Bi-scale appearance fabrication

Surfaces in the real world exhibit complex appearance due to spatial variations in both their reflectance and local shading frames (i.e. the local coordinate system defined by the normal and tangent direction). For opaque surfaces, existing fabrication solutions can reproduce well only the spatial variations of isotropic reflectance. In this paper, we present a system for fabricating surfaces with desired spatially-varying reflectance, including anisotropic ones, and local shading frames. We approximate each input reflectance, rotated by its local frame, as a small patch of oriented facets coated with isotropic glossy inks. By assigning different ink combinations to facets with different orientations, this bi-scale material can reproduce a wider variety of reflectance than the printer gamut, including anisotropic materials. By orienting the facets appropriately, we control the local shading frame. We propose an algorithm to automatically determine the optimal facets orientations and ink combinations that best approximate a given input appearance, while obeying manufacturing constraints on both geometry and ink gamut. We fabricate the resulting surface with commercially available hardware, a 3D printer to fabricate the facets and a flatbed UV printer to coat them with inks. We validate our method by fabricating a variety of isotropic and anisotropic materials with rich variations in normals and tangents.