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After inserting nodes in several loops the following final tasks are performed:

• project the external nodes on the external edges and/or faces. If an edge i on which the node lies is part of an external edge of the unrefined mesh (i.e. iexternedg(i)>0) then a projection is performed on this external edge. If not, the node is projected on an external face. To this end the faces to which the node belongs are determined. For each of these faces j a check is performed whether the face is external (i.e. iexternfa(j)>0). If so, a projection is performed on the correct external face of the unrefined mesh. To this end a loop is performed starting with face iexternfa(j) using the adjacency relationships stored in fields ifacexted and iedgeextfa, until the correct face is found (i.e. the condition that the projection lies inside the face). While applying the adjacency relations field isharp is used to assure that sharp edges are not crossed.
• generate, if requested, middle nodes and project the external midnodes on the external edges and/or faces. This is done in a similar way as for the vertex nodes.