State of the Art on Stylized Fabrication

© 2018 The Authors Computer Graphics Forum © 2018 The Eurographics Association and John Wiley & Sons Ltd. Digital fabrication devices are powerful tools for creating tangible reproductions of 3D digital models. Most available printing technologies aim at producing an accurate copy of a tridimensional shape. However, fabrication technologies can also be used to create a stylistic representation of a digital shape. We refer to this class of methods as ‘stylized fabrication methods’. These methods abstract geometric and physical features of a given shape to create an unconventional representation, to produce an optical illusion or to devise a particular interaction with the fabricated model. In this state-of-the-art report, we classify and overview this broad and emerging class of approaches and also propose possible directions for future research

Beyond developable: computational design and fabrication with auxetic materials

We present a computational method for interactive 3D design and rationalization of surfaces via auxetic materials, i.e., flat flexible material that can stretch uniformly up to a certain extent. A key motivation for studying such material is that one can approximate doubly-curved surfaces (such as the sphere) using only flat pieces, making it attractive for fabrication. We physically realize surfaces by introducing cuts into approximately inextensible material such as sheet metal, plastic, or leather. The cutting pattern is modeled as a regular triangular linkage that yields hexagonal openings of spatially-varying radius when stretched. In the same way that isometry is fundamental to modeling developable surfaces, we leverage conformal geometry to understand auxetic design. In particular, we compute a global conformal map with bounded scale factor to initialize an otherwise intractable non-linear optimization. We demonstrate that this global approach can handle non-trivial topology and non-local dependencies inherent in auxetic material. Design studies and physical prototypes are used to illustrate a wide range of possible applications

State of the art on stylized fabrication

© 2019 Copyright held by the owner/author(s). Digital fabrication devices are powerful tools for creating tangible reproductions of 3D digital models. Most available printing technologies aim at producing an accurate copy of a tridimensional shape. However, fabrication technologies can also be used to create a stylistic representation of a digital shape. We refer to this class of methods as stylized fabrication methods. These methods abstract geometric and physical features of a given shape to create an unconventional representation, to produce an optical illusion, or to devise a particular interaction with the fabricated model. In this course, we classify and overview this broad and emerging class of approaches and also propose possible directions for future research

ACM Transactions on Graphics

We present an interactive design system to create functional mechanical objects. Our computational approach allows novice users to retarget an existing mechanical template to a user-specified input shape. Our proposed representation for a mechanical template encodes a parameterized mechanism, mechanical constraints that ensure a physically valid configuration, spatial relationships of mechanical parts to the user-provided shape, and functional constraints that specify an intended functionality. We provide an intuitive interface and optimization-in-the-loop approach for finding a valid configuration of the mechanism and the shape to ensure that higher-level functional goals are met. Our algorithm interactively optimizes the mechanism while the user manipulates the placement of mechanical components and the shape. Our system allows users to efficiently explore various design choices and to synthesize customized mechanical objects that can be fabricated with rapid prototyping technologies. We demonstrate the efficacy of our approach by retargeting various mechanical templates to different shapes and fabricating the resulting functional mechanical objects

Fabrication-Aware Design with Performative Criteria

Artists and architects often need to handle multiple constraints during design of physical constructions. We define a performative constraint as any constraint on design that is tied to the performance of the model--either during fabrication, construction, daily use, or destruction. Even for small to medium scale models, there are functional criteria such as the ease of fabrication and the assembly process, or even the interplay of light with the material. Computational tools can greatly aid in this process, assisting with the lower-level performative constraints, while the designer handles the high-level artistic decisions. Additionally, using new fabrication methods, our tools can aid in lowering the difficulty of building complex constructions, making them accessible to hobbyists. In this thesis, we present three computational methods for designing with different approaches, each with a different material, fabrication method, and use case. The first method is a construction with intersecting planar pieces that can be laser cut or milled. These 3D forms are assembled by sliding pieces into each other along straight slits, and do not require other support such as glue or screws. We present a mathematical abstraction that formalizes the constraints between pieces as a graph, including fabrication and assembly constraints, and ensure global rigidity of the sculpture. We also propose an optimization algorithm to guide the user using automatic constraint satisfaction based on analysis of the constraint relation graph. We demonstrate our approach by creating several small- to medium-scale examples including functional furniture. The second method presents a solution to building a 3D sculpture out of existing building blocks that can be found in many homes. Starting from the voxelization of a 3D mesh we merge voxels to form larger bricks, and then analyze and repair structural problems based on a graph representation of the block connections. We then output layer-by-layer building instructions to allow a user to quickly and easily build the model. We also present extensions such as hollowing the models to use less bricks, limiting the number of bricks of each size, and including color constraints. We present both real and virtual brick constructions and associated timings, showing improvements over previous work. The final case presented tackles the inverse design problem of finding a surface to produce a target caustic on a receiver plane when light is refracted or reflected. This is an example where the performative constraint is the principal driver of the design. We introduce an optimal transport formulation to find a correspondence between the incoming light and the output target light distribution. We then show a 3D optimization that finds the surface that transports light based on the correspondence map. Our approach supports piecewise smooth surfaces that are as smooth as possible but allow for creases, to greatly reduce the amount of artifacts while allowing light to be completely diverted producing completely black regions. We show how this leads to a very large space of high-contrast, high-resolution caustic images, including point and line singularities of infinite light density as well as photo-realistic images. Our approach leads to surfaces that can be milled using standard CNC milling. We demonstrate the approach showing both simulated and fabricated examples

Raising public awareness of mathematics

This book arose from the presentations given at the international workshop held in Óbidos, 26–29 September 2010, as a result of a joint initiative of the Centro Internacional de Matemática and the Raising Public Awareness (RPA) committee of the European Mathematical Society (EMS). The objective was to provide a forum for general reflection with an international mix of experts on building the image of mathematics, ten years after the World Mathematical Year 2000 (WMY 2000). Óbidos, a charming town situated one hour by car to the north of Lisbon, Portugal, was also the site of the re-creation in the year 2000 of the international mathematics exhibition “Beyond the Third Dimension” (http://alem3d.obidos.org/en/) and a meeting of the EMS WMY2000 Committee. The opening of the workshop was also a public “mathematical afternoon” organised by the Portuguese Mathematical Society (SPM) in cooperation with the town of Óbidos. At this event mathematical films and lectures to the general public were presented. The first lecture was given by H. Leitão, from the University of Lisbon, on mathematics in the “Age of Discoveries”, and the second one by G.-M. Greuel, the current president of ERCOM (the EMS committee of the European Research Centres on Mathematics), on the topic “Mathematics between Research, Application and Communication”, which text is included in this book.info:eu-repo/semantics/publishedVersio

Large-Scale Rapid-Prototyping with Zometool

最近因為三維印表機的取得容易許多，使得個人化製造的相 關領域受到較多關注，但是一般市面上的三維印表機存在兩個大 問題: 需要較長的列印時間以及輸出受限於印表機大小，這些問 題使得市售的3D 印表機無法做到快速大型原型生成，在此研究 中，我們提出一個有效率的方法來使用龍圖兒(Zometool) 做出一 個近似原三維模型的結果。 為了要使組裝更容易以及使用更少材料，方法中使用了大區 塊的形狀抽象化，輸入的三維模型先以分區法分為許多類似圓柱 形的區塊，接著將各區塊的邊界轉為環形的龍圖兒結構，之後再 以搜尋最短路徑的方法找尋環形之間的連接結構，最後再順著各 分區的軸產生一些中間的環來逼近原三維模型，此論文並附上一 些實際拼出的結果圖與分析圖表來展示本研究方法的實用性。 本研究提供一個系統來實現所有論文中提到的演算法，並且 加入良好的圖形化使用者介面使的結果有更好的呈現，同時以此 介面加速使用者組合實際龍圖兒原型的過程，在最後將會附上系 統圖呈現。In recent years, personalized fabrication has attracted much attention due to the greatly improved accessibility of consumer-level 3D printers. However, consumer 3D printers still suffers from the relatively long production time and limited output size, which are undesirable factors to large-scale rapidprototyping. In this paper, we present an efficient method to approximate a given 3D shape with Zometool. To achieve ease of assembly and economic usage of building units, the proposed method generates the Zometool structures through a higher level of shape abstraction. The input model is first partitioned into a collection of generalized cylinders by mesh segmentation. The boundaries of mesh segments are converted into ring-like structures and inter-linked by finding the shortest path between them. Additional ring structures are then added along the representative axis of each segment to better approximate the underlying 3D shape. We demonstrate the effectiveness of the proposed method by a variety of 3D models along with examples of the physically fabricated objects