Sketch-based modeling and adaptive meshes

We present two sketch-based modeling systems built using adaptive meshes and editing operators. The first one has the capability to control local and global changes to the model; the second one follows geological domain constraints. To build a 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. We also take a more 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.