Abstract
We propose a new iterative algorithm for computing smooth cross fields on triangle meshes that is simple, easily parallelizable on the GPU, and finds solutions with lower energy and fewer cone singularities than state-of-the-art methods. Our approach is based on a formal equivalence, which we prove, between two formulations of the optimization problem. This equivalence allows us to eliminate the real variables and design an efficient grid search algorithm for the cone singularities. We leverage a recent graph-theoretical approximation of the resistance distance matrix of the triangle mesh to speed up the computation and enable a trade-off between the computation time and the smoothness of the output.
Highlights
Directional fields, and especially cross fields, are important objects in geometry processing
We show the connection of the minimized energy to the resistance distance matrix of the triangle mesh, and leverage a recent graph theoretical approximation to speed up the computation and allow us to trade-off the computation time and the quality of the resulting cross field
8 CONCLUSION We showed an equivalence between two existing methods for generating cross fields, which we used to formulate a new iterative algorithm that finds better solutions than state-of-the-art results in terms of the angle-based energy and number of singularities
Summary
Directional fields, and especially cross fields, are important objects in geometry processing. 91:2 Nahum Farchi and Mirela Ben-Chen, Technion Institute of Technology based approach, suggested by Crane et al [2010], encodes the angle difference per edge instead of an angle per face This representation leads to a minimum norm linear least squares optimization problem with constraints, where the integer variables arise as the constrained values. New methods have been proposed [Jakob et al 2015] for efficient cross field computation that are applicable to meshes with millions of triangles Such approaches often work locally, leading to a very efficient solution at the price of cross field quality in terms of the number of singularities and field smoothness. It would be interesting to explore their other suggested edit operations to locally improve the quadrangular mesh structure after generating the global structure using our method
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
