@inproceedings{21921,
  abstract     = {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},
  author       = {Pacheco-Tallaj, Natalia and Couplet, Matteo and Chien, Edward and Palmer, David},
  booktitle    = {SIGGRAPH Conference Papers},
  location     = {Los Angeles, CA, United States},
  publisher    = {ACM},
  title        = {{Synchronizing fields with singularities}},
  doi          = {10.1145/3799902.3811225},
  year         = {2026},
}