Chaos and GraphicsConstrained diffusion-limited aggregation in 3 dimensions
Section snippets
DLA in 3 dimensions
The rules for forming diffusion-limited aggregation (DLA) structures are very simple and were first introduced in 2 dimensions by T.A. Witten and L.M. Sander around 1981 [1]. A particle is introduced into an environment at a random position, it moves around randomly (for example: Brownian motion) until it encounters the existing structure (initially just a single stationary particle) at which stage it permanently adheres at the point of contact and becomes part of the DLA structure. As an
Constraint surfaces
In order to support very general constraint surfaces, a simple but industry standard file format was chosen to describe the geometry, namely the STL format. The STL format was developed for stereolithography, it is in common usage by the rapid prototyping industry and as such it is supported as an export format by many 3D modeling packages. The STL format describes a surface as a collection of triangles in 3 dimensions along with a normal that determines which side of the triangle is “inside”
Results
Fig. 4 shows a very simple constraint surface made up of a cylinder with an open top. The particles are added randomly on a sphere about the center of the cylinder. In the implementation discussed here no consideration is given to the cylinder until the stage at which the particle is close enough to the existing structure to adhere. This is an important implementation detail from a performance perspective. Since most of the time is spent in the random walk phase and the constraint surface may
Conclusion
The techniques described here provide the basis for an efficient DLA growth simulation which can be constrained by a surface described with a simple and well documented 3D file format that is supported by many 3D modeling packages. The DLA structures formed using the algorithm described here look like natural branching structures and could thus be used to form models for a number of computer graphics applications. In addition the structures are grown in time and therefore can be used to create
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