In this dissertation, I present a modeling framework that provides modeling of 2D smooth meshes in arbitrary topology without any need for subdivision. In the framework, each edge of a quad face is represented by a smooth spline curve, which can be manipulated using edge vertices and additional tangential points. The overall smoothness is achieved by interpolating all four edges of any given quad across the quad surface. The framework consists of simple quad preserving operations that manipulate the principal curves of the smooth model. These operations are all variants of a generic "Curve Split" and its inverse, "Region Collapse". By only using these sets of simple operations, it is possibly to model any desired shape conveniently. I also provide implementation guidelines for these operations. In the results of this dissertation, I present three main applications for this modeling framework. The major application is modeling Mock3D shapes; shapes with well defined interior normals by interpolating the normals at the boundaries of the shape across its surface which can serve as a mock 3D model to mimic a 3D CGI look. As a second application, the framework can be used in origami modeling by allowing assignment of crease patterns across the surface of 2D shapes modelled. Finally, vectorization of reference photos via modeling figures by following their contours is presented as a third application.
