13.1.2 The Cellular Approach

As the name suggests the simulation domain is divided into an homogeneous array of cuboid cells. An early implementation of a cellular approach was presented in [28]. For moving the surface two possibilities are known: the cell removal algorithm [28,143,105,68] and the structuring element algorithm [138,136,135,134,137,97,141,98].

The cell removal algorithm simply removes cells near the surface depending on the amount of etching taking place. In addition to performance problems faceting takes place and poses a serious problem. Faceting means that, e.g., an octagon instead of a circle occurs when uniform isotropic etching starting at a single seed point is simulated [57]. It is inherent to the cell removal algorithm and prompted the development of various sophisticated methods.

The structuring element algorithm is a remedy to the faceting problem and works by moving a structuring element along the surface. The shape and size of the structuring element depends on the process modeled and the local etching and deposition rate. This idea stems from digital image processing, where it is well-known [39].

For many applications the final surface has to be represented as a triangular mesh. An algorithm for translating a surface from the cellular format to a triangle mesh is described in [65,79].

The advantages of the cellular approach to surface description are its robustness and ease of implementation. One problem is that the resolution is limited by the size of the surface elements and hence representing slightly tilted surfaces requires high resolutions. Furthermore the precise calculation of surface normals is impossible, although a good solution was achieved in [97].