We propose a fast, robust, and user-controllable algorithm for knot untan-gling and volume-filling curves. We extend prior work on surface-filling curves to the more challenging case of 3D volumes, equipped with a specialized gradient preconditioner that allows larger step sizes. Our method exhibits orders of magnitude faster runtime than existing methods. Our framework provides a whole new set of parameters to guide the shape of the curve, making it ideal for interactive design applications.
@article{noma2025medialsphere,
title = {Medial Sphere Preconditioning for Knot Untangling and Volume-Filling Curves},
author = {Yuta Noma and Alec Jacobson and Karan Singh},
year = {2025},
journal = {SIGGRAPH Asia Conference Papers},
}
We thank Thea Yu for early discussions, Abhishek Madan and Karran Pandey for proofreading, Esther Lin for video narration, and John Hancock and Xuan Dam for supporting our research in the lab. Our research is funded in part by NSERC Discovery (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.