Surface-Filling Curve Flows via Implicit Medial Axes SIGGRAPH North America 2024

Yuta Noma¹², Silvia Sellán¹, Nicholas Sharp³, Karan Singh¹, Alec Jacobson¹⁴

¹University of Toronto, ²The University of Tokyo, ³NVIDIA, ⁴Adobe Research


We introduce a fast, robust, and user-controllable algorithm to generate surface-filling curves. We compute these curves through the gradient flow of a simple sparse energy, making our method several orders of magnitude faster than previous works. Our algorithm makes minimal assumptions on the topology and resolution of the input surface, achieving improved robustness. Our framework provides tuneable parameters that guide the shape of the output curve, making it ideal for interactive design applications.



  title = {Surface-Filling Curve Flows via Implicit Medial Axes},
  author = {Yuta Noma and Silvia Sellán and Nicholas Sharp and Karan Singh and Alec Jacobson},
  year = {2024},
  journal = {ACM Transactions on Graphics}, 


We thank Chris Yu for early discussions, Abhishek Madan, Chenxi Liu, Kinjal Parikh, Victor Rong, and Zhecheng Wang for help in proofreading and rendering figures, and Esther Lin for video narration. This work was supported in part by JST ACT-X (JPMJAX200L), JSPS KAKENHI (JP23KJ0582), NSERC Discovery (RGPIN–2022–04680), the Ontario Early Research Award program, the Canada Research Chairs Program, a Sloan Research Fellowship, an NSERC Vanier graduate scholarship, an Adobe Research fellowship, the DSI Catalyst Grant program, and gifts by Adobe Inc.