Parametric Computer-Aided Design Programs

Modern engineering systems, from automobiles to aircraft, are designed by using precise, continuous parametric computer-aided design (CAD) models. Evaluating design changes through numerical simulation requires meshing the continuous geometry, a computationally expensive and often brittle process that can require manual intervention and replaces the continuous representation with a discrete approximation. Most neural surrogates accelerate the simulation, but inherit this representation gap by relying on meshes, point clouds, voxels, or other sampled approximations of geometry. We introduce CANTO, a transformer neural operator that maps directly from continuous CAD geometry to physical fields, without meshing the input geometry. We develop a theoretical framework for learning operators from geometric manifolds to function spaces of physical fields, representing geometry through sequences of parametric patches. CANTO instantiates this framework by directly tokenizing non-uniform rational B-spline (NURBS) patches from their control points, knot vectors, and weights, and predicts continuous surface and volume fields at arbitrary query locations. We evaluate CANTO on four automotive and aircraft aerodynamics industry benchmarks: AhmedML, WindsorML, DrivAerML, and HiLiftAeroML. CANTO achieves state-of-the-art accuracy on most evaluated surface and volume prediction tasks, including a 19.8% reduction in surface-pressure relative $L_2$ error compared with AB-UPT on HiLiftAeroML. Differentiability with respect to CAD parameters further enables gradient-based inverse design of designs. On AhmedML, CANTO identifies designs with 4.4 to 20.4% lower drag than the best dataset designs satisfying the same volume and lift constraints, with the improvements verified using the same CFD setup used to generate the original dataset.

Assembly Sequence Planning (ASP) remains a challenging problem due to its combinatorial nature, making exhaustive planning approaches impractical for complex industrial assemblies. Furthermore, many CAD models lack reliable semantic contact information or require extensive manual preprocessing, limiting the applicability of existing methods. This paper presents a hybrid ASP framework combining learning-based relation extraction with geometric-symbolic reasoning to generate feasible robotic disassembly sequences from imperfect CAD data. A neural network predicts semantic geometric relations from point clouds, while human-in-the-loop verification enables correction of uncertain predictions and planning failures. Extracted relations are transformed into a symbolic assembly graph, enabling a geometric-symbolic planner to efficiently compute locally valid sets of robotic manipulation primitives. A visibility-based ray-casting strategy guides the search for feasible disassembly directions without requiring an exhaustive combinatorial search, while the local solution space enables efficient sequence optimization. The framework is evaluated on an introduced assembly dataset and on the ASAP test dataset. On the ASAP test dataset, the proposed planner achieves an 85.83% planning success rate while reducing the median planning time by more than one order of magnitude across all assembly sizes and by more than a factor of 50 for assemblies with more than 30 components compared to the baseline. The results demonstrate that the proposed hybrid framework enables efficient robotic assembly sequence planning from imperfect CAD data while substantially reducing planning time. By combining learning-based feature segmentation, human-in-the-loop verification, and geometric-symbolic reasoning, the framework provides a practical foundation for scalable and adaptable robotic assembly and disassembly planning.

Generative CAD models are expected to remain behaviorally correct after parameter edits, so increasing the number of edit checks is often treated as a direct route to more reliable evaluation. Under a fixed budget, however, auditing each program more thoroughly reduces the number of tasks and independent generations that can be evaluated, which can ultimately make model-level estimates less accurate. We study this phenomenon and the conditions under which it arises. We decompose behavioral evaluation into three evidence levels: task templates, stochastic generations, and within-program edits. We define an average failure risk that is invariant to audit depth, and combine three-level variance with measured execution costs to analyze the tradeoff between deeper edit auditing and broader independent coverage. Experiments across two CAD environments and five generation systems show that the value of deeper auditing depends on where evaluation uncertainty originates. When template heterogeneity or generation stochasticity dominates, additional edit checks can increase total estimation error; when within-program state variation is large and generation is expensive, deeper auditing is more valuable. Variance and cost estimates from calibration predict the direction of this change and provide a diagnostic basis for allocating evidence on held-out tasks. These results show that the thoroughness of program inspection can diverge from the reliability of model evaluation, and they help determine whether the next unit of budget should be spent on a new task, a new generation, or additional edit checks.

Parametric computer-aided design (CAD) modeling is difficult to evaluate with a single metric. Existing CAD benchmarks often emphasize synthetic or CAD-native settings, limited input modalities, or executability and IoUs alone. We introduce RealCADBench, a benchmark for intent-to-program CAD modeling from real industrial design intents. It contains 12,632 tasks from 19 factory-automation categories and spans text descriptions, 2D engineering drawings, real product pictures, and rendered images for both Part and Assembly modeling. We report results on a 1,770-task evaluation slice: 1,745 Part tasks across four input regimes and RCB-Assm25, a 25-task assembly study used in every reported assembly comparison. Each method generates FreeCAD API Python, which a shared runtime executes to export the 3D model. We evaluate the exported model using executability, Solid IoU, Surface IoU, and a rubric-based visual-semantic identity Judge. Among the nine standalone frontier large models evaluated, no model leads all four metrics. Across six frontier-scale large models, executability ranges from 0.565 to 0.812, Solid IoU from 0.2841 to 0.5379, and Surface IoU from 0.112 to 0.217 across the four Part regimes. The highest regime-balanced composite comes from a different model than the leaders on the four component metrics. On RCB-Assm25, Codex with GPT-5.5 improves executability and both IoU metrics over standalone GPT-5.5, but lowers the Judge score by 6.98 percentage points, leaving GPT-5.5 as the Judge leader. We also observe recurring failure modes, most notably missing fine structures, loss of part identity, and incorrect assembly placement. These results show that execution alone is insufficient to characterize realistic CAD modeling and that frontier models and agents differ substantially across executability, IoUs, and visual-semantic identity.

Large language models can write parametric CAD programs from a natural-language description (text-to-CAD generation), but a single sample is often wrong. Increasing test-time compute by sampling multiple candidates only helps if a good candidate can be identified, yet no ground-truth model is available at generation time. Existing systems often require a separate verifier, such as a vision-language judge, to select among candidates. We investigate whether the candidate pool itself provides enough signal for effective selection and a verifier-free alternative. We introduce 3D CAD consensus selection, hereafter consensus selection: sample $N$ parametric CAD programs, compile them to 3D models, and return the candidate that agrees most with the rest of the pool. The method is training-free and compatible with existing CAD agents. We investigate geometric and topological notions of agreement, each of which improves its corresponding evaluation metric. On the exact candidate pools of a state-of-the-art CAD generation method, geometric consensus improves all three geometric metrics over the method's verifier, while topological consensus matches it on topology. Across every tested LLM and prompt variant, geometric consensus also improves geometric accuracy over random selection from the same pool, reducing Chamfer distance by $1-10\%$.

Injection molding is the cornerstone of mass-producing plastic components. While current algorithms can automate mold design for basic geometries using standard two-piece molds, complex parts featuring undercuts, side holes, or re-entrant features present a significant challenge. These geometries often necessitate auxiliary components beyond the primary upper and lower molds. In practice, designing these intricate assemblies is a laborious process that relies heavily on expert knowledge. Furthermore, the scarcity of public datasets has hindered the development of effective learning-based solutions. To bridge these gaps, we introduce MoldCAD, a curated dataset that pairs complex single-body CAD parts with industry-standard mold assemblies. Each entry includes the upper and lower molds, parting surfaces, demolding orientations, and necessary auxiliary components. The dataset comprises 4,934 CAD models and over 3,850 mold assemblies, totaling more than 23k individual models. Building upon this dataset, we propose a comprehensive pipeline that predicts demolding orientations, identifies auxiliary components, and constructs parting surfaces to derive a complete, manufacturing-ready mold assembly for downstream CAD/CAM workflows. Our results demonstrate a promising path toward fully automated industrial mold design and contribute to the broader advancement of manufacturing-aware CAD generation.

Computer-Aided Design (CAD) underpins modern engineering, yet converting existing shapes into editable models still demands substantial expert effort. Most AI systems emit the entire CAD program in a single pass, never inspecting the intermediate geometry. In contrast, human engineers build a part feature by feature, checking after each operation what remains to be modeled. We introduce CADENA (Spanish for "chain"), a model that reconstructs a 3D mesh as a parametric CAD program, growing its sequence of operations one at a time and comparing the target with the currently predicted geometry at every step. We also address the lack of benchmarks for evaluating reverse-engineering methods on mechanical parts, introducing CADENA-Bench, a benchmark that measures performance across categories of mechanical parts. CADENA outperforms prior methods on CADENA-Bench and on the DeepCAD, Fusion 360, and MCB datasets. Code is available at https://github.com/zhemdi/cadena, model weights at https://huggingface.co/kulibinai/cadena, and CADENA-Bench at https://huggingface.co/datasets/kulibinai/cadena-bench.

Recovering Parametric CAD sequences from raster-format 2D Computer-Aided Design (CAD) drawings accumulated prior to digital transformation is important for part reproduction and manufacturing process automation. However, existing studies either process only vector drawings or are limited to specific domains, and fail to explicitly connect dimensional annotations to geometric information, limiting their use of dimensional information for 3D Parametric CAD sequences recovery. We propose Drawing-Recode, a framework that generates Parametric CAD sequences as CAD code from raster 2D CAD drawings. Drawing-Recode extracts geometric features via an image encoder and recognizes annotations through a separate text recognition module, then explicitly grounds annotations to geometric information using cross-attention and our proposed Annotation Grounding Loss (AGL). The resulting features are fed into a Large Language Model (LLM) to generate CAD code in the Structured Parametric CAD Code (SPCC) format. Experiments show that Drawing-Recode outperforms existing baselines and remains robust on scanned drawings resembling industrial conditions. We expect Drawing-Recode contributes to digitizing raster 2D CAD drawings in industrial settings and to part reproduction and manufacturing automation.

We provide a novel end-to-end framework for the execution of an assembly operation by two robotic arms, given the digital CAD models of the parts and their desired relative placement in their assembled state. We analyze and demonstrate the advantages of using two robotic arms simultaneously in tight assembly operations, compared to single-arm systems. Our method is implemented in both simulation and using physical robots. It provides theoretical guarantees on execution time and trajectory accuracy, supported by empirical evidence. In particular, we show that coordinated movement of two arms reduces average execution time by more than 50% compared to using a single arm only, produces higher-quality trajectories, and accelerates the search for valid robot placements. Furthermore, we establish bounds on the required dimensions of the robotic cell. Our open source software together with real-life video demonstrations are available in our project page.

Generative CAD modeling has broad design and application potential. Despite significant advances in Boundary Representation (B-Rep) generation, the dominant representation in CAD, existing methods largely depend on uniformly sampled point- or grid-based geometry representations, sacrificing native surface types and parameters and thereby limiting geometric fidelity and downstream usability. We present ParaCAD, an autoregressive framework for point-cloud-conditioned B-Rep generation that directly operates on native parametric surfaces. ParaCAD introduces a surface-centric tokenization that explicitly encodes each face by its exact surface type and continuous parameters, preserving the intrinsic semantics of CAD geometry. Our model first generates parametric surfaces with constrained UV domains, and then constructs a valid B-Rep by globally intersecting these surfaces to recover edges and vertices. ParaCAD places point-cloud-conditioned generation at the core of B-Rep synthesis, making it practical for user-guided reconstruction and seamless integration into existing 3D generation pipelines. Extensive experiments demonstrate that ParaCAD produces accurate B-Reps with faithful point-cloud alignment, outperforming point-based baselines in geometric precision, robustness, watertightness and downstream usability.

Large language models can write plausible CAD scripts, but reliable industrial CAD modeling requires more than syntactically valid code: every feature, placement, and assembly relation must be accepted by an exact geometric kernel while remaining editable as parametric boundary representation geometry. We present Embodied CAD, solver-grounded LLM agents for parametric B-Rep assembly modeling. Instead of generating a complete script in one pass, the agent iteratively selects actions from a stratified L0-L4 CAD skill library, resolves them into typed geometric operations, executes them in a CAD backend, and uses solver feedback to plan, repair, and learn. The framework combines action grammar constraints, deterministic parameter resolution, and solver-derived rewards for supervised warm-up and GRPO-style refinement. We evaluate Embodied CAD on multi-step mechanical, industrial equipment, and mold-oriented assembly tasks using solver-aligned metrics: executable rate, skill accuracy, operation-family accuracy, exact policy accuracy, and task completion success. The results show that solver-grounded planning executes all strong-planner workflows in the current benchmark, while learned controllers reach high executable rates and expose the remaining gap between valid tool calls and exact long-horizon policy prediction.

Text-to-3D systems can now synthesize a model from a single sentence, yet the result is a shape to render, not a design to edit. We present Arko-T, a 4B-parameter text-to-design model that maps natural-language intent directly into executable, parametric CAD programs. Rather than optimizing for code executability alone, Arko-T aligns every stage of the pipeline to a formal notion of design state, so that data curation, code normalization, and execution-grounded supervision all work to preserve the features, parameters, and construction logic that make a CAD artifact editable. Benchmarked against seven frontier LLMs across 12 metrics, Arko-T attains the best score on 8 and the second-best on 3 more, at roughly one-tenth the per-benchmark cost. The results suggest that targeted design-level training at moderate scale can match frontier general-purpose models on structured CAD generation.

Accurate registration of CAD models to CT scans is essential for establishing ground truth geometry in volumetric imaging. Obtaining reliable object masks is of growing importance in machine learning settings; as recent architectures grow more capable, huge datasets are required to fully utilise their capabilities. Traditional intensity-based methods fail when CT grayscale values lack calibration references, while point-based algorithms (e.g., ICP, RANSAC) require feature correspondence unavailable between idealized CAD geometry and noisy volumetric CT data. We propose a two-stage geometric registration method for cylindrical objects (ionization chambers) that takes advantage of the distinctive geometric features of the objects. First, we estimate the 3D rotation axis by detecting elliptical cross-sections across CT slices, fitting ellipses to edge-detected contours, and performing PCA on the fitted ellipse centers after RANSAC outlier removal. Second, we voxelize the CAD model, orient it along the detected axis, and maximize volumetric overlap with the CT scan through translational adjustment. This approach achieves robust registration with tilt and orientation errors below $0.1^\circ$ without intensity calibration or feature matching. Once registered, the aligned CAD model provides ground truth geometry for applications including machine learning-based object localization and automated analysis in industrial CT workflows.

Mid-surface abstraction is an important preprocessing step for finite element analysis of thin-walled CAD models, and face pairing is its central subproblem. Existing face-pairing methods rely on handcrafted geometric criteria whose thresholds are hard to tune when a model has multiple local wall thicknesses; their groupings depend on threshold settings and processing order, so the same model can yield inconsistent results. We present MidSurfNet, a learning-based face-pairing method that couples a learned face-pair scorer with a deterministic face-group composition. The scorer evaluates every unordered face pair with two separately learned evidence streams: a geometry stream combining continuous pairing criteria with a conditional shape correction, and an attributed-topology stream over the B-Rep face-adjacency graph. A pair-conditioned gate fuses the two streams, and independent per-pair decisions retain opposing-face support relations at one operating threshold selected once on validation data, replacing rather than adding to the per-model thresholds of rule-based pipelines. Under a connected-and-bipartite condition, the composition stage organizes the retained relations into variable-cardinality m-to-n face groups, each independent of processing order for a fixed support graph and unique up to its two side labels. We also construct the MidSurf dataset, a benchmark of 1,575 manually annotated CAD models. On the test set, MidSurfNet attains a pair-level F1-Score of 87.32%, 23.22 percentage points above the strongest rule-based baseline, and an end-to-end Completion Rate of 75.42%, including 61.90% on the multi-wall-thickness category the evaluated rule-based implementations do not support. We demonstrate practical utility by generating mid-surfaces from the composed face groups through an industrial mid-surface API and running finite element analyses on the resulting shell models.

Large language models (LLMs) have recently advanced text-driven 3D generation, yet Text-to-CAD remains far from supporting industrial product design. Existing benchmarks focus primarily on generating single-part CAD models and evaluate them using geometric similarity metrics that fail to capture functionality, manufacturability, and assemblability. To address this gap, we introduce MUSE, a Text-to-CAD benchmark focused on complex, editable boundary representation (B-Rep) assemblies. MUSE pairs practical design instances with structured Design Specifications and evaluates generated models through a three-stage protocol: code check, geometric check, and design-intent alignment. The final stage uses design-specific rubrics to assess functionality, manufacturability, and assemblability, moving beyond shape matching toward practical design quality. To enable scalable evaluation, we use a rubric-based visual language model (VLM) judge and validate its reliability through human annotation. Experiments on closed-source and open-source LLMs reveal a clear failure cascade from executable code to valid geometry and finally to engineering-ready design, with even the strongest models achieving limited success on fine-grained engineering criteria. Together, MUSE provides a realistic benchmark and evaluation framework for advancing Text-to-CAD from geometric generation toward true engineering design. Our project website, including the leaderboard, dataset, and code, is available at https://dong7313.github.io/muse-benchmark/.

Hexahedral meshes are widely used in simulation pipelines, yet automatic generation remains challenging for complex CAD geometries. Polycube-based hexahedral meshing is a representative approach due to its regular, parameterization-friendly structure, but existing polycube construction methods often rely on intricate surface segmentation and local heuristics, which can produce artifacts or fail on difficult shapes. In this paper, we propose an end-to-end framework for polycube generation based on conditional diffusion models. Given an input geometry represented as a point cloud, our method directly produces a corresponding polycube point cloud, eliminating the need for explicit surface segmentation or predefined polycube templates. At the core of our approach is a dual-latent conditional diffusion architecture that confines computationally expensive self-attention operations to a fixed-capacity, low-dimensional latent space. This design effectively decouples computational complexity from the resolution of both the input geometry and the output polycube, thereby avoiding the quadratic cost typical of point cloud self-attention mechanisms while supporting flexible input and output resolutions. To obtain a hexahedral mesh, the generated polycube is aligned to the input shape via rigid and non-rigid point cloud registration to establish surface correspondence, followed by a polycube-to-hex pipeline. We additionally create and release a paired dataset of CAD meshes and their corresponding polycube meshes, together with the core implementation of our model. Experiments show that PolycubeNet generalizes to complex CAD models with arbitrary genus and produces high-quality polycube structures within seconds, improving robustness and efficiency over prior learning-based approaches.

Text-to-CAD generation aims to create parametric CAD models from natural language, enabling rapid prototyping and intuitive design workflows. However, existing benchmarks focus on basic primitives and simple sketch-extrude sequences, lacking advanced features essential for real-world applications and covering only traditional mechanical parts. We introduce Text2CAD-Bench, the first benchmark systematically evaluating text-to-CAD across geometric complexity and application diversity. Our benchmark comprises 600 human-curated examples spanning four levels: L1-L2 cover fundamental geometry with standard features, L3 introduces complex topology and freeform surfaces, and L4 extends to real-world domains beyond mechanical parts. Each example pairs dual-style prompts -- geometric descriptions mimicking non-expert users, and procedural sequences aligned with expert-level conventions. Evaluating mainstream general LLMs and domain-specific models, we find that current models perform reasonably on basic geometry but degrade substantially on complex topology and advanced features. We release our benchmark to drive progress in text-to-CAD research.

Industrial Computer-Aided Design (CAD) code generation requires models to produce executable parametric programs from visual or textual inputs. Beyond recognizing the outer shape of a part, this task involves understanding its 3D structure, inferring engineering parameters, and choosing CAD operations that reflect how the part would be designed and manufactured. Despite the promise of Multimodal large language models (MLLMs) for this task, they are rarely evaluated on whether these capabilities jointly hold in realistic industrial CAD settings. We present BenchCAD, a unified benchmark for industrial CAD reasoning. BenchCAD contains 17,900 execution-verified CadQuery programs across 106 industrial part families, including bevel gears, compression springs, twist drills, and other reusable engineering designs. It evaluates models through visual question answering, code question answering, image-to-code generation, and instruction-guided code editing, enabling fine-grained analysis across perception, parametric abstraction, and executable program synthesis. Across 10+ frontier models, BenchCAD shows that current systems often recover coarse outer geometry but fail to produce faithful parametric CAD programs. Common failures include missing fine 3D structure, misinterpreting industrial design parameters, and replacing essential operations such as sweeps, lofts, and twist-extrudes with simpler sketch-and-extrude patterns. Fine-tuning and reinforcement learning improve in-distribution performance, but generalization to unseen part families remains limited. These results position BenchCAD as a benchmark for measuring and improving the industrial readiness of multimodal CAD automation.

Despite recent progress, recovering parametric CAD construction sequences from geometric input, such as meshes or point clouds, is a key challenge for design and manufacturing, as existing CAD reconstruction and generation methods are largely restricted to difficult-to-edit formats like meshes or Breps or editable simple sketch-and-extrude pipelines and low-complexity datasets. We introduce CADFit, a hybrid optimization-based CAD reconstruction framework that recovers complex, editable CAD construction sequences from meshes by incrementally fitting and validating parametric operations using geometric feedback. Our approach is distinguished by formulating reconstruction as an IoU-driven optimization over structured CAD programs and supporting a rich set of operations, including extrusions, revolutions, fillets, and chamfers. Experiments on multiple CAD benchmarks show that CADFit outperforms state-of-the-art mesh-to-CAD methods in volumetric Intersection-over-Union and Chamfer Distance, while substantially reducing the Invalid Ratio of reconstructed CAD programs, particularly for complex designs. We further present a multimodal pipeline that enables end-to-end reconstruction of CAD construction sequences from images by combining image-based geometry reconstruction with CADFit. By enabling accurate reconstruction of higher-complexity CAD models, CADFit provides a practical foundation for generating richer datasets and advancing future learning-based approaches to CAD reverse engineering. The code is available at: https://github.com/ghadinehme/CADFit.

Computer-aided design (CAD) is vital to modern manufacturing, yet model creation remains labor-intensive and expertise-heavy. To enable non-experts to translate intuitive design intent into manufacturable artifacts, recent large language models-based text-to-CAD efforts focus on command sequences or script-based formats like CadQuery. However, these formats are kernel-dependent and lack universality for manufacturing. In contrast, the Standard for the Exchange of Product Data (STEP, ISO 10303) file is a widely adopted, neutral boundary representation (B-rep) format directly compatible with manufacturing, but its graph-structured, cross-referenced nature poses unique challenges for auto-regressive LLMs. To address this, we curate a dataset of ~40K STEP-caption pairs and introduce novel preprocessing tailored for the graph-structured format of STEP, including a depth-first search-based reserialization that linearizes cross-references while preserving locality and chain-of-thought(CoT)-style structural annotations that guide global coherence. We integrate retrieval-augmented generation to ground predictions in relevant examples for supervised fine-tuning, and refine generation quality through reinforcement learning with a specific Chamfer Distance-based geometric reward. Experiments demonstrate consistent gains of our STEP-LLM in geometric fidelity over the Text2CAD baseline, with improvements arising from multiple stages of our framework: the RAG module substantially enhances completeness and renderability, the DFS-based reserialization strengthens overall accuracy, and the RL further reduces geometric discrepancy. Both metrics and visual comparisons confirm that STEP-LLM generates shapes with higher fidelity than Text2CAD. These results show the feasibility of LLM-driven STEP model generation from natural language, showing its potential to democratize CAD design for manufacturing.

Recovering the 9D pose of objects, both their 6D pose and 3D dimensions, under clutter and occlusion is a core requirement for warehouse automation, logistics, and manufacturing. Model-based methods are accurate but assume an instance-specific CAD model for every object, which is costly to maintain as inventories change. Model-free and category-level methods relax this assumption, yet they remain vulnerable to the symmetry, weak texture, and heavy occlusion that characterize stacked storage boxes, and they ignore the strong structural priors such scenes provide. We present \textbf{AnyBox}, an efficient zero-shot framework that exploits the geometric regularity of boxes to jointly recover pose and dimensions from a single RGB-D observation. Starting from a canonical category template, AnyBox alternates between pose and scale estimation, using the discrepancy between the reprojected template and the observed mask to drive a binary search over box dimensions. Two lightweight components make this practical: a depth-consistency filter that rejects the implausible hypotheses induced by box symmetry, and an early-stopping rule that replaces the remaining search with a single closed-form update. On public benchmarks and an in-house warehouse dataset, AnyBox improves detection AP by up to 36 points, more than doubling the previous best, and approaches instance-level pipelines that have access to ground-truth CAD models. These gains transfer downstream, raising success by 28% on a cluttered robotic box-shelving task.