Name
Abstract | ||
|---|---|---|
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. |
Year | DOI | Venue |
|---|---|---|
2013 | 10.1145/2461912.2462005 | ACM Trans. Graph. |
Keywords | Field | DocType |
cross field,optimal direction field,optimal field amount,line field,possible configuration,smooth n-direction field,guidance field,principal curvature direction,smoothest field,better quality,state-of-the-art method,singularities,discrete differential geometry | Discrete differential geometry,Mathematical optimization,Linear system,Matrix (mathematics),Quadratic equation,Principal curvature,Gravitational singularity,Smoothness,Mathematics,Eigenvalues and eigenvectors | Journal |
Volume | Issue | ISSN |
32 | 4 | 0730-0301 |
Citations | PageRank | References |
51 | 1.48 | 18 |
Authors | ||
4 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Felix Knöppel | 1 | 73 | 4.30 |
| Keenan Crane | 2 | 586 | 29.28 |
| Ulrich Pinkall | 3 | 497 | 39.52 |
| Peter Schröder | 4 | 5825 | 467.77 |