Volumetric texture synthesis using fundamental solution methods

We present a volumetric texture synthesis technology that interpolates the interior solid texture from the boundary surface texture mapping. The interpolation is based on the (poly-)cube mapping and fundamental solution method. The (poly-)cube texture map indicates the boundary constraint for the fundamental solution, which then computes two harmonic scalar fields coherent to this boundary configuration. Given a solid geometric object with a closed genus-0 boundary surface, we first map the boundary surface onto a (poly-)cube; then compute the mapping from the (poly-)cube to the 2-dimensional texture coordinates space; finally use this as the boundary condition to compute harmonic volumetric fields for interpolating the interior solid texture. We demonstrate the effectiveness of this algorithm in isotropic 3D texture synthesis.