Life cycle assessment (LCA) is a methodology for holistically measuring the environmental impact of a product from initial manufacturing to end-of-life disposal.However, the extent to which LCA informs the design of computing devices remains unclear.To understand how this information is collected and applied, we interviewed 17 industry professionals with experience in LCA or electronics design, systematically coded the interviews, and investigated common themes.These themes highlight the challenge of LCA data collection and reveal distributed decision-making processes where responsibility for sustainable design choices-and their associated costs-is often ambiguous.Our analysis identifes opportunities for HCI technologies to support LCA computation and its integration into the design process to facilitate sustainability-oriented decision-making.While this work provides a nuanced discussion about sustainable design in the information and communication technologies (ICT) hardware industry, we hope our insights will also be valuable to other sectors.

Shape grammars offer a powerful framework for computational design, but synthesizing shape programs to achieve specific goals remains challenging. Inspired by the success of gradient-based optimization in high-dimensional, nonconvex spaces such as those in machine learning, we ask: what makes a shape grammar amenable to gradient-based optimization? To explore this, we introduce Stochastic Rewrite Descent (SRD), an algorithm that interleaves structural rewrites with continuous parameter updates, taking steps in both to optimize a given objective. We analyze the core challenges which have previously prevented optimizing shape programs via descent, and identify a set of desirable properties for grammars that support effective optimization, along with concrete grammar design recommendations to achieve them. We validate this approach across three shape grammars, demonstrating its effectiveness in diverse domains including image fitting, text-driven generation, and topology optimization. Through ablations and comparisons, we show that grammars satisfying our proposed properties lead to significantly better optimization performance. The goal of this work is to open the door to more general and flexible computational paradigms for inverse design with shape grammars.

Abstract Parametric CAD systems use domain‐specific languages (DSLs) to represent geometry as programs, enabling both flexible modeling and structured editing. With the rise of large language models (LLMs), there is growing interest in generating such programs from natural language. This raises a key question: what kind of DSL best supports both CAD generation and editing, whether performed by a human or an AI? In this work, we introduce AIDL, a hierarchical, solver‐aided DSL designed to align with the strengths of LLMs while remaining interpretable and editable by humans. AIDL enables high‐level reasoning by breaking problems into abstract components and structural relationships, while offloading low‐level geometric reasoning to a constraint solver. We evaluate AIDL in a 2D text‐to‐CAD setting using a zero‐shot prompt‐based interface and compare it to OpenSCAD, a widely used CAD DSL that appears in LLM training data. AIDL produces results that are visually competitive and significantly easier to edit. Our findings suggest that language design is a powerful complement to model training and prompt engineering for building collaborative AI–human tools in CAD. Code is available at https://github.com/deGravity/aidl .

We present an algorithm that canonicalizes the algebraic representations of the topological semantics of machine knitting programs. Machine knitting is a staple technology of modern textile production where hundreds of mechanical needles are manipulated to form yarn into interlocking loop structures. Our semantics are defined using a variant of a monoidal category, and they closely correspond to string diagrams. We formulate our canonicalization as an Abstract Rewriting System (ARS) over words in our category, and prove that our algorithm is correct and runs in polynomial time.

One of the core promises of parametric Computer-Aided Design (CAD) is that users can easily edit their model at any point in time. However, due to the ambiguity of changing references to intermediate, updated geometry, parametric edits can lead to reference errors which are difficult to fix in practice. We claim that debugging reference errors remains challenging because CAD systems do not provide users with tools to understand where the error happened and how to fix it. To address these challenges, we prototype a graphical debugging tool, DeCAD, which helps comparing CAD model states both across operations and across edits. In a qualitative lab study, we use DeCAD as a probe to understand specific challenges that users face and what workflows they employ to overcome them. We conclude with design implications for future debugging tool developers.

The commonly used cut-and-sew garment construction process, in which 2D fabric panels are cut from sheets of fabric and assembled into 3D garments, contributes to widespread textile waste in the fashion industry. There is often a significant divide between the design of the garment and the layout of the panels. One opportunity for bridging this gap is the emerging study and practice of zero waste fashion design, which involves creating clothing designs with maximum layout efficiency. Enforcing the strict constraints of zero waste sewing is challenging, as edits to one region of the garment necessarily affect neighboring panels. Based on our formative work to understand this emerging area within fashion design, we present WasteBanned, a tool that combines CAM and CAD to help users prioritize efficient material usage, work within these zero waste constraints, and edit existing zero waste garment patterns. Our user evaluation indicates that our tool helps fashion designers edit zero waste patterns to fit different bodies and add stylistic variation, while creating highly efficient fabric layouts.

The growing demands for computational power in cloud computing have led to a significant increase in the deployment of high-performance servers. The growing power consumption of servers and the heat they produce is on track to outpace the capacity of conventional air cooling systems, necessitating more efficient cooling solutions such as liquid immersion cooling. The superior heat exchange capabilities of immersion cooling both eliminates the need for bulky heat sinks, fans, and air flow channels while also unlocking the potential go beyond conventional 2D blade servers to three-dimensional designs. In this work, we present a computational framework to explore designs of servers in three-dimensional space, specifically targeting the maximization of server density within immersion cooling tanks. Our tool is designed to handle a variety of physical and electrical server design constraints. We demonstrate our optimized designs can reduce server volume by 25--52% compared to traditional flat server designs. This increased density reduces land usage as well as the amount of liquid used for immersion, with significant reduction in the carbon emissions embodied in datacenter buildings. We further create physical prototypes to simulate dense server designs and perform real-world experiments in an immersion cooling tank demonstrating they operate at safe temperatures. This approach marks a critical step forward in sustainable and efficient datacenter management.

Illusion-knit fabrics reveal distinct patterns or images depending on the viewing angle. Artists have manually achieved this effect by exploiting "microgeometry," i.e., small differences in stitch heights. However, past work in computational 3D knitting does not model or exploit designs based on stitch height variation. This paper establishes a foundation for exploring illusion knitting in the context of computational design and fabrication. We observe that the design space is highly constrained, elucidate these constraints, and derive strategies for developing effective, machine-knittable illusion patterns. We partially automate these strategies in a new interactive design tool that reduces difficult patterning tasks to familiar image editing tasks. Illusion patterns also uncover new fabrication challenges regarding mixed colorwork and texture; we describe new algorithms for mitigating fabrication failures and ensuring high-quality knit results.

Virtually every object in the modern world was created, modified, analyzed and optimized using computer aided design (CAD) tools. An active CAD research area is the use of data-driven machine learning methods to learn from the massive repositories of geometric and program representations. However, the lack of labeled data in CAD's native format, i.e., the parametric boundary representation (B-Rep), poses an obstacle at present difficult to overcome. Several datasets of mechanical parts in B-Rep format have recently been released for machine learning research. However, large-scale databases are mostly unlabeled, and labeled datasets are small. Additionally, task-specific label sets are rare and costly to annotate. This work proposes to leverage unlabeled CAD geometry on supervised learning tasks. We learn a novel, hybrid implicit/explicit surface representation for B-Rep geometry. Further, we show that this pre-training both significantly improves few-shot learning performance and achieves state-of-the-art performance on several current B-Rep benchmarks.

Sub-gram flying robots have transformative potential in applications from search and rescue to precision agriculture to environmental monitoring. However, a key gap in achieving autonomous flight for these applications is the low lift to weight ratio of flapping wing and quadrotor designs around 1 g or less. To close this gap, we propose a helictoper-style design that minimizes size and weight by leveraging the high lift, reliability, and low-voltage of sub-gram motors. We take an important step to enable this goal by designing a light-weight, micfrofabricated flybar mechanism to passively stabilize such a robot. Our 48 mg flybar is folded from a flat carbon fiber laminate into a 3D mechanism that couples tilting of the flybar to a change in the angle of attack of the rotors. Our design uses flexure joints instead of ball-in-socket joints common in larger flybars. To expedite the design exploration and optimization of a microfabricated flat-folded flybar, we develop a novel user-in-the-loop bi-level optimization workflow that combines Bayesian optimization design tools and expert feedback. We develop four template designs and use this method to achieve a peak damping ratio of 0.528, an 18.9x improvement from our initial design. Compared to a flybar-less rotor with a near 0 damping ratio, our flybar-rotor mechanism maintains a stable roll and pitch with relative deviations < 1°. Our results show that, if combined with a counter-torque mechanism such as a tail rotor, our miniaturized flybar could mechanically provide attitude stability for a sub-gram helicopter.

Parametric CAD models encode entire families of shapes that should, in principle, be easy for designers to explore. However, in practice, parametric CAD models can be difficult to manipulate due to implicit semantic constraints among parameter values. Finding and enforcing these semantic constraints solely from geometry or programmatic shape representations is not possible because these constraints ultimately reflect design intent. They are informed by the designer’s experience and semantics in the real world. To address this challenge, we introduce ReparamCAD, a zero-shot pipeline that leverages pre-trained large language and image model to infer meaningful space of variations for a shape We then re-parameterize a new constrained parametric CAD program that captures these variations, enabling effortless exploration of the design space along meaningful design axes. We evaluated our approach through five examples and a user study. The result showed that the inferred spaces are meaningful and comparable to those defined by experts. Code and data are at: https://github.com/milmillin/ReparamCAD.

Abstract Procedural models (i.e. symbolic programs that output visual data) are a historically‐popular method for representing graphics content: vegetation, buildings, textures, etc. They offer many advantages: interpretable design parameters, stochastic variations, high‐quality outputs, compact representation, and more. But they also have some limitations, such as the difficulty of authoring a procedural model from scratch. More recently, AI‐based methods, and especially neural networks, have become popular for creating graphic content. These techniques allow users to directly specify desired properties of the artifact they want to create (via examples, constraints, or objectives), while a search, optimization, or learning algorithm takes care of the details. However, this ease of use comes at a cost, as it's often hard to interpret or manipulate these representations. In this state‐of‐the‐art report, we summarize research on neurosymbolic models in computer graphics: methods that combine the strengths of both AI and symbolic programs to represent, generate, and manipulate visual data. We survey recent work applying these techniques to represent 2D shapes, 3D shapes, and materials & textures. Along the way, we situate each prior work in a unified design space for neurosymbolic models, which helps reveal underexplored areas and opportunities for future research.

3D Computer-Aided Design (CAD) modeling is ubiquitous in mechanical engineering and design. Modern CAD models are programs that produce geometry and can be used to implement high-level geometric changes by modifying input parameters. While there has been a surge of recent interest in program-based tooling for the CAD domain, one fundamental problem remains unsolved. CAD programs pass geometric arguments to operations using references, which are queries that select elements from the constructed geometry according to programmer intent. The challenge is designing reference semantics that can express programmer intent across all geometric topologies achievable with model parameters, including topologies where the desired elements are not present. In current systems, both users and automated tools may create invalid models when parameters are changed, as references to geometric elements are lost or silently and arbitrarily switched. While existing CAD systems use heuristics to attempt to infer user intent in cases of this undefined behavior, this best-effort solution is not suitable for constructing automated tools to edit and optimize CAD programs. We analyze the failure modes of existing referencing schemes and formalize a set of criteria on which to evaluate solutions to the CAD referencing problem. In turn, we propose a domain-specific language that exposes references as a first-class language construct, using user-authored queries to introspect element history and define references safely over all paths. We give a semantics for fine-grained element lineage that can subsequently be queried; and show that our language meets the desired properties. Finally, we provide an implementation of a lineage-based referencing system in a 2.5D CAD kernel, demonstrating realistic referencing scenarios and illustrating how our system safely represents models that cause reference breakage in existing CAD systems.

Sheet Metal (SM) fabrication is perhaps one of the most common metalworking technique. Despite its prevalence, SM design is manual and costly, with rigorous practices that restrict the search space, yielding suboptimal results. In contrast, we present a framework for the first automatic design of SM parts. Focusing on load bearing applications, our novel system generates a high-performing manufacturable SM that adheres to the numerous constraints that SM design entails: The resulting part minimizes manufacturing costs while adhering to structural, spatial, and manufacturing constraints. In other words, the part should be strong enough, not disturb the environment, and adhere to the manufacturing process. These desiderata sum up to an elaborate, sparse, and expensive search space. Our generative approach is a carefully designed exploration process, comprising two steps. In Segment Discovery connections from the input load to attachable regions are accumulated, and during Segment Composition the most performing valid combination is searched for. For Discovery, we define a slim grammar, and sample it for parts using a Markov-Chain Monte Carlo (MCMC) approach, ran in intercommunicating instances (i.e, chains) for diversity. This, followed by a short continuous optimization, enables building a diverse and high-quality library of substructures. During Composition, a valid and minimal cost combination of the curated substructures is selected. To improve compliance significantly without additional manufacturing costs, we reinforce candidate parts onto themselves --- a unique SM capability called self-riveting. we provide our code and data in https://github.com/amir90/AutoSheetMetal. We show our generative approach produces viable parts for numerous scenarios. We compare our system against a human expert and observe improvements in both part quality and design time. We further analyze our pipeline's steps with respect to resulting quality, and have fabricated some results for validation. We hope our system will stretch the field of SM design, replacing costly expert hours with minutes of standard CPU, making this cheap and reliable manufacturing method accessible to anyone.

Large Computer-Aided Design (CAD) projects usually require collaboration across many different CAD systems as well as applications that interoperate with them for manufacturing, visualization, or simulation. A fundamental barrier to such collaborations is the ability to refer to parts of the geometry (such as a specific face) robustly under geometric and/or topological changes to the model. Persistent referencing schemes are a fundamental aspect of most CAD tools, but models that are shared across systems cannot generally make use of these internal referencing mechanisms, creating a challenge for collaboration. In this work, we address this issue by developing a novel learning-based algorithm that can automatically find correspondences between two CAD models using the standard representation used for sharing models across CAD systems: the Boundary-Representation (B-rep). Because our method works directly on B-reps it can be generalized across different CAD applications enabling collaboration.

Abstract Modern CAD tools represent 3D designs not only as geometry, but also as a program composed of geometric operations, each of which depends on a set of parameters. Program representations enable meaningful and controlled shape variations via parameter changes. However, achieving desired modifications solely through parameter editing is challenging when CAD models have not been explicitly authored to expose select degrees of freedom in advance. We introduce a novel bidirectional editing system for 3D CAD programs. In addition to editing the CAD program, users can directly manipulate 3D geometry and our system infers parameter updates to keep both representations in sync. We formulate inverse edits as a set of constrained optimization objectives, returning plausible updates to program parameters that both match user intent and maintain program validity. Our approach implements an automatically differentiable domain‐specific language for CAD programs, providing derivatives for this optimization to be performed quickly on any expressed program. Our system enables rapid, interactive exploration of a constrained 3D design space by allowing users to manipulate the program and geometry interchangeably during design iteration. While our approach is not designed to optimize across changes in geometric topology, we show it is expressive and performant enough for users to produce a diverse set of design variants, even when the CAD program contains a relatively large number of parameters.

We present an interactive design system for knitting that allows users to create template patterns that can be fabricated using an industrial knitting machine. Our interactive design tool is novel in that it allows direct control of key knitting design axes we have identified in our formative study and does so consistently across the variations of an input parametric template geometry. This is achieved with two key technical advances. First, we present an interactive meshing tool that lets users build a coarse quadrilateral mesh that adheres to their knit design guidelines. This solution ensures consistency across the parameter space for further customization over shape variations and avoids helices, promoting knittability. Second, we lift and formalize low-level machine knitting constraints to the level of this coarse quad mesh. This enables us to not only guarantee hand- and machine-knittability, but also provides automatic design assistance through auto-completion and suggestions. We show the capabilities through a set of fabricated examples that illustrate the effectiveness of our approach in creating a wide variety of objects and interactively exploring the space of design variations.

This work proposes a novel generative design tool for passive grippers---robot end effectors that have no additional actuation and instead leverage the existing degrees of freedom in a robotic arm to perform grasping tasks. Passive grippers are used because they offer interesting trade-offs between cost and capabilities. However, existing designs are limited in the types of shapes that can be grasped. This work proposes to use rapid-manufacturing and design optimization to expand the space of shapes that can be passively grasped. Our novel generative design algorithm takes in an object and its positioning with respect to a robotic arm and generates a 3D printable passive gripper that can stably pick the object up. To achieve this, we address the key challenge of jointly optimizing the shape and the insert trajectory to ensure a passively stable grasp. We evaluate our method on a testing suite of 22 objects (23 experiments), all of which were evaluated with physical experiments to bridge the virtual-to-real gap. Code and data are at https://homes.cs.washington.edu/~milink/passive-gripper/

Past work on optimizing fabrication plans given a carpentry design can provide Pareto-optimal plans trading off between material waste, fabrication time, precision, and other considerations. However, when developing fabrication plans, experts rarely restrict to a single design , instead considering families of design variations , sometimes adjusting designs to simplify fabrication. Jointly exploring the design and fabrication plan spaces for each design is intractable using current techniques. We present a new approach to jointly optimize design and fabrication plans for carpentered objects. To make this bi-level optimization tractable, we adapt recent work from program synthesis based on equality graphs (e-graphs), which encode sets of equivalent programs. Our insight is that subproblems within our bi-level problem share significant substructures. By representing both designs and fabrication plans in a new bag of parts (BOP) e-graph, we amortize the cost of optimizing design components shared among multiple candidates. Even using BOP e-graphs, the optimization space grows quickly in practice. Hence, we also show how a feedback-guided search strategy dubbed Iterative Contraction and Expansion on E-graphs (ICEE) can keep the size of the e-graph manageable and direct the search towards promising candidates. We illustrate the advantages of our pipeline through examples from the carpentry domain.

Bladed tools such as jigsaws are common tools for wood workers on job-sites and in workshops, but do not currently have sufficient autonomous hardware or path planning algorithms to enable automation. Here we present a system of an autonomous robot and a path planning algorithm for automating jigsaw operations. The robot can drill holes, insert the jigsaw, and cut plywood. Our algorithm converts complex shapes into paths for the jigsaw, drill holes, and traversal movements for the robot. The algorithm decomposes input shapes into cuttable sections and determines possible locations for drilling entry holes for inserting the blade. We cast the drill hole problem as a set coverage problem with a trade-off between number of holes and cutting distance. We characterize the algorithm on a series of shapes and determined the algorithm found valid solutions. We executed an example on the robot to demonstrate the end-to-end system.

Abstract We propose a novel method to generate fabrication blueprints from images of carpentered items. While 3D reconstruction from images is a well‐studied problem, typical approaches produce representations that are ill‐suited for computer‐aided design and fabrication applications. Our key insight is that fabrication processes define and constrain the design space for carpentered objects, and can be leveraged to develop novel reconstruction methods. Our method makes use of domain‐specific constraints to recover not just valid geometry, but a semantically valid assembly of parts, using a combination of image‐based and geometric optimization techniques. We demonstrate our method on a variety of wooden objects and furniture, and show that we can automatically obtain designs that are both easy to edit and accurate recreations of the ground truth. We further illustrate how our method can be used to fabricate a physical replica of the captured object as well as a customized version, which can be produced by directly editing the reconstructed model in CAD software.

Many compilers, synthesizers, and theorem provers rely on rewrite rules to simplify expressions or prove equivalences. Developing rewrite rules can be difficult: rules may be subtly incorrect, profitable rules are easy to miss, and rulesets must be rechecked or extended whenever semantics are tweaked. Large rulesets can also be challenging to apply: redundant rules slow down rule-based search and frustrate debugging. This paper explores how equality saturation, a promising technique that uses e-graphs to apply rewrite rules, can also be used to infer rewrite rules. E-graphs can compactly represent the exponentially large sets of enumerated terms and potential rewrite rules. We show that equality saturation efficiently shrinks both sets, leading to faster synthesis of smaller, more general rulesets. We prototyped these strategies in a tool dubbed Ruler. Compared to a similar tool built on CVC4, Ruler synthesizes 5.8× smaller rulesets 25× faster without compromising on proving power. In an end-to-end case study, we show Ruler-synthesized rules which perform as well as those crafted by domain experts, and addressed a longstanding issue in a popular open source tool.

Assembly modeling is a core task of computer aided design (CAD), comprising around one third of the work in a CAD workflow. Optimizing this process therefore represents a huge opportunity in the design of a CAD system, but current research of assembly based modeling is not directly applicable to modern CAD systems because it eschews the dominant data structure of modern CAD: parametric boundary representations (BREPs). CAD assembly modeling defines assemblies as a system of pairwise constraints, called mates , between parts, which are defined relative to BREP topology rather than in world coordinates common to existing work. We propose SB-GCN, a representation learning scheme on BREPs that retains the topological structure of parts, and use these learned representations to predict CAD type mates. To train our system, we compiled the first large scale dataset of BREP CAD assemblies, which we are releasing along with benchmark mate prediction tasks. Finally, we demonstrate the compatibility of our model with an existing commercial CAD system by building a tool that assists users in mate creation by suggesting mate completions, with 72.2% accuracy.

Manufactured parts are meticulously engineered to perform well with respect to several conflicting metrics, like weight, stress, and cost. The best achievable trade-offs reside on the Pareto front , which can be discovered via performance-driven optimization. The objectives that define this Pareto front often incorporate assumptions about the context in which a part will be used, including loading conditions, environmental influences, material properties, or regions that must be preserved to interface with a surrounding assembly. Existing multi-objective optimization tools are only equipped to study one context at a time, so engineers must run independent optimizations for each context of interest. However, engineered parts frequently appear in many contexts: wind turbines must perform well in many wind speeds, and a bracket might be optimized several times with its bolt-holes fixed in different locations on each run. In this paper, we formulate a framework for variable-context multi-objective optimization. We introduce the Pareto gamut , which captures Pareto fronts over a range of contexts. We develop a global/local optimization algorithm to discover the Pareto gamut directly, rather than discovering a single fixed-context "slice" at a time. To validate our method, we adapt existing multi-objective optimization benchmarks to contextual scenarios. We also demonstrate the practical utility of Pareto gamut exploration for several engineering design problems.

We introduce carvable volume decomposition for efficient 3-axis CNC machining of 3D freeform objects, where our goal is to develop a fully automatic method to jointly optimize setup and path planning. We formulate our joint optimization as a volume decomposition problem which prioritizes minimizing the number of setup directions while striving for a minimum number of continuously carvable volumes, where a 3D volume is continuously carvable, or simply carvable, if it can be carved with the machine cutter traversing a single continuous path. Geometrically, carvability combines visibility and monotonicity and presents a new shape property which had not been studied before. Given a target 3D shape and the initial material block, our algorithm first finds the minimum number of carving directions by solving a set cover problem. Specifically, we analyze cutter accessibility and select the carving directions based on an assessment of how likely they would lead to a small carvable volume decomposition. Next, to obtain a minimum decomposition based on the selected carving directions efficiently, we narrow down the solution search by focusing on a special kind of points in the residual volume, single access or SA points, which are points that can be accessed from one and only one of the selected carving directions. Candidate carvable volumes are grown starting from the SA points. Finally, we devise an energy term to evaluate the carvable volumes and their combinations, leading to the final decomposition. We demonstrate the performance of our decomposition algorithm on a variety of 2D and 3D examples and evaluate it against the ground truth, where possible, and solutions provided by human experts. Physically machined models are produced where each carvable volume is continuously carved following a connected Fermat spiral toolpath.

Traditional manufacturing workflows strongly decouple design and fabrication phases. As a result, fabrication-related objectives such as manufacturing time and precision are difficult to optimize in the design space, and vice versa. This paper presents HL-HELM, a high-level, domain-specific language for expressing abstract, parametric fabrication plans; it also introduces LL-HELM, a low-level language for expressing concrete fabrication plans that take into account the physical constraints of available manufacturing processes. We present a new compiler that supports the real-time, unoptimized translation of high-level, geometric fabrication operations into concrete, tool-specific fabrication instructions; this gives users immediate feedback on the physical feasibility of plans as they design them. HELM offers novel optimizations to improve accuracy and reduce fabrication time as well as material costs. Finally, optimized low-level plans can be interpreted as step-by-step instructions for users to actually fabricate a physical product. We provide a variety of example fabrication plans in the carpentry domain that are designed using our high-level language, show how the compiler translates and optimizes these plans to generate concrete low-level instructions, and present the final physical products fabricated in wood.

Hybrid unmanned aerial vehicles (UAV) combine advantages of multicopters and fixed-wing planes: vertical take-off, landing, and low energy use. However, hybrid UAVs are rarely used because controller design is challenging due to its complex, mixed dynamics. In this paper, we propose a method to automate this design process by training a mode-free, model-agnostic neural network controller for hybrid UAVs. We present a neural network controller design with a novel error convolution input trained by reinforcement learning. Our controller exhibits two key features: First, it does not distinguish among flying modes, and the same controller structure can be used for copters with various dynamics. Second, our controller works for real models without any additional parameter tuning process, closing the gap between virtual simulation and real fabrication. We demonstrate the efficacy of the proposed controller both in simulation and in our custom-built hybrid UAVs (Figure 1, 8). The experiments show that the controller is robust to exploit the complex dynamics when both rotors and wings are active in flight tests.

Despite the ubiquity of carpentered items, the customization of carpentered items remains labor intensive. The generation of laymen editable templates for carpentry is difficult. Current design tools rely heavily on CNC fabrication, limiting applicability. We develop a template based system for carpentry and a robotic fabrication system using mobile robots and standard carpentry tools. Our end-to-end design and fabrication tool democratizes design and fabrication of carpentered items. Our method combines expert knowledge for template design, allows laymen users to customize and verify specific designs, and uses robotics system to fabricate parts. We validate our system using multiple designs to make customizable, verifiable templates and fabrication plans and show an end-to-end example that was designed, manufactured, and assembled using our tools.

While computer-aided design is a major part of many modern manufacturing pipelines, the design files typically generated describe raw geometry. Lost in this representation is the procedure by which these designs were generated. In this paper, we present a method for reverse-engineering the process by which 3D models may have been generated, in the language of constructive solid geometry (CSG). Observing that CSG is a formal grammar, we formulate this inverse CSG problem as a program synthesis problem. Our solution is an algorithm that couples geometric processing with state-of-the-art program synthesis techniques. In this scheme, geometric processing is used to convert the mixed discrete and continuous domain of CSG trees to a pure discrete domain where modern program synthesizers excel. We demonstrate the efficiency and scalability of our algorithm on several different examples, including those with over 100 primitive parts. We show that our algorithm is able to find simple programs which are close to the ground truth, and demonstrate our method's applicability in mesh re-editing. Finally, we compare our method to prior state-of-the-art. We demonstrate that our algorithm dominates previous methods in terms of resulting CSG compactness and runtime, and can handle far more complex input meshes than any previous method.

Typical design for manufacturing applications requires simultaneous optimization of conflicting performance objectives: Design variations that improve one performance metric may decrease another performance metric. In these scenarios, there is no unique optimal design but rather a set of designs that are optimal for different trade-offs (called Pareto-optimal). In this work, we propose a novel approach to discover the Pareto front, allowing designers to navigate the landscape of compromises efficiently. Our approach is based on a first-order approximation of the Pareto front, which allows entire neighborhoods rather than individual points on the Pareto front to be captured. In addition to allowing for efficient discovery of the Pareto front and the corresponding mapping to the design space, this approach allows us to represent the entire trade-off manifold as a small collection of patches that comprise a high-quality and piecewise-smooth approximation. We illustrate how this technique can be used for navigating performance trade-offs in computer-aided design (CAD) models.

While collections of parametric shapes are growing in size and use, little progress has been made on the fundamental problem of shape-based matching and retrieval for parametric shapes in a collection. The search space for such collections is both discrete (number of shapes) and continuous (parameter values). In this work, we propose representing this space using descriptors that have shown to be effective for single shape retrieval. While single shapes can be represented as points in a descriptor space, parametric shapes are mapped into larger continuous regions. For smooth descriptors, we can assume that these regions are bounded low-dimensional manifolds where the dimensionality is given by the number of shape parameters. We propose representing these manifolds with a set of primitives, namely, points and bounded tangent spaces. Our algorithm describes how to define these primitives and how to use them to construct a manifold approximation that allows accurate and fast retrieval. We perform an analysis based on curvature, boundary evaluation, and the allowed approximation error to select between primitive types. We show how to compute decision variables with no need for empirical parameter adjustments and discuss theoretical guarantees on retrieval accuracy. We validate our approach with experiments that use different types of descriptors on a collection of shapes from multiple categories.

Computer Aided Design (CAD) is a multi-billion dollar industry used by almost every mechanical engineer in the world to create practically every existing manufactured shape. CAD models are not only widely available but also extremely useful in the growing field of fabrication-oriented design because they are parametric by construction and capture the engineer's design intent, including manufacturability. Harnessing this data, however, is challenging, because generating the geometry for a given parameter value requires time-consuming computations. Furthermore, the resulting meshes have different combinatorics, making the mesh data inherently discontinuous with respect to parameter adjustments. In our work, we address these challenges and develop tools that allow interactive exploration and optimization of parametric CAD data. To achieve interactive rates, we use precomputation on an adaptively sampled grid and propose a novel scheme for interpolating in this domain where each sample is a mesh with different combinatorics. Specifically, we extract partial correspondences from CAD representations for local mesh morphing and propose a novel interpolation method for adaptive grids that is both continuous/smooth and local (i.e., the influence of each sample is constrained to the local regions where mesh morphing can be computed). We show examples of how our method can be used to interactively visualize and optimize objects with a variety of physical properties.

We present an interactive system for computational design, optimization, and fabrication of multicopters. Our computational approach allows non-experts to design, explore, and evaluate a wide range of different multicopters. We provide users with an intuitive interface for assembling a multicopter from a collection of components (e.g., propellers, motors, and carbon fiber rods). Our algorithm interactively optimizes shape and controller parameters of the current design to ensure its proper operation. In addition, we allow incorporating a variety of other metrics (such as payload, battery usage, size, and cost) into the design process and exploring tradeoffs between them. We show the efficacy of our method and system by designing, optimizing, fabricating, and operating multicopters with complex geometries and propeller configurations. We also demonstrate the ability of our optimization algorithm to improve the multicopter performance under different metrics.

We propose a data-driven method for designing 3D models that can be fabricated. First, our approach converts a collection of expert-created designs to a dataset of parameterized design templates that includes all information necessary for fabrication. The templates are then used in an interactive design system to create new fabri-cable models in a design-by-example manner. A simple interface allows novice users to choose template parts from the database, change their parameters, and combine them to create new models. Using the information in the template database, the system can automatically position, align, and connect parts: the system accomplishes this by adjusting parameters, adding appropriate constraints, and assigning connectors. This process ensures that the created models can be fabricated, saves the user from many tedious but necessary tasks, and makes it possible for non-experts to design and create actual physical objects. To demonstrate our data-driven method, we present several examples of complex functional objects that we designed and manufactured using our system.

Compressive Sensing (CS) is a new paradigm in signal acquisition and compression that has been attracting the interest of the signal compression community. When it comes to image compression applications, it is relevant to estimate the number of bits required to reach a specific image quality. Although several theoretical results regarding the rate-distortion performance of CS have been published recently, there are not many practical image compression results available. The main goal of this paper is to carry out an empirical analysis of the rate-distortion performance of CS in image compression. We analyze issues such as the minimization algorithm used and the transform employed, as well as the trade-off between number of measurements and quantization error. From the experimental results obtained we highlight the potential and limitations of CS when compared to traditional image compression methods.