## Design of tangent vector fields (2007)

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- [www.geometry.caltech.edu]
- [geometry.caltech.edu]
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### Other Repositories/Bibliography

Venue: | ACM Trans. Graph |

Citations: | 41 - 4 self |

### BibTeX

@ARTICLE{Fisher07designof,

author = {Matthew Fisher and Peter Schröder},

title = {Design of tangent vector fields},

journal = {ACM Trans. Graph},

year = {2007},

volume = {26},

pages = {56}

}

### OpenURL

### Abstract

Tangent vector fields are an essential ingredient in controlling surface appearance for applications ranging from anisotropic shading to texture synthesis and non-photorealistic rendering. To achieve a desired effect one is typically interested in smoothly varying fields that satisfy a sparse set of user-provided constraints. Using tools from Discrete Exterior Calculus, we present a simple and efficient algorithm for designing such fields over arbitrary triangle meshes. By representing the field as scalars over mesh edges (i.e., discrete 1-forms), we obtain an intrinsic, coordinatefree formulation in which field smoothness is enforced through discrete Laplace operators. Unlike previous methods, such a formulation leads to a linear system whose sparsity permits efficient pre-factorization. Constraints are incorporated through weighted least squares and can be updated rapidly enough to enable interactive design, as we demonstrate in the context of anisotropic texture synthesis.