Constructing Printable Surfaces with View-Dependent Appearance

We present a method for the digital fabrication of surfaces whose appearance varies based on viewing direction. The surfaces are constructed from a mesh of bars arranged in a self-occluding colored heightfield that creates the desired view-dependent effects. At the heart of our method is a novel and simple differentiable rendering algorithm specifically designed to render colored 3D heightfields and enable efficient calculation of the gradient of appearance with respect to heights and colors. This algorithm forms the basis of a coarse-to-fine ML-based optimization process that adjusts the heights and colors of the strips to minimize the loss between the desired and real surface appearance from each viewpoint, deriving meshes that can then be fabricated using a 3D printer. Using our method, we demonstrate both synthetic and real-world fabricated results with view-dependent appearance.