Implementation Aspects

The spatial localization for the intersection check and the front management, in terms of the edge selection and searching, are considered to be general bottlenecks of the advancing front procedure. Both aspects are addressed in the presented approach. The spatial localization is implemented using the octree data structure. This exhibits the computational complexity which becomes nearly constant for a reasonable octree depth. When searching for the most suitable candidate in the neighbourhood, the local Delaunay property is used as a criterion. This reduces the probability of the consequent occurrence of an intersection. Since gradual variation of the element size is ensured, no special algorithm for the edge selection strategy is required. Therefore, the simplest approach has been chosen which always uses the first available edge in the front. This obviously leads to the constant computational complexity of the front management.

A crucial aspect of the proposed mesh generation strategy is related to the point-to-surface projection. The simple and efficient algorithms available for projection to parametric surfaces cannot be adopted simply because of missing parameterization of the limit surface. Moreover, the situation is further complicated by the fact, that the normal to the limit surface can be evaluated only at the nodes of the original or refined control grid. Therefore in order to make the projection sufficiently accurate (in terms of the distance from the limit surface and match with the exact normal), it is necessary to subdivide the control grid up to a high level. This results in a huge amount of data to be stored, which is not acceptable.

*Daniel Rypl
2005-12-03*