arXiv subjects

Shuangmin Chen

Publications and source records attributed to Shuangmin Chen.

At least 19 recordsLinked to original sources

arXiv2026

OffsetCrust: Variable-Radius Offset Approximation with Power Diagrams

Offset surfaces, defined as the Minkowski sum of a base surface and a rolling ball, play a crucial role in geometry processing, with applications ranging from coverage motion planning to brush modeling. While considerable progress has been made in computing constant-radius offset surfaces, computing variable-radius offset surfaces remains a challenging problem. In this paper, we present OffsetCrust, a novel framework that efficiently addresses the variable-radius offsetting problem by computing a power diagram. Let $R$ denote the radius function defined on the base surface $S$. The power diagram is constructed from contributing sites, consisting of carefully sampled base points on $S$ and their corresponding off-surface points, displaced along $R$-dependent directions. In the constant-radius case only, these displacement directions align exactly with the surface normals of $S$. Moreover, our method mitigates the misalignment issues commonly seen in crust-based approaches through a lightweight fine-tuning procedure. We validate the accuracy and efficiency of OffsetCrust through extensive experiments, and demonstrate its practical utility in applications such as reconstructing original boundary surfaces from medial axis transform (MAT) representations.

cs.GR↗

arXiv2026

Manifold k-NN: Accelerated k-NN Queries for Manifold Point Clouds

k-nearest neighbor (k-NN) search is a fundamental primitive in geometry processing and computer graphics. While spatial partitioning structures such as kd-trees are standard, they are often manifold-blind, failing to exploit the intrinsic low-dimensional structure of points sampled from 2-manifolds. Recent advances in dynamic programming-based nearest neighbor search (DP-NNS) leverage incrementally constructed Voronoi diagrams to accelerate queries, where each site p maintains a list of successors that progressively refine its Voronoi cell. However, DP-NNS is restricted to single nearest neighbor (k=1) searches, precluding their adoption in applications that require local neighborhood statistics. In this paper, we generalize the DP-NNS framework to support arbitrary k-NN queries for manifold-aligned data. Our approach is founded on the geometric observation that if p_i is the nearest neighbor of a query q in P, then the second nearest neighbor of q must reside either within the prefix set P_{1:i-1} = {p_1, \dots, p_{i-1}} or within p_i's successor list. By recursively extending this principle, we introduce Manifold k-NN, a recursive algorithmic scheme that significantly outperforms conventional kd-trees for manifold-aligned data. Our method achieves a 1\times--10\times speedup in volume-to-surface query scenarios and inherently supports dynamic prefix queries -- enabling k-NN searches within any subset P_{1:m} (m \leq n) with zero overhead. Furthermore, we extend the framework to support point deletion via local Delaunay updates, providing a complete suite of dynamic operations for point set modification. Comprehensive experiments on diverse geometric datasets demonstrate the efficiency and broad applicability of our approach for modern graphics pipelines. Source code is available at https://github.com/sssomeone/manifold-knn.

cs.CG↗

arXiv2026

Structural MAT: Clean and Scalable Medial Axis Simplification via Explicit Surface Correspondence

The Medial Axis Transform (MAT) is a complete shape descriptor capable of reconstructing the geometry of the original domain. A high-quality MAT should not only facilitate high-fidelity reconstruction but also capture structural features -- for instance, by aligning the MAT boundary with the locus of rolling ball centers within fillet regions. However, computing such an ideal MAT remains a significant challenge, particularly when the input is a discrete triangle mesh. In this paper, we follow the established technical pipeline of initializing the MAT via a 3D Voronoi diagram of surface samples and subsequently simplifying the Voronoi structure through a QEM-like scheme. Our key insight is to explicitly track the correspondence between MAT vertices and surface regions throughout the progressive simplification process, ensuring that the resulting MAT triangles accurately reflect the intrinsic symmetries between surface patches. We translate these geometric requirements into a suite of priority control strategies that govern the sequencing of edge collapses. Through extensive evaluation against state-of-the-art MAT algorithms, we validate the strong performance of our approach regarding runtime efficiency, structural alignment, boundary regularity, triangle quality, and robustness to noise. Our resulting MATs remain highly expressive for both articulated shapes and CAD models, even under extreme simplification -- effectively capturing the global structure of complex geometries with only a few hundred vertices.

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arXiv2026

P2M++: Enhanced Solver for Point-to-Mesh Distance Queries

Point-to-mesh distance queries are fundamental in computer graphics and geometric modeling. While the state-of-the-art P2M method achieves high-speed queries via Voronoi-based localization, it suffers from prohibitive precomputation costs. Its iterative Voronoi sweep for interference detection leads to redundant predicate evaluations and scales poorly on rotationally symmetric structures (e.g., spheres, cones or cylinders), where candidate counts grow quadratically. We propose P2M++ to address these limitations through three key contributions. First, we adaptively augment the set of mesh vertices with auxiliary sites in regions of high Voronoi vertex density to localize complex interference within minimal spatial regions. Second, we reformulate interference detection as a series of sphere-triangle collision tests centered at Voronoi cell corners, which are efficiently resolved using the base mesh's BVH. Finally, we enhance runtime performance by replacing the standard kd-tree search with a faster recursive dynamic programming implementation. Experimental results demonstrate that P2M++ is 3x-10x faster than the original P2M during preprocessing and 1.5x faster in queries, with even more pronounced gains on rotationally symmetric geometries.

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arXiv2025

Swept Volume Computation with Enhanced Geometric Detail Preservation

Swept volume computation, the determination of regions occupied by moving objects, is essential in graphics, robotics, and manufacturing. Existing approaches either explicitly track surfaces, suffering from robustness issues under complex interactions, or employ implicit representations that trade off geometric fidelity and face optimization difficulties. We propose a novel inversion of motion perspective: rather than tracking object motion, we fix the object and trace spatial points backward in time, reducing complex trajectories to efficiently linearizable point motions. Based on this, we introduce a multi field tetrahedral framework that maintains multiple distance fileds per element, preserving fine geometric details at trajectory intersections where single field methods fail. Our method robustly computes swept volumes for diverse motions, including translations and screw motions, and enables practical applications in path planning and collision detection.

cs.CG↗

arXiv2025

Toward Precise Curve Offsetting Constrained to Parametric Surfaces

Computing offsets of curves on parametric surfaces is a fundamental yet challenging operation in computer aided design and manufacturing. Traditional analytical approaches suffer from time-consuming geodesic distance queries and complex self intersection handling, while discrete methods often struggle with precision. In this paper, we propose a totally different algorithm paradigm. Our key insight is that by representing the source curve as a sequence of line segment primitives, the Voronoi decomposition constrained to the parametric surface enables localized offset computation. Specifically, the offsetting process can be efficiently traced by independently visiting the corresponding Voronoi cells. To address the challenge of computing the Voronoi decomposition on parametric surfaces, we introduce two key techniques. First, we employ intrinsic triangulation in the parameter space to accurately capture geodesic distances. Second, instead of directly computing the surface-constrained Voronoi decomposition, we decompose the triangulated parameter plane using a series of plane cutting operations. Experimental results demonstrate that our algorithm achieves superior accuracy and runtime performance compared to existing methods. We also present several practical applications enabled by our approach.

cs.CG↗

arXiv2025

Efficient Nearest Neighbor Search Using Dynamic Programming

Given a collection of points in R^3, KD-Tree and R-Tree are well-known nearest neighbor search (NNS) algorithms that rely on space partitioning and spatial indexing techniques. However, when the query point is far from the data points or the data points inherently represent a 2-manifold surface, their query performance may degrade. To address this, we propose a novel dynamic programming technique that precomputes a Directed Acyclic Graph (DAG) to encode the proximity structure between data points. More specifically, the DAG captures how the proximity structure evolves during the incremental construction of the Voronoi diagram of the data points. Experimental results demonstrate that our method achieves a 1x-10x speedup. Additionally, our algorithm demonstrates significant practical value across diverse applications. We validated its effectiveness through extensive testing in four key applications: Point to Mesh Distance Queries, Iterative Closest Point (ICP) Registration, Density Peak Clustering, and Point to Segments Distance Queries. A particularly notable feature of our approach is its unique ability to efficiently identify the nearest neighbor among the first k points in the point cloud a capability that enables substantial acceleration in low-dimensional applications like Density Peak Clustering. As a natural extension of our incremental construction process, our method can also be readily adapted for farthest point sampling tasks. These experimental results across multiple domains underscore the broad applicability and practical importance of our approach.

cs.CG↗

arXiv2025

Power Diagram Enhanced Adaptive Isosurface Extraction from Signed Distance Fields

Extracting high-fidelity mesh surfaces from Signed Distance Fields has become a fundamental operation in geometry processing. Despite significant progress over the past decades, key challenges remain namely, how to automatically capture the intricate geometric and topological structures encoded in the zero level set of SDFs. In this paper, we present a novel isosurface extraction algorithm that introduces two key innovations: 1. An incrementally constructed power diagram through the addition of sample points, which enables repeated updates to the extracted surface via its dual regular Delaunay tetrahedralization; and 2. An adaptive point insertion strategy that identifies regions exhibiting the greatest discrepancy between the current mesh and the underlying continuous surface. As the teaser figure shows, our framework progressively refines the extracted mesh with minimal computational cost until it sufficiently approximates the underlying surface. Experimental results demonstrate that our approach outperforms sofa methods, particularly for models with intricate geometric variations and complex topologies.

cs.CG↗

arXiv2025

NeurCross: A Neural Approach to Computing Cross Fields for Quad Mesh Generation

Quadrilateral mesh generation plays a crucial role in numerical simulations within Computer-Aided Design and Engineering (CAD/E). Producing high-quality quadrangulation typically requires satisfying four key criteria. First, the quadrilateral mesh should closely align with principal curvature directions. Second, singular points should be strategically placed and effectively minimized. Third, the mesh should accurately conform to sharp feature edges. Lastly, quadrangulation results should exhibit robustness against noise and minor geometric variations. Existing methods generally involve first computing a regular cross field to represent quad element orientations across the surface, followed by extracting a quadrilateral mesh aligned closely with this cross field. A primary challenge with this approach is balancing the smoothness of the cross field with its alignment to pre-computed principal curvature directions, which are sensitive to small surface perturbations and often ill-defined in spherical or planar regions. To tackle this challenge, we propose NeurCross, a novel framework that simultaneously optimizes a cross field and a neural signed distance function (SDF), whose zero-level set serves as a proxy of the input shape. Our joint optimization is guided by three factors: faithful approximation of the optimized SDF surface to the input surface, alignment between the cross field and the principal curvature field derived from the SDF surface, and smoothness of the cross field. Acting as an intermediary, the neural SDF contributes in two essential ways. First, it provides an alternative, optimizable base surface exhibiting more regular principal curvature directions for guiding the cross field. Second, we leverage the Hessian matrix of the neural SDF to implicitly enforce cross field alignment with principal curvature directions...

cs.CV↗

arXiv2024

Towards Voronoi Diagrams of Surface Patches

Extraction of a high-fidelity 3D medial axis is a crucial operation in CAD. When dealing with a polygonal model as input, ensuring accuracy and tidiness becomes challenging due to discretization errors inherent in the mesh surface. Commonly, existing approaches yield medial-axis surfaces with various artifacts, including zigzag boundaries, bumpy surfaces, unwanted spikes, and non-smooth stitching curves. Considering that the surface of a CAD model can be easily decomposed into a collection of surface patches, its 3D medial axis can be extracted by computing the Voronoi diagram of these surface patches, where each surface patch serves as a generator. However, no solver currently exists for accurately computing such an extended Voronoi diagram. Under the assumption that each generator defines a linear distance field over a sufficiently small range, our approach operates by tetrahedralizing the region of interest and computing the medial axis within each tetrahedral element. Just as SurfaceVoronoi computes surface-based Voronoi diagrams by cutting a 3D prism with 3D planes (each plane encodes a linear field in a triangle), the key operation in this paper is to conduct the hyperplane cutting process in 4D, where each hyperplane encodes a linear field in a tetrahedron. In comparison with the state-of-the-art, our algorithm produces better outcomes. Furthermore, it can also be used to compute the offset surface.

cs.GR↗

arXiv2024

ITS: Implicit Thin Shell for Polygonal Meshes

In computer graphics, simplifying a polygonal mesh surface~$\mathcal{M}$ into a geometric proxy that maintains close conformity to~$\mathcal{M}$ is crucial, as it can significantly reduce computational demands in various applications. In this paper, we introduce the Implicit Thin Shell~(ITS), a concept designed to implicitly represent the sandwich-walled space surrounding~$\mathcal{M}$, defined as~$\{\textbf{x}\in\mathbb{R}^3|ε_1\leq f(\textbf{x}) \leq ε_2, ε_1< 0, ε_2>0\}$. Here, $f$ is an approximation of the signed distance function~(SDF) of~$\mathcal{M}$, and we aim to minimize the thickness~$ε_2-ε_1$. To achieve a balance between mathematical simplicity and expressive capability in~$f$, we employ a tri-variate tensor-product B-spline to represent~$f$. This representation is coupled with adaptive knot grids that adapt to the inherent shape variations of~$\mathcal{M}$, while restricting~$f$'s basis functions to the first degree. In this manner, the analytical form of~$f$ can be rapidly determined by solving a sparse linear system. Moreover, the process of identifying the extreme values of~$f$ among the infinitely many points on~$\mathcal{M}$ can be simplified to seeking extremes among a finite set of candidate points. By exhausting the candidate points, we find the extreme values~$ε_1<0$ and $ε_2>0$ that minimize the thickness. The constructed ITS is guaranteed to wrap~$\mathcal{M}$ rigorously, without any intersections between the bounding surfaces and~$\mathcal{M}$. ITS offers numerous potential applications thanks to its rigorousness, tightness, expressiveness, and computational efficiency. We demonstrate the efficacy of ITS in rapid inside-outside tests and in mesh simplification through the control of global error.

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arXiv2024

Deep-PE: A Learning-Based Pose Evaluator for Point Cloud Registration

In the realm of point cloud registration, the most prevalent pose evaluation approaches are statistics-based, identifying the optimal transformation by maximizing the number of consistent correspondences. However, registration recall decreases significantly when point clouds exhibit a low overlap rate, despite efforts in designing feature descriptors and establishing correspondences. In this paper, we introduce Deep-PE, a lightweight, learning-based pose evaluator designed to enhance the accuracy of pose selection, especially in challenging point cloud scenarios with low overlap. Our network incorporates a Pose-Aware Attention (PAA) module to simulate and learn the alignment status of point clouds under various candidate poses, alongside a Pose Confidence Prediction (PCP) module that predicts the likelihood of successful registration. These two modules facilitate the learning of both local and global alignment priors. Extensive tests across multiple benchmarks confirm the effectiveness of Deep-PE. Notably, on 3DLoMatch with a low overlap rate, Deep-PE significantly outperforms state-of-the-art methods by at least 8% and 11% in registration recall under handcrafted FPFH and learning-based FCGF descriptors, respectively. To the best of our knowledge, this is the first study to utilize deep learning to select the optimal pose without the explicit need for input correspondences.

cs.CV↗

arXiv2024

A Hessian-Based Field Deformer for Real-Time Topology-Aware Shape Editing

Shape manipulation is a central research topic in computer graphics. Topology editing, such as breaking apart connections, joining disconnected ends, and filling/opening a topological hole, is generally more challenging than geometry editing. In this paper, we observe that the saddle points of the signed distance function (SDF) provide useful hints for altering surface topology deliberately. Based on this key observation, we parameterize the SDF into a cubic trivariate tensor-product B-spline function $F$ whose saddle points $\{\boldsymbol{s}_i\}$ can be quickly exhausted based on a subdivision-based root-finding technique coupled with Newton's method. Users can select one of the candidate points, say $\boldsymbol{s}_i$, to edit the topology in real time. In implementation, we add a compactly supported B-spline function rooted at $\boldsymbol{s}_i$, which we call a \textit{deformer} in this paper, to $F$, with its local coordinate system aligning with the three eigenvectors of the Hessian. Combined with ray marching technique, our interactive system operates at 30 FPS. Additionally, our system empowers users to create desired bulges or concavities on the surface. An extensive user study indicates that our system is user-friendly and intuitive to operate. We demonstrate the effectiveness and usefulness of our system in a range of applications, including fixing surface reconstruction errors, artistic work design, 3D medical imaging and simulation, and antiquity restoration. Please refer to the attached video for a demonstration.

cs.GR↗

arXiv2024

CWF: Consolidating Weak Features in High-quality Mesh Simplification

In mesh simplification, common requirements like accuracy, triangle quality, and feature alignment are often considered as a trade-off. Existing algorithms concentrate on just one or a few specific aspects of these requirements. For example, the well-known Quadric Error Metrics (QEM) approach prioritizes accuracy and can preserve strong feature lines/points as well but falls short in ensuring high triangle quality and may degrade weak features that are not as distinctive as strong ones. In this paper, we propose a smooth functional that simultaneously considers all of these requirements. The functional comprises a normal anisotropy term and a Centroidal Voronoi Tessellation (CVT) energy term, with the variables being a set of movable points lying on the surface. The former inherits the spirit of QEM but operates in a continuous setting, while the latter encourages even point distribution, allowing various surface metrics. We further introduce a decaying weight to automatically balance the two terms. We selected 100 CAD models from the ABC dataset, along with 21 organic models, to compare the existing mesh simplification algorithms with ours. Experimental results reveal an important observation: the introduction of a decaying weight effectively reduces the conflict between the two terms and enables the alignment of weak features. This distinctive feature sets our approach apart from most existing mesh simplification methods and demonstrates significant potential in shape understanding.

cs.GR↗

arXiv2024

NeurCADRecon: Neural Representation for Reconstructing CAD Surfaces by Enforcing Zero Gaussian Curvature

Despite recent advances in reconstructing an organic model with the neural signed distance function (SDF), the high-fidelity reconstruction of a CAD model directly from low-quality unoriented point clouds remains a significant challenge. In this paper, we address this challenge based on the prior observation that the surface of a CAD model is generally composed of piecewise surface patches, each approximately developable even around the feature line. Our approach, named NeurCADRecon, is self-supervised, and its loss includes a developability term to encourage the Gaussian curvature toward 0 while ensuring fidelity to the input points. Noticing that the Gaussian curvature is non-zero at tip points, we introduce a double-trough curve to tolerate the existence of these tip points. Furthermore, we develop a dynamic sampling strategy to deal with situations where the given points are incomplete or too sparse. Since our resulting neural SDFs can clearly manifest sharp feature points/lines, one can easily extract the feature-aligned triangle mesh from the SDF and then decompose it into smooth surface patches, greatly reducing the difficulty of recovering the parametric CAD design. A comprehensive comparison with existing state-of-the-art methods shows the significant advantage of our approach in reconstructing faithful CAD shapes.

cs.CV↗

arXiv2023

A Task-driven Network for Mesh Classification and Semantic Part Segmentation

With the rapid development of geometric deep learning techniques, many mesh-based convolutional operators have been proposed to bridge irregular mesh structures and popular backbone networks. In this paper, we show that while convolutions are helpful, a simple architecture based exclusively on multi-layer perceptrons (MLPs) is competent enough to deal with mesh classification and semantic segmentation. Our new network architecture, named Mesh-MLP, takes mesh vertices equipped with the heat kernel signature (HKS) and dihedral angles as the input, replaces the convolution module of a ResNet with Multi-layer Perceptron (MLP), and utilizes layer normalization (LN) to perform the normalization of the layers. The all-MLP architecture operates in an end-to-end fashion and does not include a pooling module. Extensive experimental results on the mesh classification/segmentation tasks validate the effectiveness of the all-MLP architecture.

cs.CV↗

arXiv2023

OAAFormer: Robust and Efficient Point Cloud Registration Through Overlapping-Aware Attention in Transformer

In the domain of point cloud registration, the coarse-to-fine feature matching paradigm has received substantial attention owing to its impressive performance. This paradigm involves a two-step process: first, the extraction of multi-level features, and subsequently, the propagation of correspondences from coarse to fine levels. Nonetheless, this paradigm exhibits two notable limitations.Firstly, the utilization of the Dual Softmax operation has the potential to promote one-to-one correspondences between superpoints, inadvertently excluding valuable correspondences. This propensity arises from the fact that a source superpoint typically maintains associations with multiple target superpoints. Secondly, it is imperative to closely examine the overlapping areas between point clouds, as only correspondences within these regions decisively determine the actual transformation. Based on these considerations, we propose {\em OAAFormer} to enhance correspondence quality. On one hand, we introduce a soft matching mechanism, facilitating the propagation of potentially valuable correspondences from coarse to fine levels. Additionally, we integrate an overlapping region detection module to minimize mismatches to the greatest extent possible. Furthermore, we introduce a region-wise attention module with linear complexity during the fine-level matching phase, designed to enhance the discriminative capabilities of the extracted features. Tests on the challenging 3DLoMatch benchmark demonstrate that our approach leads to a substantial increase of about 7\% in the inlier ratio, as well as an enhancement of 2-4\% in registration recall. =

cs.CV↗

arXiv2023

Neural-Singular-Hessian: Implicit Neural Representation of Unoriented Point Clouds by Enforcing Singular Hessian

Neural implicit representation is a promising approach for reconstructing surfaces from point clouds. Existing methods combine various regularization terms, such as the Eikonal and Laplacian energy terms, to enforce the learned neural function to possess the properties of a Signed Distance Function (SDF). However, inferring the actual topology and geometry of the underlying surface from poor-quality unoriented point clouds remains challenging. In accordance with Differential Geometry, the Hessian of the SDF is singular for points within the differential thin-shell space surrounding the surface. Our approach enforces the Hessian of the neural implicit function to have a zero determinant for points near the surface. This technique aligns the gradients for a near-surface point and its on-surface projection point, producing a rough but faithful shape within just a few iterations. By annealing the weight of the singular-Hessian term, our approach ultimately produces a high-fidelity reconstruction result. Extensive experimental results demonstrate that our approach effectively suppresses ghost geometry and recovers details from unoriented point clouds with better expressiveness than existing fitting-based methods.

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