Editing curves and surfaces is difficult in part because their mathematical representations rarely correspond to most people’s idea of a curve or surface. The implementation (and hence, behavior) of most manipulation tools is intertwined with a particular curve or surface representation; this can make reimplementing the tool with a different representation problematic. A system using a single r...

Each orientable surface with nonempty boundary can be associated with a planar model, whose edges can then be labeled with letters that read out a surface word. Then, the curve word of a free homotopy class of closed curves on a surface is the minimal sequence of edges of the planar model through which a curve in the class passes. The length of a class of curves is defined to be the number of l...

We compare Stein fillings and Milnor fibers for rational surface singularities with reduced fundamental cycle. Deformation theory this class of was studied by de Jong-van Straten in [dJvS98]; they associated a germ singular plane curve to each singularity described via deformations curve. consider links singularities, equipped their canonical contact structures, develop symplectic analog Strate...