Unified Smooth Vector Graphics: Modeling Gradient Meshes and Curve-based Approaches Jointly as Poisson Problem

TL;DR

This paper introduces a unified mathematical framework for smooth vector graphics that combines gradient meshes and curve-based methods into a single Poisson problem, enabling more flexible and integrated vector graphic representations.

Contribution

It proposes a novel Poisson-based formulation that unifies gradient meshes and curve approaches, allowing combined boundary conditions and improved compatibility with existing tools.

Findings

Successfully unifies gradient meshes and curve-based approaches

Enables new artistic freedoms with boundary condition treatment

Compatible with current vector graphics pipelines

Abstract

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.