Wenping Wang

EAAI Journal 2026 Journal Article

Damping-accumulating discrete grey power model and its application in collaborative prediction of energy transition

• Xinqing Qiao
• Wenping Wang

AAAI Conference 2026 Conference Paper

DentalGS: Pose-Free 3D Gaussian Splatting from Five Intraoral Images for Novel View Synthesis

• Honghao Dai
• Yuanfeng Zhou
• Guangshun Wei
• Zhihao Li
• Wenping Wang

Orthodontic treatment needs regular tooth alignment checks, but current methods depend on clinic visits, limiting remote care. With the emergence of 3D Gaussian Splatting (3DGS), realistic novel views can be synthesized, making it possible for clinicians to remotely monitor orthodontic conditions. However, using only five intraoral images with unknown camera poses and dynamic lighting presents major challenges in dental applications. To address these challenges, we propose DentalGS, an enhanced 3DGS framework capable of synthesizing novel intraoral views from five post-orthodontic intraoral images and pre-orthodontic intraoral scan (IOS) data as prior, without camera poses. Our method initializes a Gaussian point cloud labeled with ISO-FDI tooth classes based on the patient’s pre-orthodontic IOS data, then estimates camera poses through iterative optimization. We introduce a Progressive Pair Generation Strategy as a data augmentation method that generates damage–repair image pairs to train a RepairNet, aiming to restore degraded geometry and appearance caused by the limited number of intraoral images. Additionally, we introduce a Lighting-Aware 3DGS inspired by physical reflectance properties to mitigate the effects of dynamic lighting conditions. Experimental results show that our method produces high-quality novel views while preserving geometric structure even under extreme viewpoints, offering an efficient and reliable solution for 3D tooth visualization in remote orthodontic monitoring.

AAAI Conference 2026 Conference Paper

Dynamic Gaussian Scene Reconstruction from Unsynchronized Videos

• Zhixin Xu
• Hengyu Zhou
• Yuan Liu
• Wenhan Xue
• Hao Pan
• Wenping Wang
• Bin Wang

Multi-view video reconstruction plays a vital role in computer vision, enabling applications in film production, virtual reality, and motion analysis. While recent advances such as 3D Gaussian Splatting have demonstrated impressive capabilities in dynamic scene reconstruction, they typically rely on the assumption that input video streams are temporally synchronized. However, in real-world scenarios, this assumption often fails due to factors like camera trigger delays, frame rate discrepancies, or independent recording setups, leading to temporal misalignment across views and reduced reconstruction quality. To address this challenge, a novel temporal alignment strategy is proposed for high-quality 4DGS reconstruction from unsynchronized multi-view videos. Our method features a coarse-to-fine alignment module that estimates and compensates for each camera's time shift. The method first determines a coarse, frame-level offset and then refines it to achieve sub-frame accuracy. This strategy can be integrated as a plug-and-play module into existing 4DGS frameworks, enhancing their robustness when handling asynchronous data. Experiments show that this approach effectively processes temporally misaligned videos and significantly enhances baseline methods.

AAAI Conference 2026 Conference Paper

NeuralGS: Bridging Neural Fields and 3D Gaussian Splatting for Compact 3D Representations

• Zhenyu Tang
• Chaoran Feng
• Xinhua Cheng
• Wangbo Yu
• Junwu Zhang
• Yuan Liu
• Xiao-Xiao Long
• Wenping Wang

3D Gaussian Splatting (3DGS) achieves impressive quality and rendering speed, but with millions of 3D Gaussians and significant storage and transmission costs. In this paper, we aim to develop a simple yet effective method called NeuralGS that compresses the original 3DGS into a compact representation. Our observation is that neural fields like NeRF can represent complex 3D scenes with Multi-Layer Perceptron (MLP) neural networks using only a few megabytes. Thus, NeuralGS effectively adopts the neural field representation to encode the attributes of 3D Gaussians with MLPs, only requiring a small storage size even for a large-scale scene. To achieve this, we adopt a clustering strategy and fit the Gaussians within each cluster using different tiny MLPs, based on importance scores of Gaussians as fitting weights. We experiment on multiple datasets, achieving a 91$\times$ average model size reduction without harming the visual quality.

NeurIPS Conference 2025 Conference Paper

Surprise3D: A Dataset for Spatial Understanding and Reasoning in Complex 3D Scenes

• Jiaxin Huang
• Ziwen Li
• Hanlue Zhang
• Runnan Chen
• Zhengqing Gao
• Xiao He
• Yandong Guo
• Wenping Wang

The integration of language and 3D perception is critical for embodied AI and robotic systems to perceive, understand, and interact with the physical world. Spatial reasoning, a key capability for understanding spatial relationships between objects, remains underexplored in current 3D vision-language research. Existing datasets often mix semantic cues (e. g. , object name) with spatial context, leading models to rely on superficial shortcuts rather than genuinely interpreting spatial relationships. To address this gap, we introduce Surprise3D, a novel dataset designed to evaluate language-guided spatial reasoning segmentation in complex 3D scenes. Surprise3D consists of more than 200k vision language pairs across 900+ detailed indoor scenes from ScanNet++ v2, including more than 2. 8k unique object classes. The dataset contains 89k+ human-annotated spatial queries deliberately crafted without object name, thereby mitigating shortcut biases in spatial understanding. These queries comprehensively cover various spatial reasoning skills, such as relative position, narrative perspective, parametric perspective, and absolute distance reasoning. Initial benchmarks demonstrate significant challenges for current state-of-the-art expert 3D visual grounding methods and 3D-LLMs, underscoring the necessity of our dataset and the accompanying 3D Spatial Reasoning Segmentation (3D-SRS) benchmark suite. Surprise3D and 3D-SRS aim to facilitate advancements in spatially aware AI, paving the way for effective embodied interaction and robotic planning.

NeurIPS Conference 2025 Conference Paper

🎧MOSPA: Human Motion Generation Driven by Spatial Audio

• Shuyang Xu
• Zhiyang Dou
• Mingyi Shi
• Liang Pan
• Leo Ho
• Jingbo Wang
• Yuan Liu
• Cheng Lin

Enabling virtual humans to dynamically and realistically respond to diverse auditory stimuli remains a key challenge in character animation, demanding the integration of perceptual modeling and motion synthesis. Despite its significance, this task remains largely unexplored. Most previous works have primarily focused on mapping modalities like speech, audio, and music to generate human motion. As of yet, these models typically overlook the impact of spatial features encoded in spatial audio signals on human motion. To bridge this gap and enable high-quality modeling of human movements in response to spatial audio, we introduce the first comprehensive "Spatial Audio-Driven Human Motion" (SAM) dataset, which contains diverse and high-quality spatial audio and motion data. For benchmarking, we develop a simple yet effective diffusion-based generative framework for human "MOtion generation driven by SPatial Audio, " termed MOSPA, which faithfully captures the relationship between body motion and spatial audio through an effective fusion mechanism. Once trained, MOSPA can generate diverse realistic human motions conditioned on varying spatial audio inputs. We perform a thorough investigation of the proposed dataset and conduct extensive experiments for benchmarking, where our method achieves state-of-the-art performance on this task. Our code and model are publicly available at https: //github. com/xsy27/Mospa-Acoustic-driven-Motion-Generation. git

AAAI Conference 2024 Conference Paper

Collaborative Tooth Motion Diffusion Model in Digital Orthodontics

• Yeying Fan
• Guangshun Wei
• Chen Wang
• Shaojie Zhuang
• Wenping Wang
• Yuanfeng Zhou

Tooth motion generation is an essential task in digital orthodontic treatment for precise and quick dental healthcare, which aims to generate the whole intermediate tooth motion process given the initial pathological and target ideal tooth alignments. Most prior works for multi-agent motion planning problems usually result in complex solutions. Moreover, the occlusal relationship between upper and lower teeth is often overlooked. In this paper, we propose a collaborative tooth motion diffusion model. The critical insight is to remodel the problem as a diffusion process. In this sense, we model the whole tooth motion distribution with a diffusion model and transform the planning problem into a sampling process from this distribution. We design a tooth latent representation to provide accurate conditional guides consisting of two key components: the tooth frame represents the position and posture, and the tooth latent shape code represents the geometric morphology. Subsequently, we present a collaborative diffusion model to learn the multi-tooth motion distribution based on inter-tooth and occlusal constraints, which are implemented by graph structure and new loss functions, respectively. Extensive qualitative and quantitative experiments demonstrate the superiority of our framework in the application of orthodontics compared with state-of-the-art methods.

NeurIPS Conference 2024 Conference Paper

Era3D: High-Resolution Multiview Diffusion using Efficient Row-wise Attention

• Peng Li
• Yuan Liu
• Xiaoxiao Long
• Feihu Zhang
• Cheng Lin
• Mengfei Li
• Xingqun Qi
• Shanghang Zhang

In this paper, we introduce Era3D, a novel multiview diffusion method that generates high-resolution multiview images from a single-view image. Despite significant advancements in multiview generation, existing methods still suffer from camera prior mismatch, inefficacy, and low resolution, resulting in poor-quality multiview images. Specifically, these methods assume that the input images should comply with a predefined camera type, e. g. a perspective camera with a fixed focal length, leading to distorted shapes when the assumption fails. Moreover, the full-image or dense multiview attention they employ leads to a dramatic explosion of computational complexity as image resolution increases, resulting in prohibitively expensive training costs. To bridge the gap between assumption and reality, Era3D first proposes a diffusion-based camera prediction module to estimate the focal length and elevation of the input image, which allows our method to generate images without shape distortions. Furthermore, a simple but efficient attention layer, named row-wise attention, is used to enforce epipolar priors in the multiview diffusion, facilitating efficient cross-view information fusion. Consequently, compared with state-of-the-art methods, Era3D generates high-quality multiview images with up to a 512×512 resolution while reducing computation complexity of multiview attention by 12x times. Comprehensive experiments demonstrate the superior generation power of Era3D- it can reconstruct high-quality and detailed 3D meshes from diverse single-view input images, significantly outperforming baseline multiview diffusion methods.

NeurIPS Conference 2024 Conference Paper

Flatten Anything: Unsupervised Neural Surface Parameterization

• Qijian Zhang
• Junhui Hou
• Wenping Wang
• Ying He

Surface parameterization plays an essential role in numerous computer graphics and geometry processing applications. Traditional parameterization approaches are designed for high-quality meshes laboriously created by specialized 3D modelers, thus unable to meet the processing demand for the current explosion of ordinary 3D data. Moreover, their working mechanisms are typically restricted to certain simple topologies, thus relying on cumbersome manual efforts (e. g. , surface cutting, part segmentation) for pre-processing. In this paper, we introduce the Flatten Anything Model (FAM), an unsupervised neural architecture to achieve global free-boundary surface parameterization via learning point-wise mappings between 3D points on the target geometric surface and adaptively-deformed UV coordinates within the 2D parameter domain. To mimic the actual physical procedures, we ingeniously construct geometrically-interpretable sub-networks with specific functionalities of surface cutting, UV deforming, unwrapping, and wrapping, which are assembled into a bi-directional cycle mapping framework. Compared with previous methods, our FAM directly operates on discrete surface points without utilizing connectivity information, thus significantly reducing the strict requirements for mesh quality and even applicable to unstructured point cloud data. More importantly, our FAM is fully-automated without the need for pre-cutting and can deal with highly-complex topologies, since its learning process adaptively finds reasonable cutting seams and UV boundaries. Extensive experiments demonstrate the universality, superiority, and inspiring potential of our proposed neural surface parameterization paradigm. Our code is available at https: //github. com/keeganhk/FlattenAnything.

AAAI Conference 2024 Conference Paper

Manifold Constraints for Imperceptible Adversarial Attacks on Point Clouds

• Keke Tang
• Xu He
• Weilong Peng
• Jianpeng Wu
• Yawen Shi
• Daizong Liu
• Pan Zhou
• Wenping Wang

Adversarial attacks on 3D point clouds often exhibit unsatisfactory imperceptibility, which primarily stems from the disregard for manifold-aware distortion, i.e., distortion of the underlying 2-manifold surfaces. In this paper, we develop novel manifold constraints to reduce such distortion, aiming to enhance the imperceptibility of adversarial attacks on 3D point clouds. Specifically, we construct a bijective manifold mapping between point clouds and a simple parameter shape using an invertible auto-encoder. Consequently, manifold-aware distortion during attacks can be captured within the parameter space. By enforcing manifold constraints that preserve local properties of the parameter shape, manifold-aware distortion is effectively mitigated, ultimately leading to enhanced imperceptibility. Extensive experiments demonstrate that integrating manifold constraints into conventional adversarial attack solutions yields superior imperceptibility, outperforming the state-of-the-art methods.

IJCAI Conference 2024 Conference Paper

RealDex: Towards Human-like Grasping for Robotic Dexterous Hand

• Yumeng Liu
• Yaxun Yang
• Youzhuo Wang
• Xiaofei Wu
• Jiamin Wang
• Yichen Yao
• Sören Schwertfeger
• Sibei Yang

In this paper, we introduce RealDex, a pioneering dataset capturing authentic dexterous hand grasping motions infused with human behavioral patterns, enriched by multi-view and multimodal visual data. Utilizing a teleoperation system, we seamlessly synchronize human-robot hand poses in real time. This collection of human-like motions is crucial for training dexterous hands to mimic human movements more naturally and precisely. RealDex holds immense promise in advancing humanoid robot for automated perception, cognition, and manipulation in real-world scenarios. Moreover, we introduce a cutting-edge dexterous grasping motion generation framework, which aligns with human experience and enhances real-world applicability through effectively utilizing Multimodal Large Language Models. Extensive experiments have demonstrated the superior performance of our method on RealDex and other open datasets. The dataset and associated code are available at https: //4dvlab. github. io/RealDex_page/.

NeurIPS Conference 2023 Conference Paper

Aligning Gradient and Hessian for Neural Signed Distance Function

• Ruian Wang
• Zixiong Wang
• Yunxiao Zhang
• Shuangmin Chen
• Shiqing Xin
• Changhe Tu
• Wenping Wang

The Signed Distance Function (SDF), as an implicit surface representation, provides a crucial method for reconstructing a watertight surface from unorganized point clouds. The SDF has a fundamental relationship with the principles of surface vector calculus. Given a smooth surface, there exists a thin-shell space in which the SDF is differentiable everywhere such that the gradient of the SDF is an eigenvector of its Hessian matrix, with a corresponding eigenvalue of zero. In this paper, we introduce a method to directly learn the SDF from point clouds in the absence of normals. Our motivation is grounded in a fundamental observation: aligning the gradient and the Hessian of the SDF provides a more efficient mechanism to govern gradient directions. This, in turn, ensures that gradient changes more accurately reflect the true underlying variations in shape. Extensive experimental results demonstrate its ability to accurately recover the underlying shape while effectively suppressing the presence of ghost geometry.

AAAI Conference 2023 Conference Paper

Deep Manifold Attack on Point Clouds via Parameter Plane Stretching

• Keke Tang
• Jianpeng Wu
• Weilong Peng
• Yawen Shi
• Peng Song
• Zhaoquan Gu
• Zhihong Tian
• Wenping Wang

Adversarial attack on point clouds plays a vital role in evaluating and improving the adversarial robustness of 3D deep learning models. Current attack methods are mainly applied by point perturbation in a non-manifold manner. In this paper, we formulate a novel manifold attack, which deforms the underlying 2-manifold surfaces via parameter plane stretching to generate adversarial point clouds. First, we represent the mapping between the parameter plane and underlying surface using generative-based networks. Second, the stretching is learned in the 2D parameter domain such that the generated 3D point cloud fools a pretrained classifier with minimal geometric distortion. Extensive experiments show that adversarial point clouds generated by manifold attack are smooth, undefendable and transferable, and outperform those samples generated by the state-of-the-art non-manifold ones.

NeurIPS Conference 2023 Conference Paper

NeuroGF: A Neural Representation for Fast Geodesic Distance and Path Queries

• Qijian Zhang
• Junhui Hou
• Yohanes Adikusuma
• Wenping Wang
• Ying He

Geodesics play a critical role in many geometry processing applications. Traditional algorithms for computing geodesics on 3D mesh models are often inefficient and slow, which make them impractical for scenarios requiring extensive querying of arbitrary point-to-point geodesics. Recently, deep implicit functions have gained popularity for 3D geometry representation, yet there is still no research on neural implicit representation of geodesics. To bridge this gap, we make the first attempt to represent geodesics using implicit learning frameworks. Specifically, we propose neural geodesic field (NeuroGF), which can be learned to encode all-pairs geodesics of a given 3D mesh model, enabling to efficiently and accurately answer queries of arbitrary point-to-point geodesic distances and paths. Evaluations on common 3D object models and real-captured scene-level meshes demonstrate our exceptional performances in terms of representation accuracy and querying efficiency. Besides, NeuroGF also provides a convenient way of jointly encoding both 3D geometry and geodesics in a unified representation. Moreover, the working mode of per-model overfitting is further extended to generalizable learning frameworks that can work on various input formats such as unstructured point clouds, which also show satisfactory performances for unseen shapes and categories. Our code and data are available at https: //github. com/keeganhk/NeuroGF.

NeurIPS Conference 2023 Conference Paper

Towards Label-free Scene Understanding by Vision Foundation Models

• Runnan Chen
• Youquan Liu
• Lingdong Kong
• Nenglun Chen
• Xinge Zhu
• Yuexin Ma
• Tongliang Liu
• Wenping Wang

Vision foundation models such as Contrastive Vision-Language Pre-training (CLIP) and Segment Anything (SAM) have demonstrated impressive zero-shot performance on image classification and segmentation tasks. However, the incorporation of CLIP and SAM for label-free scene understanding has yet to be explored. In this paper, we investigate the potential of vision foundation models in enabling networks to comprehend 2D and 3D worlds without labelled data. The primary challenge lies in effectively supervising networks under extremely noisy pseudo labels, which are generated by CLIP and further exacerbated during the propagation from the 2D to the 3D domain. To tackle these challenges, we propose a novel Cross-modality Noisy Supervision (CNS) method that leverages the strengths of CLIP and SAM to supervise 2D and 3D networks simultaneously. In particular, we introduce a prediction consistency regularization to co-train 2D and 3D networks, then further impose the networks' latent space consistency using the SAM's robust feature representation. Experiments conducted on diverse indoor and outdoor datasets demonstrate the superior performance of our method in understanding 2D and 3D open environments. Our 2D and 3D network achieves label-free semantic segmentation with 28. 4\% and 33. 5\% mIoU on ScanNet, improving 4. 7\% and 7. 9\%, respectively. For nuImages and nuScenes datasets, the performance is 22. 1\% and 26. 8\% with improvements of 3. 5\% and 6. 0\%, respectively. Code is available. (https: //github. com/runnanchen/Label-Free-Scene-Understanding)

NeurIPS Conference 2021 Conference Paper

NeuS: Learning Neural Implicit Surfaces by Volume Rendering for Multi-view Reconstruction

• Peng Wang
• Lingjie Liu
• Yuan Liu
• Christian Theobalt
• Taku Komura
• Wenping Wang

We present a novel neural surface reconstruction method, called NeuS, for reconstructing objects and scenes with high fidelity from 2D image inputs. Existing neural surface reconstruction approaches, such as DVR [Niemeyer et al. , 2020] and IDR [Yariv et al. , 2020], require foreground mask as supervision, easily get trapped in local minima, and therefore struggle with the reconstruction of objects with severe self-occlusion or thin structures. Meanwhile, recent neural methods for novel view synthesis, such as NeRF [Mildenhall et al. , 2020] and its variants, use volume rendering to produce a neural scene representation with robustness of optimization, even for highly complex objects. However, extracting high-quality surfaces from this learned implicit representation is difficult because there are not sufficient surface constraints in the representation. In NeuS, we propose to represent a surface as the zero-level set of a signed distance function (SDF) and develop a new volume rendering method to train a neural SDF representation. We observe that the conventional volume rendering method causes inherent geometric errors (i. e. bias) for surface reconstruction, and therefore propose a new formulation that is free of bias in the first order of approximation, thus leading to more accurate surface reconstruction even without the mask supervision. Experiments on the DTU dataset and the BlendedMVS dataset show that NeuS outperforms the state-of-the-arts in high-quality surface reconstruction, especially for objects and scenes with complex structures and self-occlusion.

IJCAI Conference 2019 Conference Paper

MAT-Net: Medial Axis Transform Network for 3D Object Recognition

• Jianwei Hu
• Bin Wang
• Lihui Qian
• Yiling Pan
• Xiaohu Guo
• Lingjie Liu
• Wenping Wang

3D deep learning performance depends on object representation and local feature extraction. In this work, we present MAT-Net, a neural network which captures local and global features from the Medial Axis Transform (MAT). Different from K-Nearest-Neighbor method which extracts local features by a fixed number of neighbors, our MAT-Net exploits effective modules Group-MAT and Edge-Net to process topological structure. Experimental results illustrate that MAT-Net demonstrates competitive or better performance on 3D shape recognition than state-of-the-art methods, and prove that MAT representation has excellent capacity in 3D deep learning, even in the case of low resolution.

AAAI Conference 2019 Conference Paper

TrafficPredict: Trajectory Prediction for Heterogeneous Traffic-Agents

• Yuexin Ma
• Xinge Zhu
• Sibo Zhang
• Ruigang Yang
• Wenping Wang
• Dinesh Manocha

To safely and efficiently navigate in complex urban traffic, autonomous vehicles must make responsible predictions in relation to surrounding traffic-agents (vehicles, bicycles, pedestrians, etc.). A challenging and critical task is to explore the movement patterns of different traffic-agents and predict their future trajectories accurately to help the autonomous vehicle make reasonable navigation decision. To solve this problem, we propose a long short-term memory-based (LSTM-based) realtime traffic prediction algorithm, TrafficPredict. Our approach uses an instance layer to learn instances’ movements and interactions and has a category layer to learn the similarities of instances belonging to the same type to refine the prediction. In order to evaluate its performance, we collected trajectory datasets in a large city consisting of varying conditions and traffic densities. The dataset includes many challenging scenarios where vehicles, bicycles, and pedestrians move among one another. We evaluate the performance of TrafficPredict on our new dataset and highlight its higher accuracy for trajectory prediction by comparing with prior prediction methods.

AAMAS Conference 2018 Conference Paper

Efficient Reciprocal Collision Avoidance between Heterogeneous Agents Using CTMAT

• Yuexin Ma
• Dinesh Manocha
• Wenping Wang

We present a novel algorithm for reciprocal collision avoidance between heterogeneous agents of different shapes and sizes. We present a novel CTMAT representation based on medial axis transform to compute a tight fitting bounding shape for each agent. Each CTMAT is represented using tuples, which are composed of circular arcs and line segments. Based on the reciprocal velocity obstacle formulation, we reduce the problem to solving a lowdimensional linear programming between each pair of tuples belonging to adjacent agents. We precompute the Minkowski Sums of tuples to accelerate the runtime performance. Finally, we provide an efficient method to update the orientation of each agent in a local manner. We have implemented the algorithm and highlight its performance on benchmarks corresponding to road traffic scenarios and different vehicles. The overall runtime performance is comparable to prior multi-agent collision avoidance algorithms that use circular or elliptical agents. Our approach is less conservative and results in fewer false collisions.

ICRA Conference 2011 Conference Paper

CVT-based 2D motion planning with maximal clearance

• Liping Zheng
• Yi-King Choi
• Xiaoping Liu 0003
• Wenping Wang

Maximal clearance is an important property that is highly desirable in multi-agent motion planning. However, it is also inherently difficult to attain. We propose a novel approach to achieve maximal clearance by exploiting the ability of evenly distributing a set of points by a centroidal Voronoi tessellation (CVT). We adapt the CVT framework to multi agent motion planning by adding an extra time dimension and optimize the trajectories of the agents in the augmented domain. As an optimization framework, our method can work naturally on complex regions. We demonstrate the effectiveness of our algorithm in achieving maximal clearance in motion planning with some examples.

ICRA Conference 2006 Conference Paper

Efficient Continuous Collision Detection for Bounding Boxes under Rational Motion

• Dan Albocher
• Uzi Sarel
• Yi-King Choi
• Gershon Elber
• Wenping Wang

This paper presents a simple yet precise and efficient algorithm for collision prediction of two oriented bounding boxes under univariate (piecewise) rational motion. We present an analytic solution to the problem of finding the time of collision and the feature involved, or declaring that no collision should occur. Our solution can be applied to boxes of any size, under arbitrary rational rigid motion. The algorithm is based on the efficient examination of the Minkowski sum (MS) of the two boxes, using a spherical Gauss map dual representation, and a precise extraction of the collision time, if any, as a solution to a set of rational equations that are automatically derived

ICRA Conference 2003 Conference Paper

Exact Collision Detection of Two Moving Ellipsoids under Rational Motions

• Yi-King Choi
• Wenping Wang
• Myung-Soo Kim

In this paper, we describe an exact method for detecting collision between two moving ellipsoids under pre-specified rational motions. Our method is based on an algebraic condition that determines the separation status of two static ellipsoids - the condition itself is described by the signs of roots of the characteristic equation of the two ellipsoids. To deal with moving ellipsoids, we derive a bivariate function whose zero-set possesses a special topological structure. By analyzing the zero-set of this function, we are able to tell whether or not two moving ellipsoids under pre-specified rational motions are collision-free; and if not, we can determine the intervals in which they overlap.