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Design of Tangent Vector Fields

1 Stanford University 2 California Institute of Technology 3 Microsoft Research
ACM Transactions on Graphics (Proc. SIGGRAPH 2007)

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, coordinate-free 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.

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BibTeX citation:
@inproceedings{fisher2007design,
title={Design of tangent vector fields},
author={Fisher, Matthew and Schr{\"o}der, Peter and Desbrun, Mathieu and Hoppe, Hugues},
booktitle={ACM Transactions on Graphics (TOG)},
volume={26},
number={3},
pages={56},
year={2007},
organization={ACM}
}