Designing mechanical mechanisms to trace specific paths is a classic yet notoriously difficult engineering problem, characterized by a vast and complex search space of discrete topologies and continuous parameters. We introduce MechaFormer, a Transformer-based model that tackles this challenge by treating mechanism design as a conditional sequence generation task. Our model learns to translate a target curve into a domain-specific language (DSL) string, simultaneously determining the mechanism's topology and geometric parameters in a single, unified process. MechaFormer significantly outperforms existing baselines, achieving state-of-the-art path-matching accuracy and generating a wide diversity of novel and valid designs. We demonstrate a suite of sampling strategies that can dramatically improve solution quality and offer designers valuable flexibility. Furthermore, we show that the high-quality outputs from MechaFormer serve as excellent starting points for traditional optimizers, creating a hybrid approach that finds superior solutions with remarkable efficiency.

Generative AI has made remarkable progress in addressing various design challenges. One prominent area where generative AI could bring significant value is in engineering design. In particular, selecting an optimal set of components and their interfaces to create a mechanical system that meets design requirements is one of the most challenging and time-consuming tasks for engineers. This configuration design task is inherently challenging due to its categorical nature, multiple design requirements a solution must satisfy, and the reliance on physics simulations for evaluating potential solutions. These characteristics entail solving a combinatorial optimization problem with multiple constraints involving black-box functions. To address this challenge, we propose a deep generative model to predict the optimal combination of components and interfaces for a given design problem. To demonstrate our approach, we solve a gear train synthesis problem by first creating a synthetic dataset using a domain-specific language, a parts catalogue, and a physics simulator. We then train a Transformer-based model using this dataset, named GearFormer, which can not only generate quality solutions on its own, but also augment traditional search methods such as an evolutionary algorithm and Monte Carlo tree search. We show that GearFormer outperforms such search methods on their own in terms of satisfying the specified design requirements with orders of magnitude faster generation time. Additionally, we showcase the benefit of hybrid methods that leverage both GearFormer and search methods, which further improve the quality of the solutions.

We adapt alignment techniques from reasoning LLMs to the task of generating engineering sketch constraints found in computer-aided design (CAD) models. Engineering sketches consist of geometric primitives (e.g. points, lines) connected by constraints (e.g. perpendicular, tangent) that define the relationships between them. For a design to be easily editable, the constraints must effectively capture design intent, ensuring the geometry updates predictably when parameters change. Although current approaches can generate CAD designs, an open challenge remains to align model outputs with design intent, we label this problem 'design alignment'. A critical first step towards aligning generative CAD models is to generate constraints which fully-constrain all geometric primitives, without over-constraining or distorting sketch geometry. Using alignment techniques to train an existing constraint generation model with feedback from a constraint solver, we are able to fully-constrain 93% of sketches compared to 34% when using a naive supervised fine-tuning (SFT) baseline and only 8.9% without SFT. Our approach can be applied to any existing constraint generation model and sets the stage for further research bridging alignment strategies between the language and design domains. Additional results can be found at https://autodeskailab.github.io/aligning-constraint-generation/.

The boundary representation (B-Rep) is the standard data structure used in Computer-Aided Design (CAD) for defining solid models. Despite recent progress, directly generating B-Reps end-to-end with precise geometry and watertight topology remains a challenge. This paper presents AutoBrep, a novel Transformer model that autoregressively generates B-Reps with high quality and validity. AutoBrep employs a unified tokenization scheme that encodes both geometric and topological characteristics of a B-Rep model as a sequence of discrete tokens. Geometric primitives (i.e., surfaces and curves) are encoded as latent geometry tokens, and their structural relationships are defined as special topological reference tokens. Sequence order in AutoBrep naturally follows a breadth first traversal of the B-Rep face adjacency graph. At inference time, neighboring faces and edges along with their topological structure are progressively generated. Extensive experiments demonstrate the advantages of our unified representation when coupled with next-token prediction for B-Rep generation. AutoBrep outperforms baselines with better quality and watertightness. It is also highly scalable to complex solids with good fidelity and inference speed. We further show that autocompleting B-Reps is natively supported through our unified tokenization, enabling user-controllable CAD generation with minimal changes. Code is available at https://github.com/AutodeskAILab/AutoBrep.

This paper presents BrepGen , a diffusion-based generative approach that directly outputs a Boundary representation (B-rep) Computer-Aided Design (CAD) model. BrepGen represents a B-rep model as a novel structured latent geometry in a hierarchical tree. With the root node representing a whole CAD solid, each element of a B-rep model (i.e., a face, an edge, or a vertex) progressively turns into a child-node from top to bottom. B-rep geometry information goes into the nodes as the global bounding box of each primitive along with a latent code describing the local geometric shape. The B-rep topology information is implicitly represented by node duplication. When two faces share an edge, the edge curve will appear twice in the tree, and a T-junction vertex with three incident edges appears six times in the tree with identical node features. Starting from the root and progressing to the leaf, BrepGen employs Transformer-based diffusion models to sequentially denoise node features while duplicated nodes are detected and merged, recovering the B-Rep topology information. Extensive experiments show that BrepGen advances the task of CAD B-rep generation, surpassing existing methods on various benchmarks. Results on our newly collected furniture dataset further showcase its exceptional capability in generating complicated geometry. While previous methods were limited to generating simple prismatic shapes, BrepGen incorporates free-form and doubly-curved surfaces for the first time. Additional applications of BrepGen include CAD autocomplete and design interpolation. The code, pretrained models, and dataset are available at https://github.com/samxuxiang/BrepGen.

This paper presents a novel generative model for Computer Aided Design (CAD) that 1) represents high-level design concepts of a CAD model as a three-level hierarchical tree of neural codes, from global part arrangement down to local curve geometry; and 2) controls the generation or completion of CAD models by specifying the target design using a code tree. Concretely, a novel variant of a vector quantized VAE with "masked skip connection" extracts design variations as neural codebooks at three levels. Two-stage cascaded auto-regressive transformers learn to generate code trees from incomplete CAD models and then complete CAD models following the intended design. Extensive experiments demonstrate superior performance on conventional tasks such as unconditional generation while enabling novel interaction capabilities on conditional generation tasks. The code is available at https://github.com/samxuxiang/hnc-cad.

Physical products are often complex assemblies combining a multitude of 3D parts modeled in computer-aided design (CAD) software. CAD designers build up these assemblies by aligning individual parts to one another using constraints called joints. In this paper we introduce JoinABLe, a learning-based method that assembles parts together to form joints. JoinABLe uses the weak supervision available in standard parametric CAD files without the help of object class labels or human guidance. Our results show that by making network predictions over a graph representation of solid models we can outperform multiple baseline methods with an accuracy (79.53%) that approaches human performance (80%). Finally, to support future research we release the Fusion 360 Gallery assembly dataset, containing assemblies with rich information on joints, contact surfaces, holes, and the underlying assembly graph structure.

We present SkexGen, a novel autoregressive generative model for computer-aided design (CAD) construction sequences containing sketch-and-extrude modeling operations. Our model utilizes distinct Transformer architectures to encode topological, geometric, and extrusion variations of construction sequences into disentangled codebooks. Autoregressive Transformer decoders generate CAD construction sequences sharing certain properties specified by the codebook vectors. Extensive experiments demonstrate that our disentangled codebook representation generates diverse and high-quality CAD models, enhances user control, and enables efficient exploration of the design space. The code is available at https://samxuxiang.github.io/skexgen.

We present Neon, a new programming model for grid-based computation with an intuitive, easy-to-use interface that allows domain experts to take full advantage of single-node multi-GPU systems. Neon decouples data structure from computation and back end configurations, allowing the same user code to operate on a variety of data structures and devices. Neon relies on a set of hierarchical abstractions that allow the user to write their applications as if they were sequential applications, while the runtime handles distribution across multiple GPUs and performs optimizations such as overlapping computation and communication without user intervention. We evaluate our programming model on several applications: a Lattice Boltzmann fluid solver, a finite-difference Poisson solver and a finite-element linear elastic solver. We show that these applications can be implemented concisely and scale well with the number of GPUs-achieving more than 99% of ideal efficiency.

Reverse Engineering a CAD shape from other representations is an important geometric processing step for many downstream applications. In this work, we introduce a novel neural network architecture to solve this challenging task and approximate a smoothed signed distance function with an editable, constrained, prismatic CAD model. During training, our method reconstructs the input geometry in the voxel space by decomposing the shape into a series of 2D profile images and 1D envelope functions. These can then be recombined in a differentiable way allowing a geometric loss function to be defined. During inference, we obtain the CAD data by first searching a database of 2D constrained sketches to find curves which approximate the profile images, then extrude them and use Boolean operations to build the final CAD model. Our method approximates the target shape more closely than other methods and outputs highly editable constrained parametric sketches which are compatible with existing CAD software.

We introduce UV-Net, a novel neural network architecture and representation designed to operate directly on Boundary representation (B-rep) data from 3D CAD models. The B-rep format is widely used in the design, simulation and manufacturing industries to enable sophisticated and precise CAD modeling operations. However, B-rep data presents some unique challenges when used with modern machine learning due to the complexity of the data structure and its support for both continuous non-Euclidean geometric entities and discrete topological entities. In this paper, we propose a unified representation for B-rep data that exploits the U and V parameter domain of curves and surfaces to model geometry, and an adjacency graph to explicitly model topology. This leads to a unique and efficient network architecture, UV-Net, that couples image and graph convolutional neural networks in a compute and memory-efficient manner To aid in future research we present a synthetic labelled B-rep dataset, SolidLetters, derived from human designed fonts with variations in both geometry and topology. Finally we demonstrate that UV-Net can generalize to supervised and unsupervised tasks on five datasets, while outperforming alternate 3D shape representations such as point clouds, voxels, and meshes.

Boundary representation (B-rep) models are the standard way 3D shapes are described in Computer-Aided Design (CAD) applications. They combine lightweight parametric curves and surfaces with topological information which connects the geometric entities to describe manifolds. In this paper we introduce BRepNet, a neural network architecture designed to operate directly on B-rep data structures, avoiding the need to approximate the model as meshes or point clouds. BRepNet defines convolutional kernels with respect to oriented coedges in the data structure. In the neighborhood of each coedge, a small collection of faces, edges and coedges can be identified and patterns in the feature vectors from these entities detected by specific learnable parameters. In addition, to encourage further deep learning research with B-reps, we publish the Fusion 360 Gallery segmentation dataset. A collection of over 35,000 B-rep models annotated with information about the modeling operations which created each face. We demonstrate that BRepNet can segment these models with higher accuracy than methods working on meshes, and point clouds.

Boundary Representations (B-Reps) are the industry standard in 3D Computer Aided Design/Manufacturing (CAD/CAM) and industrial design due to their fidelity in representing stylistic details. However, they have been ignored in the 3D style research. Existing 3D style metrics typically operate on meshes or point clouds, and fail to account for end-user subjectivity by adopting fixed definitions of style, either through crowd-sourcing for style labels or hand-crafted features. We propose UVStyle-Net, a style similarity measure for B-Reps that leverages the style signals in the second order statistics of the activations in a pre-trained (unsupervised) 3D encoder, and learns their relative importance to a subjective end-user through few-shot learning. Our approach differs from all existing data-driven 3D style methods since it may be used in completely unsupervised settings, which is desirable given the lack of publicly available labeled B-Rep datasets. More importantly, the few-shot learning accounts for the inherent subjectivity associated with style. We show quantitatively that our proposed method with B-Reps is able to capture stronger style signals than alternative methods on meshes and point clouds despite its significantly greater computational efficiency. We also show it is able to generate meaningful style gradients with respect to the input shape, and that few-shot learning with as few as two positive examples selected by an end-user is sufficient to significantly improve the style measure. Finally, we demonstrate its efficacy on a large unlabeled public dataset of CAD models. Source code and data are available at github.com/AutodeskAILab/UVStyle-Net.

Existing methods of unstructured point cloud compression usually exploit the spatial sparseness of point clouds using hierarchical tree data structures for spatial encoding. However, such methods can be inefficient when very deep octrees are applied to sparse point cloud data to maintain low level of geometric error during compression. This paper proposes a novel octree structure called truncated octree that improves the compression ratio by representing the deep octree with a set of shallow sub-octrees which can save storage without losing the original structure. We also propose a variable length addressing scheme, to adaptively choose the length of an octree's node address based on the truncation level-shorter (resp. longer) address when octree is truncated near the leaf (resp. root) which leads to further compression. The method is able to achieve 40% to 90% compression ratio on our tested models for point clouds of different spatial distributions. For extremely sparse point clouds, the method achieves approximately 7 times higher compression ratio than previous methods. Moreover, the method is designed to run in parallel for octree construction, encoding and decoding.

Shading is a tedious process for artists involved in 2D cartoon and manga production given the volume of contents that the artists have to prepare regularly over tight schedule. While we can automate shading production with the presence of geometry, it is impractical for artists to model the geometry for every single drawing. In this work, we aim to automate shading generation by analyzing the local shapes, connections, and spatial arrangement of wrinkle strokes in a clean line drawing. By this, artists can focus more on the design rather than the tedious manual editing work, and experiment with different shading effects under different conditions. To achieve this, we have made three key technical contributions. First, we model five perceptual cues by exploring relevant psychological principles to estimate the local depth profile around strokes. Second, we formulate stroke interpretation as a global optimization model that simultaneously balances different interpretations suggested by the perceptual cues and minimizes the interpretation discrepancy. Lastly, we develop a wrinkle-aware inflation method to generate a height field for the surface to support the shading region computation. In particular, we enable the generation of two commonly-used shading styles: 3D-like soft shading and manga-style flat shading.

We introduce an interactive user-driven method to reconstruct high-relief 3D geometry from a single photo. Particularly, we consider two novel but challenging reconstruction issues: i) common non-rigid objects whose shapes are organic rather than polyhedral/symmetric, and ii) double-sided structures, where front and back sides of some curvy object parts are revealed simultaneously on image. To address these issues, we develop a three-stage computational pipeline. First, we construct a 2.5D model from the input image by user-driven segmentation, automatic layering, and region completion, handling three common types of occlusion. Second, users can interactively mark-up slope and curvature cues on the image to guide our constrained optimization model to inflate and lift up the image layers. We provide real-time preview of the inflated geometry to allow interactive editing. Third, we stitch and optimize the inflated layers to produce a high-relief 3D model. Compared to previous work, we can generate high-relief geometry with large viewing angles, handle complex organic objects with multiple occluded regions and varying shape profiles, and reconstruct objects with double-sided structures. Lastly, we demonstrate the applicability of our method on a wide variety of input images with human, animals, flowers, etc.

Furniture typically consists of assemblies of elongated and planar parts that are connected together by glue, nails, hinges, screws, or other means that do not encourage disassembly and re-assembly. An alternative approach is to use an interlocking mechanism, where the component parts tightly interlock with one another. The challenge in designing such a network of interlocking joints is that local analysis is insufficient to guarantee global interlocking, and there is a huge number of joint combinations that require an enormous exploration effort to ensure global interlocking. In this paper, we present a computational solution to support the design of a network of interlocking joints that form a globally-interlocking furniture assembly. The key idea is to break the furniture complex into an overlapping set of small groups, where the parts in each group are immobilized by a local key, and adjacent groups are further locked with dependencies. The dependency among the groups saves the effort of exploring the immobilization of every subset of parts in the assembly, thus allowing the intensive interlocking computation to be localized within each small group. We demonstrate the effectiveness of our technique on many globally-interlocking furniture assemblies of various shapes and complexity.

This paper addresses a challenging single-view modeling and animation problem with cartoon images. Our goal is to model the hairs in a given cartoon image with consistent layering and occlusion, so that we can produce various visual effects from just a single image. We propose a novel 2.5D modeling approach to deal with this problem. Given an input image, we first segment the hairs of the cartoon character into regions of hair strands. Then, we apply our novel layering metric, which is derived from the Gestalt psychology, to automatically optimize the depth ordering among the hair strands. After that, we employ our hair completion method to fill the occluded part of each hair strand, and create a 2.5D model of the cartoon hair. By using this model, we can produce various visual effects, e.g., we develop a simplified fluid simulation model to produce wind blowing animations with the 2.5D hairs. To further demonstrate the applicability and versatility of our method, we compare our results with real cartoon hair animations, and also apply our model to produce a wide variety of hair manipulation effects, including hair editing and hair braiding.

This paper presents a novel method that interactively recognizes and vectorizes hand-drawn strokes in front of a commodity webcam. Compared to existing methods, which recognize strokes on a completed drawing, our method captures both spatial and temporal information of the strokes, and faithfully vectorizes them with timestamps. By this, we can avoid various stroke recognition ambiguities, enhance the vectorization quality, and recover the stroke drawing order.