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

Xingze Tian; Tobias Günther

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arXiv · 2408.09211

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

Xingze Tian·Tobias Günther

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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.

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BibTeX RIS

Xingze Tian, Tobias Günther. 2025-04-03. Unified Smooth Vector Graphics: Modeling Gradient Meshes and Curve-based Approaches Jointly as Poisson Problem. https://arxiv.org/abs/2408.09211

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