An Approach to Modeling Dirtiness

Dirtiness in the sense Becket and Badler use is: ‘any deterioration of some preconceived, idealized notion of perfection corresponding visually to the result of human or natural processes’.
This approach's goal is not to create a model for imperfection using pure simulation of particles or liquids, but using a rule-based system to create textures. The main reason for this reduction of complexity is the fact that most imperfections are viewed from distances where exact details of distribution or local appearance are indistinct. Therefore any complete simulation of real world processed would mean enormous overcomputation. But this simplification presents the major drawback of the approach, because using textures for modeling dirtiness only works for blemishes that appear two-dimensional from standard human distances. Fortunately these two dimensional imperfections comprise a large portion of our common notion of imperfection. The whole approach involves two steps:
  1. Blemish instance modeling i.e. finding some technique to model a localized instance or concept of a blemish.
  2. Blemish placement i.e. designing rules that place or control distribution and local simulation of instances. This process constructs relevant statistical parameters for local simulation given simple object information such as shape and composition and specific contextual information such as the use of the object or location of adjoining objects.

Blemish instance modeling

Aside from Gaussian and random distribution functions, rule-guided aggregation and 2D fractal subdivision are used to create the textures representing blemish instances. Rule based aggregation can be used to construct tree like aggregates by simulating the diffusion of randomly moving particles in a ‘sticky’ environment. Whereas one or more particles are defined as sticky origins. During the diffusion simulation whenever a particle collides with a sticky origin or a stuck particle there is a chance that particle will also stick. If the moving particles are replaced by growth of the aggregation and the sticking probability replaced by a growth probability based on any set of growth rules considering such things as distance from the growth center and position of other particles, interesting blemishes like rust and complex stains can appear (See Image 1).

Image 1. Rule-based aggregation (Rust)
In the late 80’s and beginning 90’s fractal has been ‘the Magic Word’. Fractal methods were used - and sometimes misused - in virtually every scientific paper. Therefore its not a big surprise that Becket and Badler include a fractal based approach for creating textures in their paper.
2D fractal subdivision generate a 2D array of values which, when postprocessed and interpreted appropriately, can achieve blemishes exhibiting fractal boundaries or densities. The fractal dimension of the array can be

Image 2. Fractal (Coffee stain)
Blemish placement

After having discussed some techniques to model blemish instances the second step concentrates on blemish placement.
Here are two examples:

Image 3. Planes in a room increasing from left to right in scratches and from top to bottom in tar splotches.
Continue with Accessibility Shading.