Tian X, Günther T (2025)
Publication Type: Journal article
Publication year: 2025
DOI: 10.1109/TVCG.2025.3558263
Research on smooth vector graphics is separated into two independent research threads: one on interpolationbased 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.
APA:
Tian, X., & Günther, T. (2025). Unified Smooth Vector Graphics: Modeling Gradient Meshes and Curve-based Approaches Jointly as Poisson Problem. IEEE Transactions on Visualization and Computer Graphics. https://doi.org/10.1109/TVCG.2025.3558263
MLA:
Tian, Xingze, and Tobias Günther. "Unified Smooth Vector Graphics: Modeling Gradient Meshes and Curve-based Approaches Jointly as Poisson Problem." IEEE Transactions on Visualization and Computer Graphics (2025).
BibTeX: Download