Computer Vision, Graphics, and Image Processing
Proceedings of the 27th annual conference on Computer graphics and interactive techniques
Least squares conformal maps for automatic texture atlas generation
Proceedings of the 29th annual conference on Computer graphics and interactive techniques
Restricted delaunay triangulations and normal cycle
Proceedings of the nineteenth annual symposium on Computational geometry
Global conformal surface parameterization
Proceedings of the 2003 Eurographics/ACM SIGGRAPH symposium on Geometry processing
Appearance-space texture synthesis
ACM SIGGRAPH 2006 Papers
Vector field design on surfaces
ACM Transactions on Graphics (TOG)
Periodic global parameterization
ACM Transactions on Graphics (TOG)
Rotational symmetry field design on surfaces
ACM SIGGRAPH 2007 papers
Design of tangent vector fields
ACM SIGGRAPH 2007 papers
Numerical Methods for Special Functions
Numerical Methods for Special Functions
N-symmetry direction field design
ACM Transactions on Graphics (TOG)
Algorithm 887: CHOLMOD, Supernodal Sparse Cholesky Factorization and Update/Downdate
ACM Transactions on Mathematical Software (TOMS)
ACM SIGGRAPH 2009 papers
Geometry-aware direction field processing
ACM Transactions on Graphics (TOG)
Spectral conformal parameterization
SGP '08 Proceedings of the Symposium on Geometry Processing
Biquadratic Optimization Over Unit Spheres and Semidefinite Programming Relaxations
SIAM Journal on Optimization
Practical mixed-integer optimization for geometry processing
Proceedings of the 7th international conference on Curves and Surfaces
Hexagonal Global Parameterization of Arbitrary Surfaces
IEEE Transactions on Visualization and Computer Graphics
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We present a method for constructing smooth 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. 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. When a guidance field is present, finding the optimal field amounts to solving a single linear system.