In recent years, with the development of mobile phones, tablets, and web technologies, we have seen an ever-increasing need to generate vector graphics content, that is, resolution-independent images that support sharp rendering across all devices, as well as interactivity and animation. However, the tools and standards currently available to artists for authoring and distributing such vector graphics content have many limitations. Importantly, basic topological modeling, such Preface We have not yet submitted Chapter 3 for publication. This chapter builds on the ideas developed in [Dalstein et al. 2014a], providing important improvements and clari cations. I conducted most of the theoretical analysis and derivations, and wrote the manuscript. Michiel van de Panne provided guidance. v