Synchronizing fields with singularities

conference paper Synchronizing fields with singularities accepted yes Natalia Pacheco-Tallaj author Matteo Couplet author Edward Chien author David Palmer author 6574708f-2fd3-11f0-89e2-ae42ebc712a40000-0002-1931-5673 ChWo department SIGGRAPH: International Conference and Exhibition on Computer Graphics and Interactive Techniques A variety of problems in geometry processing boil down to finding the most parallel field relative to a connection. Instances of this prototypical problem show up in computing direction fields and stripe patterns, quadrilateral meshing, and visualization of fluid flows. When the class of allowed fields includes those with topological defects, a relaxation is required to make the problem well-posed. We observe that these problems can be viewed as synchronization problems, which admit a natural semidefinite relaxation. We propose a unified method of solving all these problems via the efficient Burer-Monteiro factorization method. Geometrically, this amounts to lifting the field values to a higher-dimensional manifold, naturally resolving the singular nature of defects. Practically, we show that our convex relaxation method achieves better and more reliable optima than previous work employing alternative relaxations https://research-explorer.ista.ac.at/download/21921/21922/main.pdf application/pdfno ACM2026Los Angeles, CA, United States eng SIGGRAPH Conference Papers10.1145/3799902.3811225 Pacheco-Tallaj, Natalia, et al. “Synchronizing Fields with Singularities.” SIGGRAPH Conference Papers, ACM, doi:<a href="https://doi.org/10.1145/3799902.3811225">10.1145/3799902.3811225</a>. Pacheco-Tallaj, Natalia, Matteo Couplet, Edward Chien, and David Palmer. “Synchronizing Fields with Singularities.” In SIGGRAPH Conference Papers. ACM, n.d. <a href="https://doi.org/10.1145/3799902.3811225">https://doi.org/10.1145/3799902.3811225</a>. N. Pacheco-Tallaj, M. Couplet, E. Chien, D. Palmer, in:, SIGGRAPH Conference Papers, ACM, n.d. Pacheco-Tallaj, N., Couplet, M., Chien, E., & Palmer, D. (n.d.). Synchronizing fields with singularities. In SIGGRAPH Conference Papers. Los Angeles, CA, United States: ACM. <a href="https://doi.org/10.1145/3799902.3811225">https://doi.org/10.1145/3799902.3811225</a> N. Pacheco-Tallaj, M. Couplet, E. Chien, and D. Palmer, “Synchronizing fields with singularities,” in SIGGRAPH Conference Papers, Los Angeles, CA, United States. Pacheco-Tallaj N, Couplet M, Chien E, Palmer D. Synchronizing fields with singularities. In: SIGGRAPH Conference Papers. ACM. doi:<a href="https://doi.org/10.1145/3799902.3811225">10.1145/3799902.3811225</a> Pacheco-Tallaj N, Couplet M, Chien E, Palmer D. Synchronizing fields with singularities. SIGGRAPH Conference Papers. SIGGRAPH: International Conference and Exhibition on Computer Graphics and Interactive Techniques. 219212026-05-29T12:53:59Z2026-06-02T06:26:52Z