Xifeng Gao

Teseo Schneider, Yixin Hu, Xifeng Gao et al.

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 his 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.

Teseo Schneider, Jeremie Dumas, Xifeng Gao et al.

We introduce an integrated meshing and finite element method pipeline enabling black-box 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 basis on its elements, combining triquadratic B-splines, triquadratic hexahedra (27 degrees of freedom), 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.

Yingwenqi Jiang, Jiadong Tu, Yuan Liu et al.

The advent of neural 3D Gaussians 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 representation encounters challenges when applied to scenes featuring reflective surfaces. In this paper, we present GaussianShader, a novel method that applies a simplified shading function on 3D Gaussians to enhance the neural rendering in scenes with reflective surfaces while preserving the training and rendering efficiency. The main challenge in applying the shading function lies in the accurate normal estimation on discrete 3D Gaussians. Specifically, we proposed a novel normal estimation framework based on the shortest axis directions of 3D Gaussians with a delicately 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 in PSNR on specular object datasets, exhibiting an improvement of 1.57dB. When compared to prior works handling reflective surfaces, such as Ref-NeRF, our optimization time is significantly accelerated (23h vs. 0.58h). Please click on our project website to see more results.

Yuan Li, Congyi Zhang, Xifeng Gao et al.

Autoregressive multimodal large language models (MLLMs) enable 3D generation but struggle to scale to high-resolution shapes due to inadequate 3D tokenizations. Compact set-based representations discard deterministic spatial ordering, leading to ambiguous sequence prediction, while uniform or octree-based voxel grids preserve ordering at the cost of severe redundancy and excessively long sequences. This structural trade-off limits stable and efficient autoregressive 3D generation. We present SuperVoxelGPT, a representation-first framework that resolves this tension through adaptive and deterministically ordered supervoxel tokenization. Given a prompt, we first predict a coarse geometric saliency distribution and construct a shape-adaptive supervoxel partition using saliency-guided centroidal Voronoi tessellation, allocating fine-grained cells to complex regions and larger cells to smooth regions. Conditioned on the text and ordered supervoxel layout, we introduce a SuperVoxelVAE and fine-tune a pretrained MLLM to autoregressively generate supervoxel tokens. Experiments on Trellis-500K show that SuperVoxelGPT reduces token sequence length to 12.8% of uniform voxel tokenization while achieving state-of-the-art generation quality and an average 10$\times$ speedup over prior methods.

Zeshi Yang, Zherong Pan, Manyi Li et al.

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.

Hongkun Zhang, Zherong Pan, Congyi Zhang et al.

The recent success of pre-trained diffusion models unlocks the possibility of the automatic generation of textures for arbitrary 3D meshes in the wild. However, these models are trained in the screen space, while converting them to a multi-view consistent texture image poses a major obstacle to the output quality. In this paper, we propose a novel method to enforce multi-view consistency. Our method is based on the observation that latent space in a pre-trained diffusion model is noised separately for each camera view, making it difficult to achieve multi-view consistency by directly manipulating the latent codes. Based on the celebrated Denoising Diffusion Implicit Models (DDIM) scheme, we propose to use an optimization-based color-fusion to enforce consistency and indirectly modify the latent codes by gradient back-propagation. Our method further relaxes the sequential dependency assumption among the camera views. By evaluating on a series of general 3D models, we find our simple approach improves consistency and overall quality of the generated textures as compared to competing state-of-the-arts. Our implementation is available at: https://github.com/Quantuman134/TexPainter

Quanyuan Ruan, Kewei Shi, Jiabao Lei et al.

Auto-regressive frameworks for next-scale prediction of 2D images have demonstrated strong potential for producing diverse and sophisticated content by progressively refining a coarse input. However, extending this paradigm to 3D object generation remains largely unexplored. In this paper, we introduce auto-regressive Gaussian splatting (ARGS), a framework for making next-scale predictions in parallel for generation according to levels of detail. We propose a Gaussian simplification strategy and reverse the simplification to guide next-scale generation. Benefiting from the use of hierarchical trees, the generation process requires only \(\mathcal{O}(\log n)\) steps, where \(n\) is the number of points. Furthermore, we propose a tree-based transformer to predict the tree structure auto-regressively, allowing leaf nodes to attend to their internal ancestors to enhance structural consistency. Extensive experiments demonstrate that our approach effectively generates multi-scale Gaussian representations with controllable levels of detail, visual fidelity, and a manageable time consumption budget.

Junhao Chen, Manyi Li, Zherong Pan et al.

Deep generative models learn the data distribution, which is concentrated on a low-dimensional manifold. The geometric analysis of distribution transformation provides a better understanding of data structure and enables a variety of applications. In this paper, we study the geometric properties of the diffusion model, whose forward diffusion process and reverse generation process construct a series of distributions on manifolds which vary over time. Our key contribution is the introduction of generation rate, which corresponds to the local deformation of manifold over time around an image component. We show that the generation rate is highly correlated with intuitive visual properties, such as visual saliency, of the image component. Further, we propose an efficient and differentiable scheme to estimate the generation rate for a given image component over time, giving rise to a generation curve. The differentiable nature of our scheme allows us to control the shape of the generation curve via optimization. Using different loss functions, our generation curve matching algorithm provides a unified framework for a range of image manipulation tasks, including semantic transfer, object removal, saliency manipulation, image blending, etc. We conduct comprehensive analytical evaluations to support our findings and evaluate our framework on various manipulation tasks. The results show that our method consistently leads to better manipulation results, compared to recent baselines.

Ruiqi Ni, Zherong Pan, Xifeng Gao

We propose a variant of alternating direction method of multiplier (ADMM) to solve constrained trajectory optimization problems. Our ADMM framework breaks a joint optimization into small sub-problems, leading to a low iteration cost and decentralized parameter updates. Starting from a collision-free initial trajectory, our method inherits the theoretical properties of primal interior point method (P-IPM), i.e., guaranteed collision avoidance and homotopy preservation throughout optimization, while being orders of magnitude faster. We have analyzed the convergence and evaluated our method for time-optimal multi-UAV trajectory optimizations and simultaneous goal-reaching of multiple robot arms, where we take into consider kinematics-, dynamics-limits, and homotopy-preserving collision constraints. Our method highlights an order of magnitude's speedup, while generating trajectories of comparable qualities as state-of-the-art P-IPM solver.

Zherong Pan, Min Liu, Xifeng Gao et al.

We present an algorithm to compute planar linkage topology and geometry, given a user-specified end-effector trajectory. Planar linkage structures convert rotational or prismatic motions of a single actuator into an arbitrarily complex periodic motion, \refined{which is an important component when building low-cost, modular robots, mechanical toys, and foldable structures in our daily lives (chairs, bikes, and shelves). The design of such structures require trial and error even for experienced engineers. Our research provides semi-automatic methods for exploring novel designs given high-level specifications and constraints.} We formulate this problem as a non-smooth numerical optimization with quadratic objective functions and non-convex quadratic constraints involving mixed-integer decision variables (MIQCQP). We propose and compare three approximate algorithms to solve this problem: mixed-integer conic-programming (MICP), mixed-integer nonlinear programming (MINLP), and simulated annealing (SA). We evaluated these algorithms searching for planar linkages involving $10-14$ rigid links. Our results show that the best performance can be achieved by combining MICP and MINLP, leading to a hybrid algorithm capable of finding the planar linkages within a couple of hours on a desktop machine, which significantly outperforms the SA baseline in terms of optimality. We highlight the effectiveness of our optimized planar linkages by using them as legs of a walking robot.

Xifeng Gao, Zherong Pan, Ruiqi Ni

We propose an approach to solve multi-agent path planning (MPP) problems for complex environments. Our method first designs a special pebble graph with a set of feasibility constraints, under which MPP problems have feasibility guarantee. We further propose an algorithm to greedily improve the optimality of planned MPP solutions via parallel pebble motions. As a second step, we develop a mesh optimization algorithm to embed our pebble graph into arbitrarily complex environments. We show that the feasibility constraints of a pebble graph can be converted into differentiable geometric constraints, such that our mesh optimizer can satisfy these constraints via constrained numerical optimization. We have evaluated the effectiveness and efficiency of our method using a set of environments with complex geometries, on which our method achieves an average of 99.0% free-space coverage and 30.3% robot density within hours of computation on a desktop machine.

Zherong Pan, Duo Zhang, Changhe Tu et al.

We propose an optimization-based approach to plan power grasps. Central to our method is a reformulation of grasp planning as an infinite program under complementary constraints (IPCC), which allows contacts to happen between arbitrary pairs of points on the object and the robot gripper. We show that IPCC can be reduced to a conventional finite-dimensional nonlinear program (NLP) using a kernel-integral relaxation. Moreover, the values and Jacobian matrices of the kernel-integral can be evaluated efficiently using a modified Fast Multipole Method (FMM). We further guarantee that the planned grasps are collision-free using primal barrier penalties. We demonstrate the effectiveness, robustness, and efficiency of our grasp planner on a row of challenging 3D objects and high-DOF grippers, such as Barrett Hand and Shadow Hand, where our method achieves superior grasp qualities over competitors.

Ruiqi Ni, Teseo Schneider, Daniele Panozzo et al.

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 simultaneously guarantees the validity and asymptotic optimality for known environments. \textit{Validity:} Given a feasible initial guess, our algorithm guarantees the satisfaction of all constraints throughout the process of optimization. \textit{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.

Zherong Pan, Xifeng Gao, Dinesh Manocha

We present stress-minimizing (SM) metric, a new metric of grasp qualities. Unlike previous metrics that ignore the material of target objects, we assume that target objects are made of homogeneous isotopic materials. SM metric measures the maximal resistible external wrenches without causing fracture in the target objects. Therefore, SM metric is useful for robot grasping valuable and fragile objects. In this paper, we analyze the properties of this new metric, propose grasp planning algorithms to generate globally optimal grasps maximizing the SM metric, and compare the performance of the SM metric and a conventional metric. Our experiments show that SM metric is aware of the geometries of target objects while the conventional metric are not. We also show that the computational cost of the SM metric is on par with that of the conventional metric.

Zherong Pan, Min Liu, Xifeng Gao et al.

We present a method to find globally optimal topology and trajectory jointly for planar linkages. Planar linkage structures can generate complex end-effector trajectories using only a single rotational actuator, which is very useful in building low-cost robots. We address the problem of searching for the optimal topology and geometry of these structures. However, since topology changes are non-smooth and non-differentiable, conventional gradient-based searches cannot be used. We formulate this problem as a mixed-integer convex programming (MICP) problem, for which a global optimum can be found using the branch-and-bound (BB) algorithm. Compared to existing methods, our experiments show that the proposed approach finds complex linkage structures more efficiently and generates end-effector trajectories more accurately.