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Graph."],"published-print":{"date-parts":[[2013,7,21]]},"abstract":"<jats:p>\n            We present a method for constructing smooth\n            <jats:italic>n<\/jats:italic>\n            -direction fields (line fields, cross fields,\n            <jats:italic>etc<\/jats:italic>\n            .) on surfaces that is an order of magnitude faster than state-of-the-art methods, while still producing fields of equal or better quality. Fields produced by the method are globally optimal in the sense that they minimize a simple, well-defined quadratic smoothness energy 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 such as principal curvature directions. Computationally the smoothest field is found via a sparse eigenvalue problem involving a matrix similar to the cotan-Laplacian. 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