# Physical Reproduction of Materials with Specified Reflectance and Scattering

# Physical Reproduction of Materials with Specified Reflectance and Scattering

Although real-world surfaces can exhibit significant variation in materials - glossy, diffuse, metallic, translucent, etc. - printers are usually used to reproduce color or gray-scale images. I will describe two projects that expand the range of surfaces that can be physically reproduced. First, I describe a complete system that uses appropriate inks and foils to print documents with a variety of material properties. Given a set of inks with known Bidirectional Reflectance Distribution Functions (BRDFs), our system automatically finds the optimal linear combinations to approximate the BRDFs of the target documents. Novel gamut-mapping algorithms preserve the relative glossiness between different BRDFs, and halftoning is used to produce patterns to be sent to the printer. We demonstrate the effectiveness of this approach with printed samples of a number of measured spatially-varying BRDFs. Next, I describe a complete pipeline for measuring, modeling, and fabricating objects with specified subsurface scattering behaviors. The process starts with measuring the scattering properties of a given set of base materials, determining their radial reflection and transmission profiles. A mathematical model combining Kubelka-Munk theory and the Hankel transform predicts the profiles of different stackings of base materials, at arbitrary thicknesses. In an inverse process, we can then specify a desired reflection profile and compute a layered composite material that best approximates it. Our algorithm efficiently searches the space of possible combinations of base materials, pruning unsatisfactory states imposed by physical constraints. We validate our process by producing both homogeneous and heterogeneous composites fabricated using a multi-material 3D printer. We demonstrate reproductions that have scattering properties approximating complex materials.