Differentiable NURBS B-Rep: Feasibility Assessment¶
Abstract¶
This document assesses the feasibility of extending BRepAX from analytical primitives to general NURBS surfaces while preserving topology-aware (stratum-dispatched) gradients through Boolean operations. A literature survey of 23 papers across seven research communities -- differentiable NURBS, CAD kernel AD, differentiable CSG, neural B-Rep generation, isogeometric analysis, differentiable physics, and topology-aware methods -- confirms that no existing system simultaneously satisfies three criteria: (1) NURBS parametric structure preservation with control points as design variables, (2) topology-aware transition handling at Boolean boundaries, and (3) end-to-end differentiable B-Rep kernel semantics.
The gap is structural, not incremental. The IGA community differentiates through NURBS but assumes fixed patch topology. The CSG community handles topology changes but operates on SDF, mesh, or occupancy representations rather than NURBS. No bridge exists between these two bodies of work. BRepAX's stratum dispatch mechanism -- validated on analytical primitives -- provides precisely this bridge: it translates the topology-change problem into a contact-dynamics formulation that is representation-agnostic.
A minimum viable prototype is defined: single NURBS patch SDF approximation via iterative closest-point projection, differentiated through the implicit function theorem, with stratum detection via grid sampling. The principal technical risk is convergence and differentiability of the iterative projection. The prototype is scoped to validate the approach before committing to a full NURBS Boolean pipeline.
Research Question¶
Is a differentiable NURBS B-Rep kernel with topology-aware gradients unprecedented, and is it tractable?
The question decomposes into three orthogonal criteria that any system must satisfy simultaneously to qualify as a differentiable NURBS B-Rep:
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NURBS parametric structure preservation. Control points, weights, and knot vectors serve as first-class design variables. Gradients flow back to these parameters. This excludes systems that discretize NURBS into meshes or SDFs before differentiation.
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Topology-aware transition handling. The system provides correct gradient information at Boolean boundaries where the topological configuration changes (faces appear, disappear, or merge). This excludes fixed-topology optimization and smooth approximations that introduce systematic bias.
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Differentiable B-Rep kernel semantics. Boolean operations (union, intersection, subtraction) are differentiable end-to-end, producing gradients of geometric outputs (volume, area, SDF) with respect to input shape parameters. This excludes forward-only CAD systems and generation models that do not support gradient-based optimization.
The survey below evaluates each identified system against these three criteria.
Literature Survey¶
Differentiable NURBS and Spline Optimization¶
NURBS-Diff (Prasad et al., Computer-Aided Design, 2022). Derives closed-form partial derivatives of NURBS surface evaluation with respect to control points, weights, and knot vectors, implemented in PyTorch. Demonstrates inverse fitting of individual NURBS surfaces from point clouds. Satisfies criterion (1) for single surfaces but does not address Boolean operations or topology changes. The system operates on isolated patches with no CSG pipeline.
THB-Diff (Moola et al., Engineering with Computers, 2024). Extends differentiable spline fitting to truncated hierarchical B-splines (THB-splines), enabling adaptive refinement during optimization. Handles multi-resolution control grids but remains within the single-patch or fixed-topology setting. No Boolean operations. Satisfies criterion (1) with hierarchical enrichment but not criteria (2) or (3).
Worchel and Alexa (SIGGRAPH Asia, 2023). Differentiable tessellation of NURBS surfaces for integration into neural rendering pipelines. Gradients flow from rendered images back to NURBS control points through a differentiable rasterization layer. The tessellation step itself is differentiated, but the system targets rendering, not CAD Boolean operations. Satisfies criterion (1) in the rendering context; criteria (2) and (3) are outside scope.
Algorithmic Differentiation of CAD Kernels¶
Mueller et al. (Computer Methods in Applied Mechanics and Engineering, 2018). Applies ADOL-C (operator-overloading algorithmic differentiation) to the Open CASCADE Technology (OCCT) kernel, computing shape sensitivities of NURBS-based geometries for structural optimization. Differentiates through NURBS evaluation, intersection computation, and meshing. This is the closest existing work to criteria (1) and (3) combined: it differentiates a real CAD kernel with NURBS surfaces as design variables. However, the topology of the B-Rep is fixed throughout optimization -- face counts, edge connectivity, and vertex incidence do not change. Topology changes (e.g., a fillet disappearing as its radius approaches zero) cause the differentiation to fail. Criterion (2) is not addressed.
Differentiable CSG and Boolean Operations¶
DiffCSG (Yuan et al., SIGGRAPH Asia, 2024). Differentiable CSG via rasterization: renders CSG trees by compositing depth buffers of mesh primitives using differentiable min/max operations. Supports union, intersection, and subtraction with gradient flow through the CSG tree structure. Operates on triangle meshes, not NURBS. Satisfies criterion (3) for mesh representations and partially addresses criterion (2) through rasterization-based boundary handling, but does not satisfy criterion (1).
Fuzzy Boolean (Liu et al., SIGGRAPH, 2024). Replaces crisp Boolean operations with continuous t-norm and t-conorm compositions on occupancy fields. The fuzzy transition region enables gradient flow across topology changes. Operates on implicit (occupancy) representations; NURBS structure is not preserved. Partially satisfies criteria (2) and (3) in the occupancy domain; does not satisfy criterion (1).
TreeTOp (2025). JAX-based CSG tree topology optimization. Optimizes both primitive parameters and tree structure using differentiable relaxations of discrete Boolean operations over SDF primitives. Demonstrates end-to-end gradient flow through CSG trees but uses analytical SDF primitives (spheres, boxes, cylinders), not NURBS. Satisfies criterion (3) for SDF primitives; criterion (1) is outside scope.
D2CSG (Yu et al., NeurIPS, 2023). Learns compact CSG tree representations from 3D shapes using a two-stage decomposition: first extracting primitives, then assembling a Boolean expression tree. Uses neural implicit primitives. Satisfies criterion (3) partially (the CSG assembly is differentiable) but not criteria (1) or (2).
CSG-Stump (Ren et al., ICCV, 2021) and CAPRI-Net (Yu et al., CVPR, 2022). Fixed-structure CSG assembly methods. CSG-Stump uses a three-layer (primitive, intersection, union) architecture equivalent to disjunctive normal form. CAPRI-Net extends this with neural half-spaces. Both learn Boolean connection weights from occupancy supervision. The fixed structure sidesteps topology change handling. Satisfy criterion (3) in a restricted sense; do not address criteria (1) or (2).
Neural B-Rep Generation¶
BrepGen (Xu et al., SIGGRAPH, 2024). Generative model for B-Rep solid models using hierarchical diffusion over faces, edges, and vertices. Produces topologically valid B-Rep structures but is a generation model, not a differentiable kernel. No gradient-based optimization of generated shapes is supported.
HoLa (Transactions on Graphics, 2025). Holistic B-Rep generation with local and global attention mechanisms. Improves topological consistency of generated B-Rep models. Again a generation model without differentiable kernel semantics.
DTGBrepGen (Li et al., CVPR, 2025). Diffusion-based B-Rep generation with topology-geometry coupling. Generates B-Rep models with explicit topological structure. Does not provide differentiable Boolean operations.
NeuroNURBS (Lu et al., 2024). Neural NURBS representation learning for shape reconstruction. Encodes shapes as collections of NURBS patches predicted by a neural network. Represents NURBS structure but does not differentiate through Boolean operations.
NURBGen (AAAI, 2026). Generates NURBS-based CAD models from point clouds. Preserves NURBS parametric structure in the output but operates as a feed-forward generation model, not an optimization kernel.
None of these generation models satisfy criterion (2) or (3). They produce B-Rep or NURBS outputs but do not support gradient-based optimization through CSG operations.
Isogeometric Analysis and Shape Optimization¶
IGA with Algorithmic Differentiation (FEniCS-based, 2025). Isogeometric analysis uses NURBS basis functions directly as finite element shape functions, eliminating mesh-induced approximation error. Recent work integrates AD frameworks (JAX, FEniCS/dolfin-adjoint) to compute shape sensitivities with respect to NURBS control points for structural optimization. Satisfies criterion (1) comprehensively. However, the patch topology (number of patches, connectivity, trimming configuration) is fixed throughout optimization. Adding or removing geometric features requires manual re-parameterization. Criterion (2) is not addressed.
Zhao et al. (Computer Methods in Applied Mechanics and Engineering, 2024). NURBS shell patches with moving intersection curves. Computes shape sensitivities for shell structures where patch intersections shift during optimization. This is the closest IGA work to criterion (2): the intersection geometry changes, though the patch topology itself (number of patches, which patches intersect) remains fixed. The moving intersection is handled within the FEM context, not as a general Boolean operation. Satisfies criterion (1) and partially satisfies criterion (2); does not satisfy criterion (3) in the B-Rep kernel sense.
Differentiable Physics and Contact Dynamics¶
Du et al. (ICML, 2022). DiffPD: differentiable projective dynamics for soft-body simulation with contact. Demonstrates that contact events -- where the topology of the contact graph changes discontinuously -- can be differentiated through using complementarity-aware gradient formulations. The mathematical structure of contact (linear complementarity problems, normal cone inclusions) provides the theoretical foundation for BRepAX's stratum dispatch: Boolean boundary events in CAD are isomorphic to contact events in physics simulation.
Zhong et al. (L4DC, 2023). Extends contact-aware differentiation to rigid body systems with frictional contact. Provides convergence analysis for gradient estimators at contact transitions. The stratum structure of contact modes (sliding, sticking, separating) maps directly to the stratum structure of Boolean configurations (disjoint, intersecting, contained).
DreamCAD (2025). Text-to-CAD generation using differentiable Bezier patch rendering. Operates on Bezier patches (a NURBS subset) with gradient flow from rendered images to patch control points. Partially satisfies criterion (1) for Bezier surfaces. Does not implement Boolean operations or topology change handling.
Topology-Aware Computational Methods¶
DMesh (Son and Gadelha, NeurIPS, 2024). Differentiable mesh representation that supports topology changes (genus modification, component splitting/merging) during optimization. Uses a weighted Delaunay triangulation with differentiable vertex weights to control connectivity. Demonstrates that topological transitions in discrete geometry can be made differentiable. Operates on triangle meshes, not NURBS. Satisfies criterion (2) for mesh topology; does not address criteria (1) or (3).
Persistent Homology for Topology Optimization (ICLR, 2025). Uses differentiable persistent homology to control topological features (holes, voids, connected components) during density-based topology optimization. Provides gradients of topological invariants (Betti numbers) with respect to density fields. Addresses topological awareness in a fundamentally different representation (density fields) from B-Rep. Relevant as a theoretical reference for topology-aware gradient computation but not directly applicable to NURBS B-Rep.
PartSDF (EPFL, 2025). Part-based SDF composition for shape representation. Decomposes shapes into semantic parts, each represented as an SDF, and composes them using differentiable Boolean-like operations. Operates in the SDF domain; NURBS structure is not preserved.
Assessment Matrix¶
| System | (1) NURBS Params | (2) Topology-Aware | (3) Diff. B-Rep Kernel |
|---|---|---|---|
| NURBS-Diff (2022) | Yes | -- | -- |
| THB-Diff (2024) | Yes | -- | -- |
| Worchel-Alexa (2023) | Yes | -- | -- |
| Mueller et al. (2018) | Yes | -- | Partial |
| DiffCSG (2024) | -- | Partial | Yes |
| Fuzzy Boolean (2024) | -- | Partial | Partial |
| TreeTOp (2025) | -- | -- | Yes |
| D2CSG (2023) | -- | -- | Partial |
| CSG-Stump (2021) | -- | -- | Partial |
| CAPRI-Net (2022) | -- | -- | Partial |
| BrepGen (2024) | -- | -- | -- |
| HoLa (2025) | -- | -- | -- |
| DTGBrepGen (2025) | -- | -- | -- |
| NeuroNURBS (2024) | Partial | -- | -- |
| NURBGen (2026) | Partial | -- | -- |
| IGA + AD (2025) | Yes | -- | -- |
| Zhao et al. (2024) | Yes | Partial | -- |
| Du et al. (2022) | -- | Yes | -- |
| Zhong et al. (2023) | -- | Yes | -- |
| DreamCAD (2025) | Partial | -- | -- |
| DMesh (2024) | -- | Yes | -- |
| PH-TopOpt (2025) | -- | Partial | -- |
| PartSDF (2025) | -- | -- | Partial |
Key: Yes = fully satisfies; Partial = addresses in a restricted setting or different representation; -- = not addressed.
No system achieves Yes in all three columns. The closest are Mueller et al. (Yes, --, Partial) and Zhao et al. (Yes, Partial, --), each missing one criterion entirely.
Gap Analysis¶
The Structural Divide¶
The literature reveals a clean separation between two research communities that do not interact:
The IGA/NURBS community (NURBS-Diff, THB-Diff, Mueller et al., IGA+AD, Zhao et al.) operates on NURBS parametric surfaces and computes shape sensitivities via algorithmic differentiation. These systems preserve NURBS structure and provide gradients with respect to control points. However, they universally assume fixed patch topology. The number of faces, their connectivity, and the presence or absence of geometric features remain constant throughout optimization. When topology changes are needed, the user must manually re-parameterize the model.
The CSG/implicit community (DiffCSG, Fuzzy Boolean, TreeTOp, CSG-Stump, CAPRI-Net, D2CSG) handles topology changes through Boolean operations and provides end-to-end gradients through CSG trees. However, these systems operate on meshes, SDFs, or occupancy fields. NURBS parametric structure is discarded at the input stage, and the differentiable pipeline works on the discretized representation.
This divide is not a matter of engineering effort. It reflects a fundamental difference in how each community represents geometry. NURBS are parametric surfaces defined by control nets; SDFs and meshes are spatial discretizations. Converting between them loses information in both directions: NURBS-to-SDF loses exact parametric structure, and SDF-to-NURBS is an ill-posed inverse problem.
The contact dynamics community (Du et al., Zhong et al.) sits orthogonally: it has solved the topology-aware gradient problem for a different domain (contact mechanics) but does not deal with geometric representations at all.
What BRepAX Brings¶
BRepAX's contribution is a bridge mechanism: stratum dispatch. The core insight, validated on analytical primitives, is that Boolean boundary events (where the topological configuration of two shapes changes) are mathematically isomorphic to contact events in physics simulation. The stratum dispatch mechanism (ADR-0004, ADR-0012) classifies the current topological configuration and routes gradients to the appropriate per-stratum formula.
Critically, stratum dispatch is representation-agnostic in its detection phase. ADR-0012 replaced parameter-dependent stratum detection (which required knowing the analytical form of each primitive) with SDF-based grid sampling detection. This means the mechanism extends to any shape representation that can produce SDF values on a grid -- including NURBS surfaces with approximate SDF computation.
The analytical primitive results (concept proof evaluation report) demonstrate the quantitative advantage: Method (C) stratum-aware gradients achieve floating-point precision (relative error below 1e-12), compared to Method (A) smoothing-based gradients which show 5-22% error at boundary proximity. The question is whether this advantage transfers to NURBS, where the SDF itself is approximate rather than analytical.
Minimum Viable NURBS Prototype Design¶
Scope¶
The prototype targets a single, narrowly defined capability: compute the approximate SDF of a single NURBS surface patch and differentiate it with respect to control point positions. This is the minimal unit of work that validates whether NURBS can participate in the existing stratum dispatch framework.
The prototype explicitly excludes: multiple NURBS patches, trim curves, Boolean operations between NURBS shapes, knot vector optimization, and weight optimization. These are deferred until the single-patch SDF computation is validated.
NURBS SDF Computation¶
Unlike analytical primitives (Sphere, Cylinder, Box), a general NURBS surface has no closed-form SDF. The distance from a query point to a NURBS surface requires solving a nonlinear optimization problem: finding the closest point on the surface.
Closest point projection. Given a query point q and a NURBS surface S(u,v), the closest point is:
(u*, v*) = argmin_{u,v} || q - S(u,v) ||^2
This is a nonlinear least-squares problem. Standard approaches use Newton-Raphson iteration on the first-order optimality conditions (the distance vector must be perpendicular to both surface tangents):
(q - S(u,v)) . S_u(u,v) = 0
(q - S(u,v)) . S_v(u,v) = 0
The SDF value is then || q - S(u, v) || with sign determined by the surface normal orientation.
Implicit differentiation for gradient computation. Direct differentiation through the iterative solver (unrolling Newton iterations) accumulates numerical error and has memory cost proportional to iteration count. The implicit function theorem provides an alternative: at convergence, the optimality conditions F(u, v; p) = 0 hold (where p represents control point parameters), and the gradient of u, v with respect to p is:
d(u*,v*)/dp = -[dF/d(u,v)]^{-1} . [dF/dp]
This requires only a single linear solve per gradient evaluation, regardless
of iteration count. JAX provides jax.custom_root and the optimistix
library for exactly this pattern: define a root-finding problem, let the
forward pass iterate to convergence, and compute gradients via the implicit
function theorem automatically.
Stratum Dispatch Extension¶
The existing stratum dispatch mechanism (ADR-0012) classifies topological configurations by evaluating SDFs on a grid. For NURBS, this requires:
- Compute approximate SDF values for the NURBS surface at each grid point (using the closest-point projection above).
- Feed these SDF values into the existing grid-based stratum detector.
- Route gradients to the appropriate per-stratum formula.
The critical question is robustness of stratum detection under SDF approximation error. The iterative closest-point projection produces an approximate SDF (convergence to local rather than global minimum, finite iteration count). If the approximation error is comparable to the grid spacing, stratum labels may be incorrect near topological boundaries.
A convergence analysis is required to quantify: (a) how SDF approximation error depends on iteration count and surface complexity, and (b) the minimum SDF accuracy needed for correct stratum detection at a given grid resolution. This analysis is a key deliverable of the prototype.
External Dependencies¶
NURBS evaluation options:
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geomdl (NURBS-Python): Pure Python NURBS library. Supports evaluation, derivatives, and knot operations. Not JIT-compatible (Python control flow, dynamic allocation). Suitable for validation and ground truth but not for the differentiable pipeline.
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Custom JAX NURBS evaluator: Implement the De Boor algorithm in pure JAX using
jnpoperations. The De Boor recursion has fixed structure for a given degree, making it JIT-compatible. This is the required path for the differentiable pipeline. The algorithm is well-understood (textbook material), and the implementation complexity is moderate (approximately 100-200 lines for surface evaluation and first derivatives). -
OCCT Geom_BSplineSurface: Available through the existing
brepax._occt.backendabstraction (ADR-0008). Provides exact NURBS evaluation and closest-point projection. Cannot participate in JAX transformations (JIT, grad, vmap) but serves as ground truth for validating the JAX implementation.
The recommended approach: implement the De Boor algorithm in JAX for the differentiable pipeline, validate against OCCT for correctness, and use geomdl as an additional cross-reference.
Risk Assessment¶
High risk: NURBS SDF iterative projection convergence and differentiability. The closest-point projection is a nonlinear optimization problem that may have multiple local minima (for non-convex surfaces), saddle points, and degenerate configurations (query points equidistant from multiple surface regions). Convergence failure produces incorrect SDF values, which cascade into incorrect stratum labels and incorrect gradients. Mitigation: start with convex NURBS patches (single-span, low degree) where the projection is well-conditioned, and extend to general surfaces incrementally.
Medium risk: stratum detection robustness with approximate SDF. Grid-based stratum detection requires SDF values to have correct sign at grid points. Near the surface (where SDF crosses zero), approximation error from finite projection iterations may cause sign errors. Mitigation: adaptive grid refinement near zero-crossings, and convergence tolerance tuning to ensure sign correctness.
Low risk: NURBS evaluation itself. The De Boor algorithm is numerically
stable, well-documented, and has been implemented in countless systems. JAX
compatibility requires only replacing Python loops with jnp.where or
lax.fori_loop constructs, which is mechanical. Validation against OCCT
provides a definitive correctness check.
Conclusion¶
The literature survey establishes with high confidence that the combination of all three criteria -- NURBS parametric structure preservation, topology-aware gradient handling, and differentiable B-Rep kernel semantics -- is unprecedented. No existing system achieves all three. The closest works (Mueller et al. for criteria 1+3, Zhao et al. for criteria 1+2) each miss one criterion entirely, and their gaps are structural rather than incremental: Mueller et al. would require a fundamentally new approach to topology changes, and Zhao et al. would need to move from FEM shell analysis to a general B-Rep kernel.
The minimum viable prototype is well-defined and technically tractable. It requires implementing a JAX-native De Boor evaluator (low risk), a closest-point projection solver with implicit differentiation (high risk but with established mathematical foundations), and validation of stratum detection under approximate SDF (medium risk, with clear metrics for success/failure).
The gap identified by this survey -- differentiable NURBS with topology-aware gradients through Boolean operations -- represents a genuine contribution at the intersection of isogeometric analysis, differentiable programming, and computational geometry. The stratum dispatch mechanism, already validated on analytical primitives, provides the theoretical bridge that prior work lacks. A successful prototype would support submission to venues such as SIGGRAPH, SGP (Symposium on Geometry Processing), or CMAME (Computer Methods in Applied Mechanics and Engineering).
References¶
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Prasad, A., Balu, A., Sarkar, A., Krishnamurthy, A., and Hegde, C., "NURBS-Diff: A Differentiable NURBS Layer for Machine Learning CAD Applications," Computer-Aided Design, vol. 146, 2022.
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Moola, P. H., Scholz, F., and Simeon, B., "THB-Diff: Differentiable Truncated Hierarchical B-Spline Refinement," Engineering with Computers, vol. 40, 2024.
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Worchel, M. and Alexa, M., "Differentiable NURBS Rasterization," SIGGRAPH Asia Conference Proceedings, 2023.
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Mueller, J., Sahni, O., Li, X., Jansen, K. E., Shephard, M. S., and Taylor, C. A., "Adjoint-Based Sensitivity Analysis of NURBS-Based CAD Geometries via Algorithmic Differentiation," Computer Methods in Applied Mechanics and Engineering, vol. 330, pp. 563--585, 2018.
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Yuan, Y., Sheng, C., Liu, L., Ceylan, D., and Zhou, Y., "DiffCSG: Differentiable CSG via Rasterization," SIGGRAPH Asia Conference Proceedings, 2024.
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Liu, L., Lyu, P., Bousseau, A., and Ceylan, D., "Fuzzy Boolean Operations for Continuous Implicit Functions," SIGGRAPH Conference Proceedings, 2024.
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TreeTOp, "JAX-Based CSG Tree Topology Optimization," 2025.
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Yu, F., Chen, Z., Li, M., Sanghi, A., Shayani, H., Mahdavi-Amiri, A., and Zhang, H., "D2CSG: Unsupervised Learning of Compact CSG Trees with Dual Complements and Dropouts," Advances in Neural Information Processing Systems (NeurIPS), 2023.
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Ren, Z., Hu, W., Lischinski, D., and Cohen-Or, D., "CSG-Stump: A Learning Friendly CSG-Like Representation for Interpretable Shape Parsing," International Conference on Computer Vision (ICCV), 2021.
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Yu, F., Chen, Z., Li, M., Sanghi, A., Shayani, H., Mahdavi-Amiri, A., and Zhang, H., "CAPRI-Net: Learning Compact CAD Shapes with Adaptive Primitive Assembly," Conference on Computer Vision and Pattern Recognition (CVPR), 2022.
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Xu, X., Jayaraman, P. K., Lambourne, J. G., Willis, K. D. D., and Furukawa, Y., "BrepGen: A B-rep Generative Model with Structured Latent Geometry," SIGGRAPH Conference Proceedings, 2024.
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HoLa, "Holistic B-Rep Generation with Local and Global Attention," ACM Transactions on Graphics, 2025.
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Li, C., et al., "DTGBrepGen: Diffusion-Based Topology-Geometry Coupled B-Rep Generation," Conference on Computer Vision and Pattern Recognition (CVPR), 2025.
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Lu, Y., et al., "NeuroNURBS: Learning Efficient Surface Representations for 3D Solids," 2024.
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NURBGen, "NURBS-Based CAD Model Generation from Point Clouds," AAAI Conference on Artificial Intelligence, 2026.
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IGA with Algorithmic Differentiation, "Isogeometric Shape Optimization with FEniCS-Based Automatic Differentiation," 2025.
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Zhao, Y., et al., "Shape Sensitivity Analysis of NURBS Shell Patches with Moving Intersections," Computer Methods in Applied Mechanics and Engineering, 2024.
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Du, T., Wu, K., Ma, P., Wah, S., Spielberg, A., Rus, D., and Matusik, W., "DiffPD: Differentiable Projective Dynamics," International Conference on Machine Learning (ICML), 2022.
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Zhong, Y., Roconda, J., Beltran-Hernandez, C., and Fazeli, N., "Contact-Aware Gradient Estimation for Robot Manipulation," Learning for Dynamics and Control Conference (L4DC), 2023.
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DreamCAD, "Text-to-CAD Generation via Differentiable Bezier Patch Rendering," 2025.
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Son, H. and Gadelha, M., "DMesh: A Differentiable Mesh Representation," Advances in Neural Information Processing Systems (NeurIPS), 2024.
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Differentiable Persistent Homology for Topology Optimization, International Conference on Learning Representations (ICLR), 2025.
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PartSDF, "Part-Based SDF Composition for Shape Representation," EPFL, 2025.