Only top parent model vertices (vertices which are not fixed to any other vertex) are discretized. Each vertex is associated with its tree node created during the first phase of the tree building process. If the vertex is fixed to a curve, surface, or region, the terminal cell which contains the vertex is localized in the parametric tree structure built over the parent model entity of the vertex. Each corner node of this cell is then examined and the tree node, which is nearest to the vertex and is also classified to the vertex parent model entity, is merged with the already existing vertex tree node. If the nearest tree node is not classified to the vertex parent model entity the vertex discretization fails.