4.2 Erosion model based on rewriting of matrices

Mar'ak et. al  [7] presented new method for synthetical terrain erosion, that is based on rewriting process of matrices representing terrain patches. Rewriting process is context sensitive and is defined as a set of productions A tex2html_wrap_inline783 B

where A,B are matrices of real number of type tex2html_wrap_inline785 . The patches are rewritten according to certain user-defined set of rules representing an erosion process. This method uses three kind of rewriting. The absolute rewriting allows to erode objects in predefined altitude. Rewriting with the reference point can erode arbitrary object in any altitude. The last method erodes some shapes in any scale. An example of simulation of thermal erosion using this algorithm can be seen in Figure 10.

Figure: Terrain erosion using rewriting of matrices. a) represents an uneroded terrain. On b) c) d) there are the same terrains after 200, 400 and 600 iterations.

The advantage of this method is that the algorithm can be controlled by some external rules and it can simulate thus wide classes of erosion.

Ivo Marak - marak@sgi.felk.cvut.cz