Before revision: Cross fields are auxiliary in the generation of quadrangular meshes. A method to generate cross fields on surface manifolds is presented in this paper . Algebraic topology constraints on quadrangular meshes are first discussed.
After revision: This paper proposes a method to compute crossfields based on the Ginzburg-Landau theory. The Ginzburg-Landau functional has two terms: the Dirichlet energy of the distribution and a term penalizing the mismatch between the fixed and actual norm of the distribution. Directional fields on surfaces are known to have a number of critical points, which are properly identified with the Ginzburg-Landau approach: the asymptotic behavior of Ginzburg-Landau problem provides well-distributed critical points over the 2-manifold, whose indices are as low as possible. The central idea in this paper . Algebraic topology constraints on quadrangular meshes are first discussed.