Modeling n -Symmetry Vector Fields using Higher-Order Energies

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.