Appearance-mimicking surfaces

We consider the problem of reproducing the look and the details of a 3D object on a surface that is confined to a given volume. Classic examples of such "appearance-mimicking" surfaces are bas-reliefs: decorations and artwork depicting recognizable 3D scenes using only a thin volumetric space. The design of bas-reliefs has fascinated humankind for millennia and it is extensively used on coins, medals, pottery and other art forms. We propose a unified framework to create surfaces that depict certain shapes from prescribed viewpoints, as a generalization of bas-reliefs. Given target shapes, viewpoints and space restrictions, our method finds a globally optimal surface that delivers the desired appearance when observed from the designated viewpoints, while guaranteeing exact, per-vertex depth bounds. We use 3D printing to validate our approach and demonstrate our results in a variety of applications, ranging from standard bas-reliefs to optical illusions and carving of complex geometries.