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View all- Chen JSchaefer FDesbrun M(2024)Lightning-fast Method of Fundamental SolutionsACM Transactions on Graphics10.1145/365819943:4(1-16)Online publication date: 19-Jul-2024
An Adaptive Fast-Multipole-Accelerated Hybrid Boundary Integral Equation Method for Accurate Diffusion Curves
Article No.: 215, Pages 1 - 28
Abstract
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.
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Index Terms
- An Adaptive Fast-Multipole-Accelerated Hybrid Boundary Integral Equation Method for Accurate Diffusion Curves
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Publication History
Published: 05 December 2023
Published in TOG Volume 42, Issue 6
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- Swiss National Science Foundation's Early Postdoc.Mobility fellowship
- NSERC Discovery Grants
- National Research Foundation, Korea
- Canada Research Chairs Program
- Sloan Research Fellowship
- Ontario Early Research Award program
- NSERC Discovery Grant
- DSI Catalyst Grant program
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View all- Chen JSchaefer FDesbrun M(2024)Lightning-fast Method of Fundamental SolutionsACM Transactions on Graphics10.1145/365819943:4(1-16)Online publication date: 19-Jul-2024
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