In this work, we propose a new transfinite interpolation Coons scheme for constructing G1 continuous surface patches allowing T-junctions. In detail, for each patch, with the T-junctions’ parametric coordinates, we develop new piecewise cubic blending functions. We further provide the corresponding compatibility conditions required for G1 continuity. Then we use the classical Boolean sum operator to blend four given G1 boundary curves together. We prove that the resulting G1 isoparametric transfinite elements are C1 continuous by reparameterization. And we show that the new Coons scheme possesses the local linear reproduction property. The applications of the novel scheme in reconstructing open 3D triangular meshes and bivariate functions are given. In the application of solving numerical Poisson’s equation with Dirichlet boundary condition based on multipatch isoparametric transfinite element analysis, the novel Coons scheme allowing T-junctions can achieve C1 continuity with simple constraints on unknowns, and can interpolate the boundary conditions exactly. What is more, the transfinite interpolation property of Coons scheme with T-junctions makes it suitable to represent complicated domains exactly, which shows some advantages in solving numerical Poisson’s equation with Dirichlet boundary condition by multipatch.
In this work, we improved the analytic framework for seamless parameterization on genus-zero surfaces from the perspective of flat metrics induced by meromorphic quartic differentials. The transition of the differential between stereographic charts is proven to differ only by a constant factor, enabling stable and globally consistent metric construction. By embedding the quartic differential into a metric formulation, branch ambiguity is eliminated, and within this framework, we derive a unified expression for the parameterization metric change induced by singularity relocation, insertion, and merging. The distortion variation admits a closed-form evaluation without reconstructing the differential or re-solving the parameterization, which enables parallel computation. Experimental results demonstrate that our method achieves runtime comparable to heuristic approaches while producing area distortion similar to optimization-based methods, introducing only slightly more singularities than optimization-based methods and fewer than heuristic approaches.
The surface form errors and deformations of high-precision mechanical components significantly influence the final assembly deviations. However, existing analytical methods often fail to adequately account for the effects of surface morphology and deformation. This paper proposes a novel Multi-Vector-Loop method, which is based on the Skin Model Shapes and a multi-closed-loop structure, for three-dimension macro-micro assembly deviation analysis. The method is employed to establish a high-precision mathematical model that directly links surface morphology, deformation, and assembly concentricity deviations. The stop-bolt mechanism is used as the study object. Firstly, an approach is introduced to construct a Skin Model Shapes that represents non-ideal surfaces due to machining errors. Then, force-deformation relationships for various surface morphological characteristics are derived through finite element method and interpolation methods. Finally, the development of a steady assembly state search algorithm has been achieved to obtain the final assembly state, and the Multi-Vector-Loop deviations transfer model was utilized to predict concentricity deviations. The numerical calculations of concentricity deviation for the three cases showed errors of 13.90% (Case 1), 20.46% (Case 2), and 9.93% (Case 3) relative to the finite element calculations. The results confirm the effectiveness of the proposed high-precision error transfer model.
Point cloud denoising aims to restore high-fidelity surfaces from noisy observations—a fundamental yet ill-posed problem, as multiple plausible clean surfaces may correspond to the same degraded input. Existing methods typically adopt single-step regression that directly predicts clean points by minimizing a distance metric. However, such one-shot prediction often leads to a regression-to-the-mean (RTM) artifact, where diverse possible solutions are averaged, resulting in oversmoothed results. To overcome this limitation, we present PointInDI, a novel denoising framework built upon Inversion by Direct Iteration (InDI). Instead of a one-shot prediction, PointInDI decomposes denoising into a sequence of small iterative refinements along a continuous degradation path, progressively improving geometric fidelity. This iterative design mitigates the RTM artifact, enabling the recovery of more complete structures and richer details. Extensive experiments on both synthetic and real-world datasets show that PointInDI achieves state-of-the-art performance, producing more faithful results than competing baselines.
Mid-surface abstraction is essential for finite element analysis of thin-walled CAD models, yet existing face pairing-based methods suffer from quadratic complexity and CPU-bound bottlenecks, limiting scalability for variable-thickness models. We present gMidSurf, a GPU-accelerated pipeline that transforms the two computational bottlenecks in mid-surface abstraction (face pairing and mid-point generation) into massively parallel operations. For face pairing, we introduce a hierarchical filtering strategy that progressively culls candidate pairs through three GPU-optimized gates: normal compatibility, simplified overlap criterion, and LBVH-based distance queries, reducing the search space by 10–100× while maintaining cache coherence. For mid-point generation, we employ parallel distance dilation followed by bracket-and-bisect refinement for precise equidistant point localization. This method handles variable-thickness models with complex surfaces through complete dilation, thereby avoiding gaps and truncations that occur in previous methods. Experimental results on real-world benchmarks demonstrate that gMidSurf achieves 4.2×–18.5× speedups in face pairing and 4.8×–9.8× in mid-point generation compared to CPU implementations, yielding 5×–15× acceleration on a commodity GPU (NVIDIA RTX 5090D) compared to state-of-the-art methods while maintaining geometric accuracy.
We present a high-performance GPU algorithm for constructing 3D Delaunay triangulations of large-scale point sets, optimized for minimal memory footprint and high throughput. Traditional GPU approaches based on halfspace intersection typically maintain explicit local triangle meshes to represent the Delaunay one-ring of each vertex. This strategy incurs significant memory redundancy-as each tetrahedron is shared by four vertices-and leads to excessive memory traffic that bottlenecks scalability. We observe that the global triangulation can be recovered by computing only a specific, striped subset of each one-ring, which we term the Local Delaunay Wall (Local DeWall). The Local DeWall admits a highly compact representation as an ordered list of points that implicitly encodes local connectivity, reducing pervertex memory usage by over 2/3 and bypassing the need for explicit mesh storage. Building directly on this compact representation, we introduce an incremental traversal algorithm that constructs the Local DeWall by "walking" across adjacent tetrahedra using only point-based operations. By combining the compact Local DeWall representation with incremental traversal, our method avoids repeatedly storing, loading, and updating explicit local mesh structures, leading to nearly an order-of-magnitude reduction in memory throughput and significantly alleviating the memory bottleneck of GPU-based Delaunay construction To ensure scalability and robustness against workload imbalance and geometric degeneracies, we employ a two-phase execution strategy: a high-throughput main phase utilizing fast predicate filtering, followed by a targeted post-processing phase using exact arithmetic for difficult cases. Our implementation achieves a substantial leap in performance, delivering more than 2 & times; speedup over state-of-the-art GPU methods and up to an order of magnitude improvement over parallel CPU implementations. We demonstrate the utility of our method through two demanding applications: Centroidal Voronoi Tessellation (CVT), where our rapid iterations enable near-real-time Lloyd's relaxation, and Restricted Delaunay Triangulation, providing efficient volumetric meshing of complex manifolds. Our implementation scales to over 1.2 billion points (8.4 billion tetrahedra) on a single GPU, surpassing the previous state-of-the-art GPU capacity by a factor of 2.4 & times; and demonstrating the feasibility of billion-scale 3D Delaunay triangulation on consumer-grade hardware.
Implicit neural representations (INRs), especially signed distance functions (SDFs) parameterized by neural decoders, are widely used for learning continuous 3D shape spaces. While geometry-driven objectives enable accurate shape decoding, they largely ignore global topological structures, often leading to topological inconsistencies such as disconnected components, unintended handles, or spurious voids in decoded shapes. To address this limitation, we propose a topology-aware shape space learning framework that introduces explicit topological control for implicit neural decoders. Our method is built upon a DeepSDF-style architecture and incorporates a differentiable topological loss based on persistent homology. By encoding topological priors as target persistence diagrams and focusing on features near the zero level set, the proposed loss enables unified optimization for enforcing desired topological structures while suppressing undesired ones. Experiments demonstrate that explicitly optimizing topology significantly improves the structural consistency of decoded shapes across the latent space. Moreover, our framework supports controlled topological editing through persistence diagram manipulation, without modifying the network architecture or decoder formulation.
Lattice structures offer exceptional performance in additive manufacturing, yet ensuring their geometric validity under complex design constraints poses a significant computational geometry challenge. This paper addresses the scalability bottleneck in processing million-scale lattice models by proposing a high-performance framework based on Hybrid Spatial-Topological Index. Our approach leverages a priority-driven heuristic solver integrated with a local topology update strategy, decouples computational cost from the total topological complexity of the model. Besides, the framework introduces a series of atomic operators to resolve coupled DfAM constraints, such as overhang angle, pillar ratio, and connectivity. Compared to isotropic remeshing, our framework strictly enforces physical DfAM constraints rather than merely pursuing topological regularity, preventing the inadvertent introduction of new geometric violations. Furthermore, against state-of-the-art self-supporting topology optimization methods, our approach achieves higher overhang correction rates while avoiding the severe boundary distortion and secondary dimensional violations caused by global scaling. The proposed framework can resolve complex geometric violations within tens of seconds for models exceeding 106 elements, maintaining a high degree of geometric fidelity and structural integrity, provides a scalable computational foundation for the next generation of CAD tools capable of handling extreme-scale lattice designs.
Netlist partitioning stands as a pivotal technology in electronic design automation and hardware security domains, enhancing design efficiency through decomposition of complex circuit structures. To address existing challenges in graph neural network-based partitioning methods, including poor adaptability in unseen scenarios, preset cluster number bias, and hypergraph structure conversion distortion, this paper proposes a hypergraph pseudo-label learning framework integrating neighborhood consistency constraint and diffusion potential label propagation. By excavating implicit physical neighborhood relationships within netlist hypergraphs, our method establishes a pseudo-label learning mechanism that jointly optimizes hypergraph representation and label propagation processes, thereby achieving efficient unseen netlist partitioning with minimal prompt nodes. Extensive experiments on real-world netlists demonstrate that compared with existing techniques, our approach achieves superior performance on 92% of unseen netlists with an average improvement exceeding 5%. Moreover, the partition quantity dynamically adapts to prompt nodes, ensuring rational partitioning configuration.
Global boundaries of spline surfaces require special treatment due to the lack of a complete neighborhood, in particular in the presence of extraordinary vertices (EVs). Spline surfaces with EVs and/or n-sided facets in their polyhedral control net are akin to generalized subdivision surfaces but cannot leverage infinite refinability to satisfy boundary or semi-sharp crease constraints. The new boundary and crease treatment for high-end, free-form spline surface algorithms aims to replicate subdivision options by using as much as possible the algorithm developed for closed spline surfaces, i.e. eschewing special rules at the level of B & eacute;zier coefficients or trying to define knot spacing for EVs. In particular, by virtually augmenting the control net, the new rules offer interpolation and approximation of the curve defined by the global boundary of the original control net, corner treatment and semi-sharp creases.
Technical textiles and their use in composites are crucial for many high-performance applications. Utilizing them in applications dominated by iteration and individualization requires flexible manufacturing processes. One such process is Incremental Sheet Forming (ISF), the 3D-Printing of forming processes, which is currently being adapted to composites. Enabling ISF, and other dieless processes, and leveraging their flexibility, requires optimization and path planning tools. Such tools must consider material behavior, which in turn necessitates the use of simulation. While highly sophisticated methods for increasingly accurate modelling have been developed, the speed requirements of CAM workflows and optimizations have kept simple yet efficient approximations relevant; the most prominent being kinematic draping algorithms. This work presents a novel heat-method based alternative that globally computes fabricdraping under an assumption of uniform tow distances. This assumption makes it especiallywell-suited for the subsequently implemented drape-aware ISF paths. Additionally, the developed algorithm is highly computationally efficient, which is harnessed for visualization andoptimization. While these are only explored computationally, the path-planning is employed to produce and compare a demonstrator part in a double sided ISF process. The initial results for the draping algorithm show an up to 80x speed increase compared to kinematic draping. This allows for real-time draping visualization and sub-minute optimization. The demonstrator part proofs that the derived paths can counteract wrinkling, an important failure mode observed with conventional strategies. These results demonstrate the great potential of geodesic draping for ISF in specific and flexible manufacturing, optimization and visualization tasks in general.
Multi-axis additive manufacturing (AM) overcomes traditional limitations through non-planar slicing and local build direction control, enabling the fabrication of complex, support-free geometries. To fully exploit these capabilities, integrating features of multi-axis AM into the design phase is essential for exploring a broader design space and achieving high-performance designs. Existing methods for non-planar slicing often rely on solving auxiliary partial differential equations (PDEs) to define the fabrication sequence. This work proposes a simpler parameterization method, where the slicing field combines a Euclidean distance field (to maintain sequence) with a perturbation field (to adjust local layer profiles). The perturbation field is optimized concurrently with the density field to achieve self-supporting designs. Leveraging the spatial gradients of these fields, a global constraint is formulated to enforce local overhang angle control. To further address the boundary oscillations inherent to spatial-gradient-based formulations, an additional global constraint is introduced, which acts by regulating the local volume fraction along overhang boundaries. The efficacy of the proposed non-planar slicing and overhang control methods is validated through both 2D and 3D numerical examples in linear elasticity and heat conduction problems.
Knitted textures are widely used in functional surfaces and fabricated objects, where stitch-level geometry plays an important role in both visual appearance and physical interaction. Although high-quality knitted geometric details can be manually authored, the process is labor-intensive and requires substantial domain expertise. Recent generative approaches for 3D content creation often struggle to reproduce the fine-scale structural characteristics of knitted patterns, typically producing overly smooth surfaces that lack explicit yarn-level organization. In this paper, we present Knit2Vector, an inverse procedural modeling framework for reconstructing structure-aware knitted surface geometry from a single unconstrained image. Our key insight is that knitted textures can be naturally represented as collections of vectorized yarn segments organized according to stitch-level structures. Based on this observation, we introduce a differentiable vectorization framework that reconstructs explicit and editable yarn-level representations using B & eacute;zier primitives. Crucially, we leverage these vectorized priors to infer the underlying structural arrangement of yarns, enabling the reconstruction of geometrically consistent surface relief that preserves stitch-level structural coherence. Rather than directly estimating geometry from image appearance, our method derives geometry-aware cues from the reconstructed yarn layout to guide surface optimization. Compared with existing appearance-driven generative approaches, our method produces more structure-consistent knitted surface details with explicit and editable yarn-level representations. The resulting representation provides structure-aware geometric assets for applications including solid modeling, virtual prototyping, digital fashion, and high-end rendering.
We present a denoising algorithm based on the damping limit Sine–Gordon Model. This algorithm combines the alternating direction implicit (ADI) method with the explicit Euler method via an operator splitting strategy. In the time direction, the ADI method is used to handle the diffusion term, while the explicit Euler method is used to handle the nonlinear term. This model achieves the separation of feature detection and smoothing processes through a two-variable coupling system, and introduces a fidelity term based on the initial state, effectively suppressing volume collapse and geometric distortion, and enhancing the robustness and conformality of the algorithm. The experimental results show that our method not only preserves the key geometric features but also enhances the smoothness, possesses excellent noise reduction effect and wide application range.
This paper presents a stress-driven and user-guided framework for generating Pythagorean–Hodograph (PH) print-paths in additive manufacturing (AM). PH curves are employed due to their unique properties, including polynomial representation, exact arc-length parametrization, and closed-form expressions for curvature. In this work, PH-based print-paths are introduced as a novel input representation for additive manufacturing. To execute these paths efficiently, a G-code interpolator tailored for PH curves is developed. Principal stress directions obtained from FEM analysis or user-defined constraints are used to construct smooth orthonormal vector fields, from which print-path points, tangents, and extruder orientations are derived. PH curves are then fitted to these points and tangents, representing the PH-based AM print-paths. The proposed method is validated using both an AM simulator and a physical machine.
Surface skinning is a classical modeling method that fits a surface through a set of given cross-sectional curves. Unlike non-uniform rational B-spline (NURBS) surface skinning, T-spline surface skinning does not require knot compatibility of the given cross-sectional curves and avoids superfluous control points. However, existing T-spline surface skinning methods achieve interpolation by introducing intermediate curves, which do not fully leverage the potential of the data compression ability of T-splines. In this paper, a T-spline surface skinning method is presented, where the skinning process is formulated as an inverse process of Bézier extraction. After the T-mesh pre-image is first generated from composite of the cross-sectional curves’ knot vectors, Bézier patches induced by Bézier extraction are constructed and interpolated from the given cross-sectional curves using Hermite interpolation. To ensure consistency with the to-be-generated T-spline surface, the continuity conditions required between adjacent Bézier patches are analytically derived and implemented. The T-spline control points are then generated through the inverse of the Bézier extraction operators, enabling exact construction without the need for intermediate curves. The proposed method offers significant advantages, including usually fewer control points and a more concise T-mesh structure, which makes the skinning process more intuitive. Furthermore, by adjusting the tangent information, shape control is supported during the patch construction. Several numerical examples demonstrate the effectiveness of the proposed method.
Computer-aided design (CAD) plays a central role in engineering, manufacturing, and 3D content creation, but producing precise CAD models directly from natural language is still difficult. We propose Text2CSG, a two-stage framework for producing high-quality CAD models from text. Our approach uses Constructive Solid Geometry (CSG) as an intermediate representation to capture the structured and hierarchical nature of CAD construction. Unlike prior approaches based on sketch-extrusion sequences, Text2CSG exploits the Boolean compositional logic of CSG trees to represent complex shapes. The system consists of two primary components: (1) a geometry decoder that reconstructs 3D shapes from CSG programs, and (2) a structure-aware Transformer conditioned on high-level semantics extracted from a frozen large language model (LLM). By decoupling semantic understanding from geometric generation, our approach benefits from pre-trained LLMs without requiring fine-tuning. Experiments on a newly constructed CSG dataset demonstrate that Text2CSG achieves higher geometric accuracy and stronger structural consistency than existing methods. Furthermore, the utilization of structured CSG programs makes the generation process interpretable and editable, enabling flexible text-driven CAD design. We will release the source code and dataset.
