Globally Optimal Direction Fields

This video is a presentation of the paper, "Globally Optimal Direction Fields" given by Keenan Crane in summer 2013 -- see http://keenan.is/here for more information.

Globally Optimal Direction Fields
Felix Knöppel, Keenan Crane, Ulrich Pinkall, Peter Schröder
SIGGRAPH 2013

Abstract: This paper presents a method for constructing smooth unit n-direction fields (line fields, cross fields, etc.) on surfaces that is an order of magnitude faster than state-of-the-art methods, while still producing fields of equal or better quality. The method is based on a simple quadratic energy whose minimizers are globally optimal in the sense that they produce the smoothest fields over all possible configurations of singularities (number, location, and index). The method is fully automatic and can optionally produce fields aligned with a given guidance field, for example, principal curvature directions. Computationally the smoothest field is found via a sparse eigenvalue problem involving a matrix similar to the cotan-Laplacian. When a guidance field is present, finding the optimal field amounts to solving a single linear Poisson problem.