Research on smooth vector graphics is separated into two independent research threads: one on interpolation-based gradient meshes and the other on diffusion-based curve formulations. With this paper, we propose a mathematical formulation that unifies gradient meshes and curve-based approaches as solution to a Poisson problem. To combine these two well-known representations, we first generate a non-overlapping intermediate patch representation that specifies for each patch a target Laplacian and boundary conditions. Unifying the treatment of boundary conditions adds further artistic degrees of freedoms to the existing formulations, such as Neumann conditions on diffusion curves. To synthesize a raster image for a given output resolution, we then rasterize boundary conditions and Laplacians for the respective patches and compute the final image as solution to a Poisson problem. We evaluate the method on various test scenes containing gradient meshes and curve-based primitives. Since our mathematical formulation works with established smooth vector graphics primitives on the front-end, it is compatible with existing content creation pipelines and with established editing tools. Rather than continuing two separate research paths, we hope that a unification of the formulations will lead to new rasterization and vectorization tools in the future that utilize the strengths of both approaches.

The field of smooth vector graphics explores the representation, creation, rasterization, and automatic generation of light-weight image representations, frequently used for scalable image content. Over the past decades, several conceptual approaches on the representation of images with smooth gradients have emerged that each led to separate research threads, including the popular gradient meshes and diffusion curves. As the computational models matured, the mathematical descriptions diverged and article started to focus more narrowly on subproblems, such as on the representation and creation of vector graphics, or the automatic vectorization from raster images. Most of the work concentrated on a specific mathematical model only. With this survey, we describe the established computational models in a consistent notation to spur further knowledge transfer, leveraging the recent advances in each field. We therefore categorize vector graphics article from the last decades based on their underlying mathematical representations as well as on their contribution to the vector graphics content creation pipeline, comprising representation, creation, rasterization, and automatic image vectorization. This survey is meant as an entry point for both artists and researchers. We conclude this survey with an outlook on promising research directions and challenges to overcome in the future.