On Smooth Frame Field Design

Nicolas Ray (1) , Dmitry Sokolov (1)

1 ALICE - Geometry and Lighting

We analyze actual methods that generate smooth frame fields both in 2D and in 3D. We formalize the 2D problem by representing frames as functions (as it was done in 3D), and show that the derived optimization problem is the one that previous work obtain via " representation vectors ". We show (in 2D) why this non linear optimization problem is easier to solve than directly minimizing the rotation angle of the field, and observe that the 2D algorithm is able to find good fields. Now, the 2D and the 3D optimization problems are derived from the same formulation (based on representing frames by functions). Their energies share some similarities from an optimization point of view (smoothness , local minima, bounds of partial derivatives, etc.), so we applied the 2D resolution mechanism to the 3D problem. Our evaluation of all existing 3D methods suggests to initialize the field by this new algorithm, but possibly use another method for further smoothing.

Mots clés: surface; Categories and Subject Descriptors: I35 [Computational Geometry and Object Modeling]: Curve; solid; and object representations General Terms: Frame field; 3D mesh Additional Key Words and Phrases: smooth frame fields; remeshing ACM Reference Format:

Domaines: Géométrie algorithmique [cs.CG]

Nicolas Ray, Dmitry Sokolov. On Smooth Frame Field Design. 2016. ⟨hal-01245657⟩