Abstract: We present a theoretical approach to the problem of sketch-based surface modeling (SBSM) and introduce a framework for SBSM systems based on adaptive meshes. The main advantage of this approach is a clear separation between the modeling operators and the final representation, thus enabling the creation of SBSM systems suited to specific domains with different demands. To support the proposed approach we present two different sketch-based modeling systems built using this framework. The first one has the capability to control local and global changes to the model; the second one follows geological data constraints. To build the first system that provides the user with control of local modifications we developed a mathematical theory of vertex label and atlas structure for adaptive meshes based on stellar operators.