the center and again normalize it as we did in the previous noises.

Checkerboard grid

Now for every square on this grid, we can generate a random value that can be used to transform the UVs.

Random values

Step 2 - Rotate textures

One of the transformations that you can do is rotation. Rotation will break some directional continuality on your texture (if you have a color gradient in your texture or if your texture is a bit anisotropic). For every mask that you have made, we can have a different rotated texture. We can use a simple 2D rotation function.

One problem we have with rotating the textures is, that most people have continuous UVs (UVs that go from 0 to a big number). Our UVs are non-continuous (they repeat from [0 - 1]). Because of this we cant freely rotate the textures. If we would freely rotate the textures they will no longer tile. Rotating them quarterly / 90° would still work.

Texture rotated by 90°

We could also rotate them by 45° but then the scale would be incorrect. When the texture is diagonal we need to scale it by √2 (the diagonal length of a square).

Texture rotated 45° and scaled

If you use “Checkerboard grid“ then here are a few more things you can do. First, we need to change the random 0-1 values that we generated for the rotation to [0 - TAU] and make sure the rotations only go in steps of 4 or 8.

Step 3 - Blending

Linear blending

The simplest and cheapest way to blend the 3 textures is to multiply them with their corresponding hexagon grid color and then add them together.

Linear blending

This gives a decent result from a distance, but if you get close you will see the ugly linear blending.
You will see multiple elements being blended (dry grass and tree roots). You could decrease the blending distance but then some texture elements would randomly stop.

Linear blending fade

Linear blending lack of continuation

Height blending

Another option is height blending. This will use the height map to determine how to blend the different textures. With height blending, you retain some continuation in texture elements (like the roots)

Here is a simple function for doing height blending.

Linear blending linear - Linear blending height

Step 4 - Fixing normal maps

An issue you can experience is that your tangent space normal maps don't work correctly anymore. You will see that some parts of the normal map are lit from different angles. Fortunately, there is a simple solution. You can use the same 2D rotation function, that is used to rotate the UVs, to rotate the XY / RB components of the tangent normal map. You can use the same rotation values as used when rotating the UVs. You don't need to normalize the normal map post rotation as the function doesn't change the length of the normal.

Wrong normal map directions - Corrected normals

Conclusion

After using these techniques you should have reduced or completely removed tilling from your terrain!
All this will come at a performance cost but, for big stretches of land using only a few textures, this will improve the visual quality and immersion a lot.