Procedural Textures

Introduction

When someone thinks of a texture, they probably think of an image used to 'paint' a model in order to give it a certain appearance. This refers to bitmapped textures, because the texture is made of pixels from an actual bitmap image. These can be very realistic, especially if taken from photographs of actual surfaces. However, one major restriction applies to bitmapped textures: a bitmapped texture has a fixed amount of detail. It cannot be scaled larger without looking softer, it will never yield any more detail than what is already captured in the pixels.

Procedural textures take an entirely different approach. Instead of creating an image by defining a large, unchanging block of pixels, procedurals create the texture from the ground up. This is where the term 'procedural' comes from. The texture is defined only by the procedure needed to create it. You only need to give the computer a (relatively) small formula, instead of a huge block of pixels. With this formula, the computer is able to create the texture at any scale, in any orientation, extending as far as you need.

Using these techniques, 3D software is armed and ready to synthesize an infinite number of textures at your command. Simply tweaking a few parameters can vary the texture widely. You can think of these textures as space full of unique shapes and features, extending in all directions, waiting to be explored. The features in this space are all defined by the interactions between a set of formulas. These formulas take in a particular coordinate, and they will report back what sort of feature is at that coordinate. In our case, these features are colors, and we put those colors on a 3D model.

A procedural function will take a coordinate, and give a color back. A particular function may also have any number of dimensions to it. That is, a 2D procedural, being most like a bitmap image, takes two coordinates, one for X and one for Y, and returns a color. This can be thought of like looking up the color of a pixel in an image. What's the difference? First, n the case of an image, the pixel must be stored explicitly in memory in order to be sampled. As a procedural, the color value doesn't "really" exist until it is sampled, since it is pulled from a formula. Second, again in the case of the image, the space between pixels is undefined. There are only so many pixels in an image, and if you want to see more than that, too bad. In contrast, a procedural texture will let you take a sample anywhere. This is what gives it one of its most remarkable qualities.

It is easier to show some of the results of using procedural textures rather than simply talking about their benefits, so here are four examples of using procedural textures in an actual scene.

Example 1

This mushroom is entirely textured with procedural functions. It uses a 3D noise function to drive its surface bumpiness. Its color variations are created by a volumetric "billow" function, remapped by a color gradient of various browns and tans. The specular highlight strength is varied by a smooth, low-frequency noise function, in order to give the surface a more natural inconsistent shine. Finally, the contrast of the color function is modified by the slope of the surface, so there is a blotchy pattern along the rim where the slope is extremely vertical.

This texture, which took very little time to design, is very robust and requires no UV mapping at all. It takes relatively little processing power to compute and needs no external image files.

Example 2

The bumpiness on the neurons is created by two voronoi textures blended together at two slightly different sizes, used as a bump map. This is able to give the neuron surfaces a wrinkly, pitted look commonly attributed to photographs in microscopic scale. The same texture is also used to modify the specularity of the texture, so as to limit how shiny the pits will be. This increases their apparent depth. There is a larger 3D noise texture at about five times the scale of the voronoi texture to give a broad, large-scale color variation. If this had been left out, the neurons would have appeared very bland and noisy from a distance (or, to quote Ken Perlin slightly out of context, like salt without food).

It would have been extremely difficult to texture a scene like this with image maps, due to the complex and convoluted surface shapes involved. Where I was able to simply define a few 3D volumetric textures, map their values to colors, and apply them to the entire scene with procedurals, using image textures would have requried me to UV map the neurons and tile textures over their surfaces. Not only would this have been much more tedious, it would have also looked a lot worse without extra work.

Example 3

Here, procedural textures also allow me to automatically give a surface-feature-based appearance to an object, much like the blotches added to the mushroom when the vertical slope was high.

In this example, the look of wet snow and ice were added to the top of the '"rock" by using the facing direction of the surface. Where the surface faced up towards the sky (Y+), a second procedural texture resembling snow and ice was added to the base procedural texture. The base procedural texture was also slightly darkened to resemble a diffuse shadow cast by the snow where there were breaks in the snow texture. Finally, the dry, powdery snow teture on the ground was created by a noise function scaled up along Z (east-west) to make it appear wind-blown in one direction.

All of these functions are automatic and require very little extra attention of the artist in order to make them work on any surface. In extremely large scenes consisting of many of the same objects (for example, a scene showing miles of rocks in snow), procedural texturing methods are almost essential.

Procedurals need not only apply to shader attributes, but they may be used to sculpt the actual geometry of a surface, as seen in the last example.

Example 4

This image of a strange, surreal landscape was created with the output of only one procedural function. The function is commonly referred to as a Worley procedural, named after Stephen Worley, who has done a lot of work on creating cellular texture functions. The Worley procedural is very closely related to Voronoi textures, and is in fact a clever variation of one.

This landscape was originally just a flat plane, but has been displaced by a large-scale Worley texture. The color comes from the same texture, where it has been remapped to a green-to-gray gradient. There are no other textures involved.

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