Abstract To address the storage overhead of lightmaps and the limitations of existing compression techniques, we propose a novel UV‐space compression framework based on per‐triangle processing. By mapping triangles to a standardized domain, we cluster and repack color‐coherent regions into a compact atlas, generating a cascade texture refined via differentiable rendering. Experimental results show an average storage reduction of 83% with approximately 10 dB higher PSNR than existing methods. Our approach is the first dedicated lightmap compression framework compatible with standard block‐based formats, offering an effective solution for memory‐efficient 3D asset delivery.

Abstract Creation of collision objects for 3D models is a time‐consuming task, requiring modelers to manually place primitives such as bounding boxes, capsules, spheres, and other convex primitives to approximate complex meshes. While there has been work in automatic approximate convex decompositions of meshes using convex hulls, they are not practical for applications with tight performance budgets such as games due to slower collision detection and inability to manually modify the output while maintaining convexity as compared to manually placed primitives. Rather than convex decomposition with convex hulls, we devise an approach for bottom‐up decomposition of an input mesh into convex primitives specifically for rigid body simulation inspired by quadric mesh simplification. This approach fits primitives to complex, real‐world meshes that provide plausible simulation performance and are guaranteed to enclose the input surface. We test convex primitive decomposition on over 60 models from Sketchfab, showing the algorithm's effectiveness. On this dataset, convex primitive decomposition has lower oneway mean and median Hausdorff and Chamfer distance from the collider to the input compared to V‐HACD and CoACD, with less than one‐third of the complexity as measured by total bytes for each collider. On top of that, rigid‐body simulation performance measured by wall‐clock time is consistently improved across 24 tested models.

Accurately estimating human internal states, such as personality traits or behavioral patterns, is critical for enhancing the effectiveness of human–robot interaction, particularly in multi-agent settings. These insights are key in applications ranging from social navigation to autism diagnosis. However, prior methods are limited by scalability and passive observation, making real-time estimation in complex, multi-human settings difficult. In this work, we propose a practical method for active human personality estimation in crowds, with a focus on applications related to Autism Spectrum Disorder (ASD). Our method combines a personality-conditioned behavior model, based on the Eysenck 3-Factor theory, with an active robot information-gathering policy that triggers human behaviors through a receding-horizon planner. The robot’s belief about human personality is then updated via Bayesian inference. We demonstrate the effectiveness of our approach through proof-of-concept studies in simulation, user studies with typical adults, and preliminary experiments involving participants with ASD. Our results show that our method can scale to tens of humans and reduce personality estimation error by 29.2% and uncertainty by 79.9% in simulation compared to the passive baseline. User studies with typical adults confirm the method’s ability to generalize across complex personality distributions. Additionally, we explore its application in autism-related scenarios, demonstrating that the method can identify the difference between neurotypical and autistic behavior. The results suggest that our framework could serve as a foundation for future ASD-specific applications.

We introduce a new offset meshing method that handles clean 3D surface meshes of arbitrary geometry and topology—where “clean” refers to meshes that are watertight, manifold, and free of self-intersections. Our approach also extends to imperfect, or “dirty,” meshes that violate these conditions, although the problem becomes significantly more difficult in such scenarios, and faithful feature preservation near defective areas cannot always be assured. In contrast to prior techniques, which have largely focused on constant-radius offsets, our method is, to our knowledge, the first to support mitered offsets while effectively preserving sharp features. Our method is designed based on several core principles: (1) explicitly generating the offset vertices and triangles with feature-capturing energy and constraints; (2) prioritizing the generation of the offset geometry before establishing its connectivity, (3) employing exact algorithms in critical pipeline steps for robustness, balancing the use of floating-point computations for efficiency, (4) applying various conservative speed up strategies including early reject non-contributing computations to the final output. Our approach further uniquely supports variable offset distances on input surface elements, offering a wider range of practical applications compared to conventional methods. For benchmarking purposes, we performed an extensive comparison against state-of-the-art offset methods using a curated subset of the Thingi10K dataset. Our results demonstrate the superiority of our approach over current state-of-the-art methods in terms of element count, feature preservation, and non-uniform offset distances of the resulting offset mesh surfaces, marking a significant advancement in the field.

Robot simulators are indispensable tools across many fields, and recent research has significantly improved their functionality by incorporating additional gradient information. However, existing differentiable robot simulators suffer from non-differentiable singularities, when robots undergo substantial shape changes. To address this, we present the Shape-Differentiable Robot Simulator (SDRS), designed to be differentiable under significant robot shape changes. The core innovation of SDRS lies in its representation of robot shapes using a set of convex polyhedrons. This approach allows us to generalize smooth, penalty-based contact mechanics for interactions between any pair of convex polyhedrons. Using the separating hyperplane theorem, SDRS introduces a separating plane for each pair of contacting convex polyhedrons. This separating plane functions as a zero-mass auxiliary entity, with its state determined by the principle of least action. This setup ensures global differentiability, even as robot shapes undergo significant geometric and topological changes. To demonstrate the practical value of SDRS, we provide examples of robot co-design scenarios, where both robot shapes and control movements are optimized simultaneously.

Occlusion culling is a cornerstone of real-time rendering, particularly in mobile games where limited GPU bandwidth demands highly efficient scene management. At the heart of occlusion culling lies the use of simplified proxy geometry-called occluders-that approximate scene geometry for rapid visibility testing. However, producing high-quality occluders that are low in polygon count, conservative in coverage, and tightly aligned with the original geometry remains a manual and labor-intensive process. In this paper, we present a fast and fully automated two-stage approach for robust occluder generation tailored to real-world game assets. Our method begins with a novel strategy for inward offset mesh computation, followed by a conservative simplification step leveraging a new variant of Quadric Error Metrics (QEM). This approach effectively handles noisy and topologically complex inputs, generating production-ready occluders in seconds. Extensive experiments on a wide range of asset types demonstrate that our technique achieves aggressive triangle reduction while preserving critical occlusion fidelity. By offering a practical and scalable solution, our method bridges the gap between academic research and demanding needs for game development.

Modular robotic structures simplify robot design and manufacturing by using standardized modules, enhancing flexibility and adaptability. However, the need for manual input in design and assembly limit their potential. Current methods to automate this process still require significant human effort and technical expertise. This paper introduces a novel approach that employs Large Language Models (LLMs) as intelligent agents to automate the creation of modular robotic structures. We decompose the modular robot creation task and develop two agents based on LLM to plan and assemble the modular robots from text prompts. By inputting a textual description, users can generate robot designs that are validated in both simulated and real-world environments. This method reduces the need for manual intervention and lowers the technical barrier to creating complex robotic systems.

Maintaining memory-efficient 3D assets is critical for game development due to size constraints for applications, as well as runtime costs such as GPU data transfers. While most prior work on 3D modeling focuses on reducing triangle count, few works focus on reducing texture sizes. We propose an automatic approach to reduce the texture size for 3D models while maintaining the rendered appearance of the original input. The two core components of our approach are (1) overlapping identical UV charts and folding mirrored regions within charts through an optimal transport optimization, and (2) carving redundant and void texels in a UV-aware and texture-aware way without inverting the UV mesh. The first component creates additional void space, whereas the second removes void space, and their combination can greatly increase texels utilized by the UV mesh at lower texture resolutions. Our method is robust and general, and can process a 3D model with arbitrary UV layout and multiple textures without modifying the 3D mesh. We evaluate our approach on 110 models from the Google Scanned Object dataset and 64 models from Sketchfab. Compared to other approaches, ours has on average 1 to 3 dB PSNR higher rendering similarity and reduces pixelation in visual comparisons.

Approximate Convex Decomposition (ACD) aims to approximate complex 3D shapes with convex components, which is widely applied to create compact collision representations for real-time applications, including VR/AR, interactive games, and robotic simulations. Efficiency and optimality are critical for ACD algorithms in approximating large-scale, complex 3D shapes, enabling high-quality decompositions with minimal components. Unfortunately, existing methods either employ sub-optimal greedy strategies or rely on computationally intensive multi-step searches. In this work, we propose RL-ACD, a data-driven, reinforcement learning-based approach for efficient and near-optimal convex shape decomposition. We formulate ACD as a Markov Decision Process (MDP), where cutting planes are iteratively applied based on the current stage's mesh fragments rather than the entire fine-grained mesh, leading to a novel, efficient geometric encoding. To train near-optimal policies for ACD, we propose a novel dual-state Bellman loss and analyze its convergence using a Q-learning algorithm. Comprehensive evaluations across diverse datasets validate the efficiency and accuracy of RL-ACD for convex decomposition tasks. Our method outperforms the multi-step tree search by 15× in terms of computational speed, while reducing the number of resulting components by 16% compared to the current state-of-the-art greedy algorithms, significantly narrowing the sub-optimality gap and enhancing downstream task performance.

Current 3D asset creation pipelines typically consist of three stages: creating multi-view concept art, producing 3D meshes based on the artwork, and painting textures for the meshes—an often labor-intensive process. Automated texture generation offers significant acceleration, but prior methods, which fine-tune 2D diffusion models with multi-view input images, often fail to preserve pixel-level details. These methods primarily emphasize semantic and subject consistency, which do not meet the requirements of artwork-guided texture workflows. To address this, we present AlignTex , a novel framework for generating high-quality textures from 3D meshes and multi-view artwork, ensuring both appearance detail and geometric consistency. AlignTex operates in two stages: aligned image generation and texture refinement. The core of our approach, AlignNet , resolves complex misalignments by extracting information from both the artwork and the mesh, generating images compatible with orthographic projection while maintaining geometric and visual fidelity. After projecting aligned images into the texture space, further refinement addresses seams and self-occlusion using an inpainting model and a geometry-aware texture dilation method. Experimental results demonstrate that AlignTex outperforms baseline methods in generation quality and efficiency, offering a practical solution to enhance 3D asset creation in gaming and film production.

Hair cards remain a widely used representation for hair modeling in real-time applications, offering a practical trade-off between visual fidelity, memory usage, and performance. However, generating high-quality hair card models remains a challenging and labor-intensive task. This work presents an automated pipeline for converting strand-based hair models into hair card models with a limited number of cards and textures while preserving the hairstyle appearance. Our key idea is a novel differentiable representation where each strand is encoded as a projected 2D curve in the texture space, which enables end-to-end optimization with differentiable rendering while respecting the structures of the hair geometry. Based on this representation, we develop a novel algorithm pipeline, where we first cluster hair strands into initial hair cards and project the strands into the texture space. We then conduct a two-stage optimization, where our first stage optimizes the orientation of each hair card separately, and after strand projection, our second stage conducts joint optimization over the entire hair card model for fine-tuning. Our method is evaluated on a range of hairstyles, including straight, wavy, curly, and coily hair. To capture the appearance of short or coily hair, our method comes with support for hair caps and cross-card.

Autonomous underwater vehicles (AUVs) face significant challenges in trajectory tracking due to nonlinear dynamics, actuator faults, and environmental disturbances. To address these issues, this article proposes a novel fault-tolerant control strategy that ensures fixed-time trajectory tracking with prescribed accuracy for underactuated AUVs. The proposed approach integrates boundary functions with a constraint-handling mechanism, enabling guaranteed tracking performance within a fixed time horizon while satisfying output constraints. Unlike existing approaches, the controller does not rely on accurate system models, parameter estimation, or external observers, and avoids the computation of virtual control derivatives, resulting in reduced computational complexity. Moreover, the control scheme maintains robustness against time-varying actuator faults and environmental disturbances without auxiliary adaptation or learning mechanisms. Simulation results demonstrate the effectiveness and superior performance of the proposed approach compared with existing methods, validating its capability to maintain tracking accuracy and closed-loop stability under adverse operating conditions.

Predicting the state evolution of ultra high-dimensional, time-reversible fluid dynamic systems is a crucial but computationally expensive task. Existing physics-informed neural networks either incur high inference cost or cannot preserve the time-reversible nature of the underlying dynamics system. We propose a model-based approach to identify low-dimensional, time reversible, nonlinear fluid dynamic systems. Our method utilizes the symplectic structure of reduced Eulerian fluid and use stochastic Riemann optimization to obtain a low-dimensional bases that minimize the expected trajectory-wise dimension-reduction error over a given distribution of initial conditions. We show that such minimization is well-defined since the reduced trajectories are differentiable with respect to the subspace bases over the entire Grassmannian manifold, under proper choices of timestep sizes and numerical integrators. Finally, we propose a loss function measuring the trajectory-wise discrepancy between the original and reduced models. By tensor precomputation, we show that gradient information of such loss function can be evaluated efficiently over a long trajectory without time-integrating the high-dimensional dynamic system. Through evaluations on a row of simulation benchmarks, we show that our method reduces the discrepancy by 50-90 percent over conventional reduced models and we outperform PINNs by exactly preserving the time reversibility.

In this paper, a low consumption control problem for a class of time-delay systems with sudden non-affine faults is studied. The finite covering lemma and fuzzy logic systems are utilized to eliminate the effect of unknown time delays. The mean value theorem and nussbaum function are used to handle non-affine structures. And then, unknown functions present in the system will be approximated using RBF neural networks. Finally, the event-triggered mechanism is combined with the backstepping framework to achieve low consumption control of the system.

The advent of neural 3D Gaussians [21] has recently brought about a revolution in the field of neural rendering, facilitating the generation of high-quality renderings at real-time speeds. However, the explicit and discrete repre-sentation encounters challenges when applied to scenes fea-turing reflective surfaces. In this paper, we present Gaus-sian Shader, a novel method that applies a simplified shading function on 3D Gaussians to enhance the neural ren-dering in scenes with reflective surfaces while preserving the training and rendering efficiency. The main challenge in applying the shading function lies in the accurate nor-mal estimation on discrete 3D Gaussians. Specifically, we proposed a novel normal estimation framework based on the shortest axis directions of 3D Gaussians with a deli-cately designed loss to make the consistency between the normals and the geometries of Gaussian spheres. Experiments show that GaussianShader strikes a commendable balance between efficiency and visual quality. Our method surpasses Gaussian Splatting [21] in PSNR on specular object datasets, exhibiting an improvement of 1.57dB. When compared to prior works handling reflective surfaces, such as Ref-NeRF [45], our optimization time is significantly accelerated (23h vs. 0.58h). Please click on our project web-site to see more results

Strand-based hair simulations have recently become increasingly popular for a range of real-time applications. However, accurately simulating the full number of hair strands remains challenging. A commonly employed technique involves simulating a subset of guide hairs to capture the overall behavior of the hairstyle. Details are then enriched by interpolation using linear skinning. Hair interpolation enables fast real-time simulations but frequently leads to various artifacts during runtime. As the skinning weights are often pre-computed, substantial variations between the initial and deformed shapes of the hair can cause severe deviations in fine hair geometry. Straight hairs may become kinked, and curly hairs may become zigzags. This work introduces a novel physical-driven hair interpolation scheme that utilizes existing simulated guide hair data. Instead of directly operating on positions, we interpolate the internal forces from the guide hairs before efficiently reconstructing the rendered hairs based on their material model. We formulate our problem as a constraint satisfaction problem for which we present an efficient solution. Further practical considerations are addressed using regularization terms that regulate penetration avoidance and drift correction. We have tested various hairstyles to illustrate that our approach can generate visually plausible rendered hairs with only a few guide hairs and minimal computational overhead, amounting to only about 20% of conventional linear hair interpolation. This efficiency underscores the practical viability of our method for real-time applications.

Level of detail has been widely used in interactive computer graphics. In current industrial 3D modeling pipelines, artists rely on commercial software to generate highly detailed models with UV maps and then bake textures for low-poly counterparts. In these pipelines, each step is performed separately, leading to unsatisfactory visual appearances for low polygon count models. Moreover, existing texture baking techniques assume the low-poly mesh has a small geometric difference from the high-poly, which is often not true in practice, especially with extremely low poly count models. To alleviate the visual discrepancy of the low-poly mesh, we propose to jointly optimize UV mappings during texture baking, allowing for low-poly models to faithfully replicate the appearance of the high-poly even with large geometric differences. We formulate the optimization within a differentiable rendering framework, allowing the automatic adjustment of texture regions to encode appearance information. To compensate for view parallax when two meshes have large geometric differences, we introduce a spherical harmonic parallax mapping, which uses spherical harmonic functions to modulate per-texel UV coordinates based on the view direction. We evaluate the effectiveness and robustness of our approach on a dataset composed of online downloaded models, with varying complexities and geometric discrepancies. Our method achieves superior quality over state-of-the-art techniques and commercial solutions.

Simulating high-resolution cloth poses computational challenges in real-time applications. In the gaming industry, the proxy mesh technique offers an alternative, simulating a simplified low-resolution cloth geometry, proxy mesh. This proxy mesh's dynamics drive the detailed high-resolution geometry, visual mesh , through Linear Blended Skinning (LBS). However, generating a suitable proxy mesh with appropriate skinning weights from a given visual mesh is non-trivial, often requiring skilled artists several days for fine-tuning. This paper presents an automatic pipeline to convert an ill-conditioned highresolution visual mesh into a single-layer low-poly proxy mesh. Given that the input visual mesh may not be simulation-ready, our approach then simulates the proxy mesh based on specific use scenarios and optimizes the skinning weights, relying on differential skinning with several well-designed loss functions to ensure the skinned visual mesh appears plausible in the final simulation. We have tested our method on various challenging cloth models, demonstrating its robustness and effectiveness.

We present a semi-infinite program (SIP) solver for trajectory optimizations of general articulated robots. These problems are more challenging than standard nonlinear program by involving an infinite number of nonconvex, collision constraints. Prior SIP solvers based on constraint sampling cannot guarantee the satisfaction of all constraints. Instead, our method uses a conservative bound on articulated body motions to ensure the solution feasibility throughout the optimization procedure. We further use subdivision to adaptively reduce the error in conservative motion estimation. Combined, we prove that our SIP solver guarantees feasibility while approaching the optimal solution of SIP problems up to arbitrary user-provided precision. We demonstrate our method toward several trajectory optimization problems in simulation, including industrial robot arms and UAVs. The results demonstrate that our approach generates collision-free locally optimal trajectories within a couple of minutes.

Mesh repair is a long-standing challenge in computer graphics and related fields. Converting defective meshes into watertight manifold meshes can greatly benefit downstream applications such as geometric processing, simulation, fabrication, learning, and synthesis. In this work, by assuming the model is visually correct, we first introduce three visual measures for visibility, orientation, and openness, based on ray-tracing. We then present a novel mesh repair framework incorporating visual measures with several critical steps, i.e., open surface closing, face reorientation, and global optimization, to effectively repair meshes with defects (e.g., gaps, holes, self-intersections, degenerate elements, and inconsistent orientations) and preserve visual appearances. Our method reduces unnecessary mesh complexity without compromising geometric accuracy or visual quality while preserving input attributes such as UV coordinates for rendering. We evaluate our approach on hundreds of models randomly selected from ShapeNet and Thingi10K, demonstrating its effectiveness and robustness compared to existing approaches.

Deformable robots are notoriously difficult to model or control due to its high-dimensional configuration spaces. Direct trajectory optimization suffers from the curse-of-dimensionality and incurs a high computational cost, while learning-based controller optimization methods are sensitive to hyper-parameter tuning. To overcome these limitations, we hypothesize that high fidelity soft robots can be both simulated and controlled by restricting to low-dimensional spaces. Under such assumption, we propose a two-stage algorithm to identify such simulation- and control-spaces. Our method first identifies the so-called simulation-space that captures the salient deformation modes, to which the robot's governing equation is restricted. We then identify the control-space, to which control signals are restricted. We propose a multi-fidelity Riemannian Bayesian bilevel optimization to identify task-specific control spaces. We show that the dimension of control-space can be less than 10 for a high-DOF soft robot to accomplish walking and swimming tasks, allowing low-dimensional MPC controllers to be applied to soft robots with tractable computational complexity.

Optimizing the memory footprint of 3D models can have a major impact on the user experiences during real-time rendering and streaming visualization, where the major memory overhead lies in the high-resolution texture data. In this work, we propose a robust and automatic pipeline to content-aware, lossy compression for texture atlas. The design of our solution lies in two observations: 1) mapping multiple surface patches to the same texture region is seamlessly compatible with the standard rendering pipeline, requiring no decompression before any usage; 2) a texture image has background regions and salient structural features, which can be handled separately to achieve a high compression rate. Accordingly, our method contains joint operations of image segmentation, re-meshing, UV unwrapping, and texture baking. To evaluate the efficacy of our approach, we batch-processed a dataset containing 100 models collected online. On average, our method achieves a texture atlas compression ratio of 81.41% with an averaged PSNR and MS-SSIM scores of 40.90 and 0.98, a marginal error in visual appearance.

We propose a height-field-based real-time simulation method for sand and water mixtures. Inspired by the shallow-water assumption, our approach extends the governing equations to handle two-phase flows of sand and water using height fields. Our depth-integrated governing equations can model the elastoplastic behavior of sand, as well as sand-water-mixing phenomena such as friction, diffusion, saturation, and momentum exchange. We further propose an operator-splitting time integrator that is both GPU-friendly and stable under moderate time step sizes. We have evaluated our method on a set of benchmark scenarios involving large bodies of heterogeneous materials, where our GPU-based algorithm runs at real-time frame rates. Our method achieves a desirable trade-off between fidelity and performance, bringing an unprecedentedly immersive experience for real-time applications.

Topology Optimization (TO) is an essential tool for optimizing the structural robustness of load-bearing mechanical parts. An ideal TO solver should be computationally efficient for designers to preview the results, while ultimately converge to locally optimal designs. However, existing TO solvers either incur a high iterative cost or fail to provide the convergence guarantee. Borrowing ideas from recent advances in first-order bilevel optimization, we propose a new TO solver combining the Projected Gradient Descent (PGD) algorithm and inexact Finite Element Analysis (FEA). We further show that our method is convergent to a first-order critical point . Our proposed First-Order Bilevel Topology Optimization (FBTO) can solve several, important problems in the robot design paradigm, including TO under self-weight and multiple external loads. Finally, we evaluate and compare FBTO with prior TO solvers on a row of 2D and 3D problems.

Superpixel generation is increasingly an important area for computer vision tasks. While superpixels with highly regular shapes are preferred to make the subsequent processing easier, the accuracy of the superpixel boundaries is also necessary. Previous methods usually depend on a distance function considering both spatial and color coherency regularization on the whole image, which however is hard to balance between shape regularity and boundary adherence, especially when the desired number of superpixels is small. In addition, non-adaptive parameters and insufficient contour information also affect the performance of segmentation. To mitigate these problems, we propose a robust divide-and-conquer superpixel segmentation method, of which the core idea is that we apply a new contour information extraction and a pixel clustering to separate the input image into flat and non-flat regions, where the former targets shape regularity and the latter emphasizes boundary adherence, followed by an efficient hierarchical merging to clean up tiny and dangling superpixels. Our algorithm requires no additional parameter tuning except the desired number of superpixels since our internal parameters are self-adaptive to the image contents. Experimental results demonstrate that for public benchmark datasets, our algorithm consistently generates more regular superpixels with stronger boundary adherence than state-of-the-art methods while maintaining a competitive efficiency. The source code is available athttps://github.com/YunyangXu/HQSGRD.

We propose a robust re-meshing approach that can automatically generate visual-preserving low-poly meshes for any high-poly models found in the wild. Our method can be seamlessly integrated into current mesh-based 3D asset production pipelines. Given an input high-poly, our method proceeds in two stages: 1) Robustly extracting an offset surface mesh that is feature-preserving, and guaranteed to be watertight, manifold, and self-intersection free; 2) Progressively simplifying and flowing the offset mesh to bring it close to the input. The simplicity and the visual-preservation of the generated low-poly is controlled by a user-required target screen size of the input: decreasing the screen size reduces the element count of the low-poly but enlarges its visual difference from the input. We have evaluated our method on a subset of the Thingi10K dataset that contains models created by practitioners in different domains, with varying topological and geometric complexities. Compared to state-of-the-art approaches and widely used software, our method demonstrates its superiority in terms of the element count, visual preservation, geometry, and topology guarantees of the generated low-polys.

Lagrangian/Eulerian hybrid strand-based hair simulation techniques have quickly become a popular approach in VFX and real-time graphics applications. With Lagrangian hair dynamics, the inter-hair contacts are resolved in the Eulerian grid using the continuum method, i.e., the MPM scheme with the granular Drucker-Prager rheology, to avoid expensive collision detection and handling. This fuzzy collision handling makes the authoring process significantly easier. However, although current hair grooming tools provide a wide range of strand-based modeling tools for this simulation approach, the crucial sag-free initialization functionality remains often ignored. Thus, when the simulation starts, gravity would cause any artistic hairstyle to sag and deform into unintended and undesirable shapes. This paper proposes a novel four-stage sag-free initialization framework to solve stable quasistatic configurations for hybrid strand-based hair dynamic systems. These four stages are split into two global-local pairs. The first one ensures static equilibrium at every Eulerian grid node with additional inequality constraints to prevent stress from exiting the yielding surface. We then derive several associated closed-form solutions in the local stage to compute segment rest lengths, orientations, and particle deformation gradients in parallel. The second global-local step solves along each hair strand to ensure all the bend and twist constraints produce zero net torque on every hair segment, followed by a local step to adjust the rest Darboux vectors to a unit quaternion. We also introduce an essential modification for the Darboux vector to eliminate the ambiguity of the Cosserat rod rest pose in both initialization and simulation. We evaluate our method on a wide range of hairstyles, and our approach can only take a few seconds to minutes to get the rest quasistatic configurations for hundreds of hair strands. Our results show that our method successfully prevents sagging and has minimal impact on the hair motion during simulation.

Kinetic solvers for incompressible fluid simulation were designed to run efficiently on massively parallel architectures such as GPUs. While these lattice Boltzmann solvers have recently proven much faster and more accurate than the macroscopic Navier-Stokes-based solvers traditionally used in graphics, it systematically comes at the price of a very large memory requirement: a mesoscopic discretization of statistical mechanics requires over an order of magnitude more variables per grid node than most fluid solvers in graphics. In order to open up kinetic simulation to gaming and simulation software packages on commodity hardware, we propose a HighOrder Moment-Encoded Lattice-Boltzmann-Method solver which we coined HOME-LBM, requiring only the storage of a few moments per grid node, with little to no loss of accuracy in the typical simulation scenarios encountered in graphics. We show that our lightweight and lightspeed fluid solver requires three times less memory and runs ten times faster than state-of-the-art kinetic solvers, for a nearly-identical visual output.

In this article, we provide a detailed survey of techniques for hexahedral mesh generation. We cover the whole spectrum of alternative approaches to mesh generation, as well as post-processing algorithms for connectivity editing and mesh optimization. For each technique, we highlight capabilities and limitations, also pointing out the associated unsolved challenges. Recent relaxed approaches, aiming to generate not pure-hex but hex-dominant meshes, are also discussed. The required background, pertaining to geometrical as well as combinatorial aspects, is introduced along the way.

2D irregular shape packing is a necessary step to arrange UV patches of a 3D model within a texture atlas for memory-efficient appearance rendering in computer graphics. Being a joint, combinatorial decision-making problem involving all patch positions and orientations, this problem has well-known NP-hard complexity. Prior solutions either assume a heuristic packing order or modify the upstream mesh cut and UV mapping to simplify the problem, which either limits the packing ratio or incurs robustness or generality issues. Instead, we introduce a learning-assisted 2D irregular shape packing method that achieves a high packing quality with minimal requirements from the input. Our method iteratively selects and groups subsets of UV patches into near-rectangular super patches, essentially reducing the problem to bin-packing, based on which a joint optimization is employed to further improve the packing ratio. In order to efficiently deal with large problem instances with hundreds of patches, we train deep neural policies to predict nearly rectangular patch subsets and determine their relative poses, leading to linear time scaling with the number of patches. We demonstrate the effectiveness of our method on three datasets for UV packing, where our method achieves a higher packing ratio over several widely used baselines with competitive computational speed.

Abstract Occlusion culling has become a prevalent method in modern game engines. It can significantly reduce the rendering cost by using an approximate coarse mesh (occluder) for culling hidden objects. An ideal occluder should use as few faces as possible to represent the high‐resolution input mesh with a high culling accuracy. We address the open problem of automatic occluder generation for 3D building models with complex topology and interior structures. Our method first generates two coarse sets of faces via patch‐based and voxel‐based mesh simplification techniques. A metric‐guided selection algorithm chooses the best subset of faces to form the occluder, achieving a high occlusion rate and accuracy. Over an evaluation of 77 building models, our method compares favorably against state‐of‐the‐arts in terms of occlusion accuracy, occlusion rate, and face number.

Wrapping objects using ropes is a common practice in our daily life. However, it is difficult to design and tie ropes on a 3D object with complex topology and geometry features while ensuring wrapping security and easy operation. In this article, we propose to compute a rope net that can tightly wrap around various 3D shapes. Our computed rope net not only immobilizes the object but also maintains the load balance during lifting. Based on the key observation that if every knot of the net has four adjacent curve edges, then only a single rope is needed to construct the entire net. We reformulate the rope net computation problem into a constrained curve network optimization. We propose a discrete-continuous optimization approach, where the topological constraints are satisfied in the discrete phase and the geometrical goals are achieved in the continuous stage. We also develop a hoist planning to pick anchor points so that the rope net equally distributes the load during hoisting. Furthermore, we simulate the wrapping process and use it to guide the physical rope net construction process. We demonstrate the effectiveness of our method on 3D objects with varying geometric and topological complexity. In addition, we conduct physical experiments to demonstrate the practicability of our method.

The Finite Element Method (FEM) is widely used to solve discrete Partial Differential Equations (PDEs) in engineering and graphics applications. The popularity of FEM led to the development of a large family of variants, most of which require a tetrahedral or hexahedral mesh to construct the basis. While the theoretical properties of FEM basis (such as convergence rate, stability, etc.) are well understood under specific assumptions on the mesh quality, their practical performance, influenced both by the choice of the basis construction and quality of mesh generation, have not been systematically documented for large collections of automatically meshed 3D geometries. We introduce a set of benchmark problems involving most commonly solved elliptic PDEs, starting from simple cases with an analytical solution, moving to commonly used test problem setups, and using manufactured solutions for thousands of real-world, automatically meshed geometries. For all these cases, we use state-of-the-art meshing tools to create both tetrahedral and hexahedral meshes, and compare the performance of different element types for common elliptic PDEs. The goal of this benchmark is to enable comparison of complete FEM pipelines, from mesh generation to algebraic solver, and exploration of relative impact of different factors on the overall system performance. As a specific application of our geometry and benchmark dataset, we explore the question of relative advantages of unstructured (triangular/ tetrahedral) and structured (quadrilateral/hexahedral) discretizations. We observe that for Lagrange-type elements, while linear tetrahedral elements perform poorly, quadratic tetrahedral elements perform equally well or outperform hexahedral elements for our set of problems and currently available mesh generation algorithms. This observation suggests that for common problems in structural analysis, thermal analysis, and low Reynolds number flows, high-quality results can be obtained with unstructured tetrahedral meshes, which can be created robustly and automatically. We release the description of the benchmark problems, meshes, and reference implementation of our testing infrastructure to enable statistically significant comparisons between different FE methods, which we hope will be helpful in the development of new meshing and FEA techniques.

The task of explicit surface reconstruction is to generate a surface mesh by interpolating a given point cloud. Explicit surface reconstruction is necessary when the point cloud is required to appear exactly on the surface. However, for a non-perfect input, such as lack of normals, low density, irregular distribution, thin and tiny parts, and high genus, a robust explicit reconstruction method that can generate a high-quality manifold triangulation is missing. We propose a robust explicit surface reconstruction method that starts from an initial simple surface mesh, alternately performs a Filmsticking step and a Sculpting step of the initial mesh, and converges when the surface mesh interpolates all input points (except outliers) and remains stable. The Filmsticking is to minimize the geometric distance between the surface mesh and the point cloud through iteratively performing a restricted Voronoi diagram technique on the surface mesh, whereas the Sculpting is to bootstrap the Filmsticking iteration from local minima by applying appropriate geometric and topological changes of the surface mesh. Our algorithm is fully automatic and produces high-quality surface meshes for non-perfect inputs that are typically considered to be challenging for prior state of the art. We conducted extensive experiments on simulated scans and real scans to validate the effectiveness of our approach.

This article investigates the problem of model-free tracking control for a class of continuum manipulators. A new type of robust control strategy is provided to address the problem, which primarily consists of two parts. First, to achieve output tracking with the desired accuracy, an error transformation scheme is constructed. Moreover, because of the robustness of the error transformation scheme against model uncertainties, no knowledge of the manipulator model is required, leading to a model-free control solution. Then, a tuning function is used to modify certain error variables to relax the requirements on the initial conditions of the error transformation scheme. In this way, the global stability of the closed-loop system can be guaranteed. Finally, both simulation and experimental results validate the expected performance of the presented control method.

Knitting can efficiently fabricate stretchable and durable soft surfaces. These surfaces are often designed to be worn on solid objects as covers, garments, and accessories. Given a 3D model, we consider a knit for it wearable if the knit not only reproduces the shape of the 3D model but also can be put on and taken off from the model without deforming the model. This "wearability" places additional constraints on surface design and fabrication, which existing machine knitting approaches do not take into account. We introduce the first practical automatic pipeline to generate knit designs that are both wearable and machine knittable. Our pipeline handles knittability and wearability with two separate modules that run in parallel. Specifically, given a 3D object and its corresponding 3D garment surface, our approach first converts the garment surface into a topological disc by introducing a set of cuts. The resulting cut surface is then fed into a physically-based unclothing simulation module to ensure the garment's wearability over the object. The unclothing simulation determines which of the previously introduced cuts could be sewn permanently without impacting wearability. Concurrently, the cut surface is converted into an anisotropic stitch mesh. Then, our novel, stochastic, any-time flat-knitting scheduler generates fabrication instructions for an industrial knitting machine. Finally, we fabricate the garment and manually assemble it into one complete covering worn by the target object. We demonstrate our method's robustness and knitting efficiency by fabricating models with various topological and geometric complexities. Further, we show that our method can be incorporated into a knitting design tool for creating knitted garments with customized patterns.

Generating locally optimal UAV-trajectories is challenging due to the non-convex constraints of collision avoidance and actuation limits. We present the first local, optimization-based UAV-trajectory generator that simultane-ously guarantees validity and asymptotic optimality for known environments. Validity: Given a feasible initial guess, our algo-rithm guarantees the satisfaction of all constraints throughout the process of optimization. Asymptotic Optimality: We use an asymptotic exact piecewise approximation of the trajectory with an automatically adjustable resolution of its discretization. The trajectory converges under refinement to the first-order stationary point of the exact non-convex programming problem. Our method has additional practical advantages including joint optimality in terms of trajectory and time-allocation, and robustness to challenging environments as demonstrated in our experiments.

We propose a decentralized, learning-based solution to the challenging problem of unlabeled multi-agent navigation among obstacles, where robots need to simultaneously tackle the problems of goal assignment, local collision avoidance, and navigation. Our method has each robot infer their desired action by communicating with each other as well as a set of position-fixed routers. The inference is carried out on a graph neural network (GNN) with both robot and router nodes. We train our GNN using imitation learning on a small group of robots, where we modify the centralized version of the concurrent goal assignment and planning algorithm (CAPT) as our expert. By sharing weights among all robots and routers, our model can scale to unseen environments with any number of possibly kinodynamic agents during test time. We have achieved a success rate of 91.2% and 85.6% for point and car-like robots, respectively. Source code will be publicly available upon the publication of the work.

This article is concerned with the fault-tolerant tracking control problem for pneumatic continuum manipulator (PCM) systems with actuator faults. Conventional control strategies applied to PCMs have difficulty addressing the tracking control issue for systems subject to actuator faults. In this article, we provide a robust fault-tolerant control strategy for solving this issue. We first present an error transformation approach that possesses potential robustness against model uncertainties and unknown actuator faults. To relax certain restrictions in the error transformation approach, we then adopt a tuning function to adjust the error variables. By doing so, global stability of the closed-loop system is ensured. Finally, the effectiveness of this control strategy is validated through experiments on a PCM.

Inspired by natural cellular materials such as trabecular bone, lattice structures have been developed as a new type of lightweight material. In this paper we present a novel method to design lattice structures that conform with both the principal stress directions and the boundary of the optimized shape. Our method consists of two major steps: the first optimizes concurrently the shape (including its topology) and the distribution of orthotropic lattice materials inside the shape to maximize stiffness under application-specific external loads; the second takes the optimized configuration (i.e., locally-defined orientation, porosity, and anisotropy) of lattice materials from the previous step, and extracts a globally consistent lattice structure by field-aligned parameterization. Our approach is robust and works for both 2D planar and 3D volumetric domains. Numerical results and physical verifications demonstrate remarkable structural properties of conforming lattice structures generated by our method.

We present a new method to generate optimal grasps for brittle and fragile objects using a novel stress- minimization (SM) metric. Our approach is designed for objects that are composed of homogeneous isotopic materials. Our SM metric measures the maximal resistible external wrenches that would not result in fractures in the target objects. In this paper, we propose methods to compute our new metric. We also use our SM metric to design optimal grasp planning algorithms. Finally, we compare the performance of our metric and conventional grasp metrics, including Q1,Q∞,QG11,QMSV,QVEW. Our experiments show that our SM metric takes into account the material characteristics and object shapes to indicate the fragile regions, where prior methods may not work well. We also show that the computational cost of our SM metric is on par with prior methods. Finally, we show that grasp planners guided by our metric can lower the probability of breaking target objects.

Given an articulated robot arm, we present a method to identify two regions with non-empty interiors. The first region is a subset of the configuration space where every point in the region is manipulable. The second region is a subset of the workspace where every point in the region is reachable by the end-effector. Our method expresses the kinematic state of the robot arm using the maximal coordinates, so that the kinematic constraints take polynomial forms. We then reformulate the optimization-based inverse kinematics (IK) algorithm as gradient flows. Finally, we use sum-of-squares (SOS) programming to certify the convergence of each gradient flow. Our main result shows that the feasibility of an SOS programming problem is a sufficient condition for the manipulability and reachability of the sublevel sets of polynomial functions. Our method can be used to certify manipulable or reachable regions by solving a set of linear matrix inequalities (LMIs) or to maximize the volume of a region by solving a set of bilinear matrix inequalities (BMIs). These identified regions can then be used in various motion planning problems as hard safety constraints.

Abstract We propose an octree‐based algorithm to tessellate the interior of a closed surface with hexahedral cells. The generated hexahedral mesh (1) explicitly preserves sharp features of the original input, (2) has a maximal, user‐controlled distance deviation from the input surface, (3) is composed of elements with only positive scaled jacobians (measured by the eight corners of a hex [SEK*07]), and (4) does not have self‐intersections. We attempt to achieve these goals by proposing a novel pipeline to create an initial pure hexahedral mesh from an octree structure, taking advantage of recent developments in the generation of locally injective 3D parametrizations to warp the octree boundary to conform to the input surface. Sharp features in the input are bijectively mapped to poly‐lines in the output and preserved by the deformation, which takes advantage of a scaffold mesh to prevent local and global intersections. The robustness of our technique is experimentally validated by batch processing a large collection of organic and CAD models, without any manual cleanup or parameter tuning. All results including mesh data and statistics in the paper are provided in the additional material. The open‐source implementation will be made available online to foster further research in this direction.

Abstract Image vectorization is an important yet challenging problem, especially when the input image has rich content. In this paper, we develop a novel method for automatically vectorizing natural images with feature‐aligned quad‐dominant meshes. Inspired by the quadrangulation methods in 3D geometry processing, we propose a new directional field optimization technique by encoding the color gradients, sidestepping the explicit computing of salient image features. We further compute the anisotropic scales of the directional field by accommodating the distance among image features. Our method is fully automatic and efficient, which takes only a few seconds for a 400×400 image on a normal laptop. We demonstrate the effectiveness of the proposed method on various image editing applications.

We propose a robust 2D meshing algorithm, TriWild , to generate curved triangles reproducing smooth feature curves, leading to coarse meshes designed to match the simulation requirements necessary by applications and avoiding the geometrical errors introduced by linear meshes. The robustness and effectiveness of our technique are demonstrated by batch processing an SVG collection of 20k images, and by comparing our results against state of the art linear and curvilinear meshing algorithms. We demonstrate for our algorithm the practical utility of computing diffusion curves, fluid simulations, elastic deformations, and shape inflation on complex 2D geometries.

We introduce an integrated meshing and finite-element method pipeline enabling solution of partial differential equations in the volume enclosed by a boundary representation. We construct a hybrid hexahedral-dominant mesh, which contains a small number of star-shaped polyhedra, and build a set of high-order bases on its elements, combining triquadratic B-splines, triquadratic hexahedra, and harmonic elements. We demonstrate that our approach converges cubically under refinement, while requiring around 50% of the degrees of freedom than a similarly dense hexahedral mesh composed of triquadratic hexahedra. We validate our approach solving Poisson’s equation on a large collection of models, which are automatically processed by our algorithm, only requiring the user to provide boundary conditions on their surface.

We introduce the first fully automatic pipeline to convert arbitrary 3D shapes into knit models. Our pipeline is based on a global parametrization remeshing pipeline to produce an isotropic quad-dominant mesh aligned with a 2-RoSy field. The knitting directions over the surface are determined using a set of custom topological operations and a two-step global optimization that minimizes the number of irregularities. The resulting mesh is converted into a valid stitch mesh that represents the knit model. The yarn curves are generated from the stitch mesh and the final yarn geometry is computed using a yarn-level relaxation process. Thus, we produce topologically valid models that can be used with a yarn-level simulation. We validate our algorithm by automatically generating knit models from complex 3D shapes and processing over a hundred models with various shapes without any user input or parameter tuning. We also demonstrate applications of our approach for custom knit model generation using fabrication via 3D printing.

We propose a novel tetrahedral meshing technique that is unconditionally robust, requires no user interaction, and can directly convert a triangle soup into an analysis-ready volumetric mesh. The approach is based on several core principles: (1) initial mesh construction based on a fully robust, yet efficient, filtered exact computation (2) explicit (automatic or user-defined) tolerancing of the mesh relative to the surface input (3) iterative mesh improvement with guarantees, at every step, of the output validity. The quality of the resulting mesh is a direct function of the target mesh size and allowed tolerance: increasing allowed deviation from the initial mesh and decreasing the target edge length both lead to higher mesh quality. Our approach enables "black-box" analysis, i.e. it allows to automatically solve partial differential equations on geometrical models available in the wild, offering a robustness and reliability comparable to, e.g., image processing algorithms, opening the door to automatic, large scale processing of real-world geometric data.

For a given PDE problem, three main factors affect the accuracy of FEM solutions: basis order, mesh resolution, and mesh element quality. The first two factors are easy to control, while controlling element shape quality is a challenge, with fundamental limitations on what can be achieved. We propose to use p -refinement (increasing element degree) to decouple the approximation error of the finite element method from the domain mesh quality for elliptic PDEs. Our technique produces an accurate solution even on meshes with badly shaped elements, with a slightly higher running time due to the higher cost of high-order elements. We demonstrate that it is able to automatically adapt the basis to badly shaped elements, ensuring an error consistent with high-quality meshing, without any per-mesh parameter tuning. Our construction reduces to traditional fixed-degree FEM methods on high-quality meshes with identical performance. Our construction decreases the burden on meshing algorithms, reducing the need for often expensive mesh optimization and automatically compensates for badly shaped elements, which are present due to boundary constraints or limitations of current meshing methods. By tackling mesh generation and finite element simulation jointly, we obtain a pipeline that is both more efficient and more robust than combinations of existing state of the art meshing and FEM algorithms.

Abstract Hexahedral (hex‐) meshes are important for solving partial differential equations (PDEs) in applications of scientific computing and mechanical engineering. Many methods have been proposed aiming to generate hex‐meshes with high scaled Jacobians. While it is well established that a hex‐mesh should be inversion‐free (i.e. have a positive Jacobian measured at every corner of its hexahedron), it is not well‐studied that whether the scaled Jacobian is the most effective indicator of the quality of simulations performed on inversion‐free hex‐meshes given the existing dozens of quality metrics for hex‐meshes. Due to the challenge of precisely defining the relations among metrics, studying the correlations among different quality metrics and their correlations with the stability and accuracy of the simulations is a first and effective approach to address the above question. In this work, we propose a correlation analysis framework to systematically study these correlations. Specifically, given a large hex‐mesh dataset, we classify the existing quality metrics into groups based on their correlations, which characterizes their similarity in measuring the quality of hex‐elements. In addition, we rank the individual metrics based on their correlations with the accuracy and stability metrics for simulations that solve a number of elliptic PDE problems. Our preliminary experiments suggest that metrics that assess the conditioning of the elements are more correlated to the quality of solving elliptic PDEs than the others. Furthermore, an inversion‐free hex‐mesh with higher average quality (measured by any quality metrics) usually leads to a more accurate and stable computation of elliptic PDEs. To support our correlation study and address the lack of a publicly available large hex‐mesh dataset with sufficiently varying quality metric values, we also propose a two‐level perturbation strategy to generate the desired dataset from a small number of meshes to exclude the influences of element numbers, vertex connectivity, and volume sizes to our study.

Abstract Hexahedral (or Hex‐) meshes are preferred in a number of scientific and engineering simulations and analyses due to their desired numerical properties. Recent state‐of‐the‐art techniques can generate high‐quality hex‐meshes. However, they typically produce hex‐meshes with uniform element sizes and thus may fail to preserve small‐scale features on the boundary surface. In this work, we present a new framework that enables users to generate hex‐meshes with varying element sizes so that small features will be filled with smaller and denser elements, while the transition from smaller elements to larger ones is smooth, compared to the octree‐based approach. This is achieved by first detecting regions of interest (ROIs) of small‐scale features. These ROIs are then magnified using the as‐rigid‐as‐possible deformation with either an automatically determined or a user‐specified scale factor. A hex‐mesh is then generated from the deformed mesh using existing approaches that produce hex‐meshes with uniform‐sized elements. This initial hex‐mesh is then mapped back to the original volume before magnification to adjust the element sizes in those ROIs. We have applied this framework to a variety of man‐made and natural models to demonstrate its effectiveness.

As one of the most popular image oversegmentations, superpixel has been commonly used as supporting regions for primitives to reduce computations in various computer vision tasks. In this paper, we propose a novel superpixel segmentation approach based on a distance function that is designed to balance among boundary adherence, intensity homogeneity, and compactness (COM) characteristics of the resulting superpixels. Given an expected number of superpixels, our method begins with initializing the superpixel seed positions to obtain the initial labels of pixels. Then, we optimize the superpixels iteratively based on the defined distance measurement. We update the positions and intensities of superpixel seeds based on the three-sigma rule. The experimental results demonstrate that our algorithm is more effective and accurate than previous superpixel methods and achieves a comparable tradeoff between superpixel COM and adherence to object boundaries.

We propose a robust and efficient field-aligned volumetric meshing algorithm that produces hex-dominant meshes, i.e. meshes that are predominantly composed of hexahedral elements while containing a small number of irregular polyhedra. The latter are placed according to the singularities of two optimized guiding fields, which allow our method to generate meshes with an exceptionally high amount of isotropy. The field design phase of our method relies on a compact quaternionic representation of volumetric octa-fields and a corresponding optimization that explicitly models the discrete matchings between neighboring elements. This optimization naturally supports alignment constraints and scales to very large datasets. We also propose a novel extraction technique that uses field-guided mesh simplification to convert the optimized fields into a hexdominant output mesh. Each simplification operation maintains topological validity as an invariant, ensuring manifold output. These steps easily generalize to other dimensions or representations, and we show how they can be an asset in existing 2D surface meshing techniques. Our method can automatically and robustly convert any tetrahedral mesh into an isotropic hex-dominant mesh and (with minor modifications) can also convert any triangle mesh into a corresponding isotropic quad-dominant mesh, preserving its genus, number of holes, and manifoldness. We demonstrate the benefits of our algorithm on a large collection of shapes provided in the supplemental material along with all generated results.

We introduce a robust and automatic algorithm to simplify the structure and reduce the singularities of a hexahedral mesh. Our algorithm interleaves simplification operations to collapse sheets and chords of the base complex of the input mesh with a geometric optimization, which improves the elements quality. All our operations are guaranteed not to introduce elements with negative Jacobians, ensuring that our algorithm always produces valid hex-meshes, and not to increase the Hausdorff distance from the original shape more than a user-defined threshold, ensuring a faithful approximation of the input geometry. Our algorithm can improve meshes produced with any existing hexahedral meshing algorithm --- we demonstrate its effectiveness by processing a dataset of 194 hex-meshes created with octree-based, polycube-based, and field-aligned methods.

In this paper, we introduce a volumetric partitioning strategy based on a generalized sweeping framework to seamlessly partition the volume of an input triangle mesh into a collection of deformed cuboids. This is achieved by a user-designed volumetric harmonic function that guides the decomposition of the input volume into a sequence of two-manifold level sets. A skeletal structure whose corners correspond to corner vertices of a 2D parameterization is extracted for each level set. Corners are placed so that the skeletal structure aligns with features of the input object. Then, a skeletal surface is constructed by matching the skeletal structures of adjacent level sets. The surface sheets of this skeletal surface partition the input volume into the deformed cuboids. The collection of cuboids does not exhibit T-junctions, significantly simplifying the hexahedral mesh generation process, and in particular, it simplifies fitting trivariate B-splines to the deformed cuboids. Intersections of the surface sheets of the skeletal surface correspond to the singular edges of the generated hex-meshes. We apply our technique to a variety of 3D objects and demonstrate the benefit of the structure decomposition in data fitting.

Recently, generating a high quality all-hex mesh of a given volume has gained much attention. However, little, if any, effort has been put into the optimization of the hex-mesh structure, which is equally important to the local element quality of a hex-mesh that may influence the performance and accuracy of subsequent computations. In this paper, we present a first and complete pipeline to optimize the global structure of a hex-mesh. Specifically, we first extract the base-complex of a hex-mesh and study the misalignments among its singularities by adapting the previously introduced hexahedral sheets to the base-complex. Second, we identify the valid removal base-complex sheets from the base-complex that contain misaligned singularities. We then propose an effective algorithm to remove these valid removal sheets in order. Finally, we present a structure-aware optimization strategy to improve the geometric quality of the resulting hex-mesh after fixing the misalignments. Our experimental results demonstrate that our pipeline can significantly reduce the number of components of a variety of hex-meshes generated by state-of-the-art methods, while maintaining high geometric quality.

Co-registering pre- and intra- operative MR data is an important yet challenging problem due to different acquisition parameters, resolutions, and plane orientations. Despite its importance, previous approaches are often computationally intensive and thus cannot be employed in real-time. In this paper, a novel three-step approach is proposed to dynamically register pre-operative 4D MR data with intra-operative 2D RT-MRI to guide intracardiac procedures. Specifically, a novel preparatory step, executed in the pre-operative phase, is introduced to generate bridging information that can be used to significantly speed up the on-the-fly registration in the intraoperative procedure. Our experimental results demonstrate an accuracy of 0.42 mm and a processing speed of 26 FPS of the proposed approach on an off-the-shelf PC. This approach, is in particularly developed for performing intra-cardiac procedures with real-time MR guidance.

In this article we propose a novel, robust, and high-capacity watermarking method for 3D meshes with arbitrary connectivities in the spatial domain based on affine invariants. Given a 3D mesh model, a watermark is embedded as affine-invariant length ratios of one diagonal segment to the residing diagonal intersected by the other one in a coplanar convex quadrilateral. In the extraction process, a watermark is recovered by combining all the watermark pieces embedded in length ratios through majority voting. Extensive experimental results demonstrate the robustness, high computational efficiency, high capacity, and affine-transformation-invariant characteristics of the proposed approach.