Irregular pit placement for dithering images by self-occlusion

We propose a complete system for designing, simulating, and fabricating surfaces with shading due to self-occlusion that induce desired input images. Our work is based on a simple observation. Consider a cylindrical hole (a pit) in a planar surface. As the depth of the hole increases, the radiance emitted from the surface patch that contains the hole decreases. This is because more light is trapped and absorbed in the hole. First, we propose a measurement-based approach that derives a mapping between average albedo of the surface patch containing the hole and the hole depth. Given this mapping and an input image, we show how to produce a distribution of holes with varied depth that approximates the image well. We demonstrate that by aligning holes with image features, while still maintaining an irregular distribution, we can obtain reproductions that look better than those resulting from regular hole patterns—despite using less holes. We validate this method on a variety of images and corresponding surfaces fabricated with a computer-controlled milling machine and a 3D printer. & 2012 Elsevier Ltd. All rights reserved.