Modeling n-Symmetry Vector Fields using Higher-Order Energies
C. Brandt (TU Delft - Computer Graphics and Visualisation)
Leonardo Scandolo (TU Delft - Computer Graphics and Visualisation)
E. Eisemann (TU Delft - Computer Graphics and Visualisation)
K. Hildebrandt (TU Delft - Computer Graphics and Visualisation)
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Abstract
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.