An Adaptive Fast-Multipole-Accelerated Hybrid Boundary Integral Equation Method for Accurate Diffusion Curves SIGGRAPH Asia 2023

Seungbae Bang1,2, Kirill Serkh1, Oded Stein3,4, Alec Jacobson1,5

1University of Toronto, 2Amazon, 3USC, 4MIT, 5Adobe Research Toronto


In theory, diffusion curves promise complex color gradations for infinite-resolution vector graphics. In practice, existing realizations suffer from poor scaling, discretization artifacts, or insufficient support for rich boundary conditions. Previous applications of the boundary element method to diffusion curves have relied on polygonal approximations, which either forfeit the high-order smoothness of Bézier curves, or, when the polygonal approximation is extremely detailed, result in large and costly systems of equations that must be solved. In this paper, we utilize the boundary integral equation method to accurately and efficiently solve the underlying partial differential equation. Given a desired resolution and viewport, we then interpolate this solution and use the boundary element method to render it. We couple this hybrid approach with the fast multipole method on a non-uniform quadtree for efficient computation. Furthermore, we introduce an adaptive strategy to enable truly scalable infinite-resolution diffusion curves.


Supplemental Video


This work was supported by the National Research Foundation, Korea (NRF-2020R1A6A3A0303841311), the Swiss National Science Foundation's Early Postdoc.Mobility fellowship, the NSERC Discovery Grants RGPIN-2020-06022 and DGECR-2020-00356, and NSERC Discovery Grant RGPIN-2022-04680, the Ontario Early Research Award program, the Canada Research Chairs Program, a Sloan Research Fellowship, the DSI Catalyst Grant program and gifts by Adobe Inc.

We express deep gratitude to Professor Eitan Grinspun for leading in-depth discussions during the early stages of the research. We thank Silvia Sellán and Otman Benchekoun for their help in conducting experiments and performing proofreading.