Modeling n-Symmetry Vector Fields using Higher-Order Energies

ACM Transactions on Graphics, Volume 37, Number 2, page 18:1--18:18 - 2018
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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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BibTex references

@Article { BSEH18,
  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",
  number       = "2",
  volume       = "37",
  pages        = "18:1--18:18",
  year         = "2018",
  url          = ""

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» Christopher Brandt
» Leonardo Scandolo
» Elmar Eisemann
» Klaus Hildebrandt