The subject of the article concerns the issues of remeshing, transforming a polygonal mesh into a triangular mesh adapted to surface. From the initial polygonal mesh the curvature of surface and boundary is retrieved and used to calculate a metric tensor varying in three-dimensional space. In the proposed approach the curvature is computed using local approximation of surfaces and curves on the basis of vertices of the polygonal mesh. An essential part of the presented remeshing procedure is creation of a control space structure based on the retrieved discrete data. The subsequent process of remeshing is then supervised by the contents of this auxiliary structure. The article presents various aspects related to the procedure of initialization, creation and adjusting the control space structure.