ACM Transactions on Graphics

Modeling n-Symmetry Vector Fields using Higher-Order Energies

Christopher Brandt, Leonardo Scandolo, Elmar Eisemann, and Klaus Hildebrandt

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We introduce a variational approach for modeling n-symmetry vector and direction fields on surfaces that supports interpolation and alignment constraints, placing singularities and local editing, while providing real-time responses. The approach is based on novel biharmonic and m-harmonic energies for n-fields on surface meshes and the integration of hard constraints to the resulting optimization problems. Real-time computation rates are achieved by a model reduction approach employing a Fourier-like n-vector field decomposition, which associates frequencies and modes to n-vector fields on surfaces. To demonstrate the benefits of the proposed n-field modeling approach, we use it for controlling stroke directions in line-art drawings of surfaces and for the modeling of anisotropic BRDFs which define the reflection behavior of surfaces.

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@article{bib:brandt:2018,
    author       = { Brandt, Christopher and Scandolo, Leonardo and Eisemann, Elmar and Hildebrandt, Klaus },    
    title        = { Modeling n-Symmetry Vector Fields using Higher-Order Energies },
    journal      = { ACM Transactions on Graphics },
    volume       = { 37 },
    year         = { 2018 },
    pages        = { 18 },
    doi          = { 10.1145/3177750 },
    dblp         = { journals/tog/BrandtSEH18 },
    url          = { https://publications.graphics.tudelft.nl/papers/201 },
}