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.
The authors thank the anonymous reviewers for their helpful comments and suggestions. Some of the models shown in the paper were provided by AIM@SHAPE and the Stanford Computer Graphics Laboratory. This work was supported in part by the ERC grant iModel (StG-2012-306877).