Spec2Fab: A reducer-tuner model for translating specifications to 3D prints The MIT Faculty has made this article openly available. Please share how this access benefits you. Your story matters. Citation Desai Chen, David I. W. Levin, Piotr Didyk, Pitchaya Sitthi-Amorn, and Wojciech Matusik. 2013. Spec2Fab: a reducer-tuner model for translating specifications to 3D prints. ACM Trans. Graph. 32, 4, Article 135 (July 2013), 10 pages. As Published http://dx.doi.org/10.1145/2461912.2461994 Publisher Association for Computing Machinery (ACM) Version Author's final manuscript Citable link http://hdl.handle.net/1721.1/90395 Terms of Use Creative Commons Attribution-Noncommercial-Share Alike Detailed Terms http://creativecommons.org/licenses/by-nc-sa/4.0/ Spec2Fab: A Reducer-Tuner Model for Translating Specifications to 3D Prints Desai Chen David I.W. Levin Piotr Didyk Pitchaya Sitthi-Amorn Wojciech Matusik MIT CSAIL Deformation + texture Caustic + Texture Goal specication Goal specication Figure 1: 3D-printed objects with various effects designed using our reducer-tuner model. Our generalized approach to fabrication enables an easy and intuitive design of objects with different material properties. On the left: a miniature of Earth with a prescribed deformation behavior. On the right: an optimized surface producing a caustic image under proper illumination as well as casting a shadow of a previously designed shape. Insets visualize an input to our system. Abstract 1 Introduction 3D printing receives a lot of attention as it aims to democratize fab- Multi-material 3D printing allows objects to be composed of com- rication. The ever expanding range of printing materials allows for plex, heterogeneous arrangements of materials. It is often more nat- fabrication of complex objects with spatially varying appearance, ural to define a functional goal than to define the material composi- optical characteristics, and mechanical properties. One of the most tion of an object. Translating these functional requirements to fabri- important unsolved problems in this area is how to compute an ob- cable 3D prints is still an open research problem. Recently, several ject’s material composition from a functional or behavioral descrip- specific instances of this problem have been explored (e.g., appear- tion. We call this process specification to fabrication translation ance or elastic deformation), but they exist as isolated, monolithic (Spec2Fab). The goal of this work is to provide a convenient ab- algorithms. In this paper, we propose an abstraction mechanism straction for specifying such translators. This is necessary to move that simplifies the design, development, implementation, and reuse past the current direct specification model of 3D printing. of these algorithms. Our solution relies on two new data structures: a reducer tree that efficiently parameterizes the space of material Today, 3D printing of an object requires a material be directly spec- assignments and a tuner network that describes the optimization ified for each voxel inside the object volume. This approach is process used to compute material arrangement. We provide an ap- fraught with difficulties. First, 3D printable models become spe- plication programming interface for specifying the desired object cific to a single printer type, i.e., the models are built from materials and for defining parameters for the reducer tree and tuner network. provided by a given printer. Consider the inconvenience that would We illustrate the utility of our framework by implementing several result from word processing documents being compatible with spe- fabrication algorithms as well as demonstrating the manufactured cific 2D printers. Second, working directly with printing materials results. rather than material properties is extremely challenging for users. Imagine the difficulty in finding the right combination of printing materials that would provide a specific color, stiffness, or refractive CR Categories: I.3.8 [Computer Graphics]: Applications; index. Our work is motivated by the recent research efforts in the com- Keywords: 3D printing, goal-based material design, fabrication puter graphics community to create specific instances of the transla- Links: DL PDF WEB DATA CODE tion process, for example, subsurface scattering [Hasanˇ et al. 2010; Dong et al. 2010] or deformation properties [Bickel et al. 2010]. However, each of these instances is a custom, monolithic solution which is difficult to extend, combine, or modify. Our main insight is that all these process instances share a similar structure. First, they rely on the ability to accurately simulate the physical proper- ties of an object given its geometry and material assignment. They use this simulation within an optimization framework to search the space of all possible material assignments in order to find the one that best reproduces the desired properties. Due to the combinato- rial nature of the search space the naive optimization approach is not tractable. For example, when the printing volume has N voxels and each of these voxels can be assigned to one of M base materials, the search space has N M dimensions. To overcome this problem, the search space is reduced to a lower-dimensional space using a reduction model. The goal of the reduction step is to aggressively compute surface micro-geometry that yields a desired BRDF. Simi- shrink the search space in a domain-specific manner such that it still lar approaches have been proposed [Finckh et al. 2010; Papas et al. contains good approximations to the optimal solution. This search 2011] to produce refractive surfaces that form user-defined caus- space reduction combined with the right choice of the optimization tics. These methods have been extended to optically decrypt hidden algorithm delivers a computationally tractable approximation. images [Papas et al. 2012]. Complementary work examines fab- ricating surfaces with spatially varying reflectance [Matusik et al. The reduction-optimization structure suggests that it is possible to 2009; Malzbender et al. 2012] and diffuse shading [Alexa and Ma- provide a more general abstraction mechanism for translating 3D tusik 2010]. Another set of approaches uses optimization to com- models to printer and material-specific representations. In this pa- pute shadow casting surfaces and volumes [Mitra and Pauly 2009; per we take the first step in achieving this goal. Our solution re- Bermano et al. 2012; Baran et al. 2012] that reproduce a given set lies on two novel data structures which are designed to aid the fab- of input images. Finally, optimization-based approaches have also rication process. The reducer tree is a tree-based data structure been employed to control the subsurface scattering of 3D printed that allows us to parameterize the space of material assignments. multi-layered models [Dong et al. 2010; Hasanˇ et al. 2010]. We The tuner network is a data structure for specifying the optimiza- seek to exploit the common form of the above works in order to tion process. Our solution also provides an API for specifying the generalize them. desired object, setting up the simulation, and defining parameters for the reducer tree and tuner network. In general, our framework There have been studies of material assignment representations in simplifies the construction of new computational fabrication algo- other fields, primarily in mechanical engineering. Here we only list rithms. More specifically, different components of the process can a few representative works. Kumar et al. [1999] describe material be easily replaced and other components easily reused. Various composition by dividing a volume into sub-volumes. They perform optimization strategies can also be explored with lower implemen- material interpolation using local, sub-volume coordinate systems. tation burden. In order to show these advantages, we illustrate how Jackson [2000] explores several mesh data structures for spatial existing computational design processes fit into this framework and sub-division. Kou and Tan [2007] give a comprehensive review of how they can be combined. We demonstrate the results of these spatial partition schemes and material interpolation functions. Kou algorithms on a variety of different examples fabricated using 3D et al. [2012] use a hierarchy of procedures to define material com- printers. position with a small number of design parameters. They run par- ticle swarm optimization [Kennedy and Eberhart 1995] on the de- sign parameters to minimize thermal stress of an object. Their work 2 Related Work focused on smoothly varying materials. There is no discussion of high-frequency discrete material assignment for capturing details. Our new data structures draw ideas from previous work in ren- They are limited to global optimization algorithms such as Particle dering and optimization. The reducer tree is inspired by Cook’s Swarm Optimization because the dependency structure between the shade trees [Cook 1984] and their modern implementation in cur- design variables is not modeled. In computer graphics, procedural rent rendering systems (e.g., Maya, RenderMan, etc.). Using these descriptions for material assignment have also been studied. Cut- approaches, complex effects can be achieved by combining a set of ler et al. [2002] describe a scripting language for specifying lay- basic shading blocks. The reducer tree also uses a tree data struc- ered solid models and describing material composition. Vidimceˇ ture that combines a set of primitives to compute a material as- et