spatial-field transformations for motion

This paper addresses the challenge of enabling intuitive, view-dependent 3D deformation of non-photorealistic (NPR) models through 2D interactions. To this end, we propose a novel view-aware 3D editing framework that synthesizes view-conditioned deformation fields, supporting layer-like 2D deformation composition. Our method unifies 2D deformable mesh control over both Gaussian splatting and mesh-based representations for the first time, incorporating multi-view geometric consistency constraints and differentiable rendering optimization. Key technical components include 2D mesh-based editing, view-aware 3D deformation field interpolation, and spatial deformation of Gaussian splats. Experiments demonstrate effective editing of cartoon characters, hand-drawn portraits, occlusion repair, and classic NPR-style 3D models—achieving a favorable balance among editing intuitiveness, geometric fidelity, and view continuity.

This work addresses the lack of a rigorous definition for coherent structures in large-scale streamline data, which hinders efficient interactive exploration. The authors propose a web-based interactive system whose core innovation lies in constructing a Curve Segment Neighborhood Graph (CSNG) to encode adjacency relationships among streamline segments. By integrating rapid community detection with an enhanced force-directed layout, the system enables multi-scale structural discovery. Leveraging adjacency matrix compression and parallel processing techniques, it achieves real-time, in-browser interactivity on datasets comprising hundreds of thousands of streamline segments, effectively revealing spatial clusters and coherent patterns within complex vector fields.

Three-dimensional (3D) mappings are fundamental in computational mechanics (CAE), computer graphics, and medical imaging; however, conventional vertex-coordinate-based representations struggle to simultaneously ensure geometric fidelity and intuitive, controllable editing. To address this, we propose the first theoretically rigorous and computationally tractable 3D quasiconformal representation—extending the Beltrami coefficient to three dimensions—to characterize local scaling distortion in a mathematically sound manner. We further design an invertible reconstruction algorithm that stably and accurately recovers the original mapping from its distortion representation. Our approach integrates 3D quasiconformal theory, partial differential equation (PDE)-based modeling, and numerical optimization. Experiments demonstrate that our method significantly outperforms state-of-the-art alternatives in 3D mapping reconstruction, keyframe interpolation, and compression—achieving superior accuracy, robustness, and editability while preserving theoretical guarantees.

This work introduces the first end-to-end method for generating vector displacement maps (VDMs) from a single input image, enabling artists to seamlessly embed and edit fine geometric details on 3D model surfaces. The approach first estimates multi-view normal maps from the image, then employs a differentiable, normal-constrained reconstruction pipeline to invert them into attachable and editable geometric stamps. Key contributions include: (1) formalizing and implementing the VDM generation paradigm; (2) proposing the first fully automatic algorithm for extracting VDMs from 3D objects; (3) releasing the first open-source academic VDM dataset; and (4) focusing on modeling locally embeddable geometric components—distinct from holistic shape generation. Experiments demonstrate significant improvements over existing baselines in geometric accuracy, editability, and industrial compatibility. The method supports interactive customization and iterative re-editing, and has been successfully integrated into mainstream 3D modeling pipelines.

To address the challenge of balancing reconstruction speed and quality in real-time novel-view synthesis for monocular dynamic scenes, this paper proposes a forward-deformable learnable 3D Gaussian field. It employs template Gaussians as primitives, couples a time-aware forward deformation field to model non-rigid motion, and imposes a static prior to constrain deformation exclusively to moving regions. The method introduces the first forward-deformation Gaussian representation, designs an inductive-bias-aware initialization for explicit static-dynamic decoupling, and adopts end-to-end self-supervised optimization. Leveraging differentiable Gaussian rendering and self-supervised photometric losses, training on real-world scenes takes only ~20 minutes; real-time rendering achieves 96 FPS on an RTX 3090. Quantitatively, the approach outperforms state-of-the-art NeRF- and Gaussian-based methods in both PSNR and LPIPS metrics.

Traditional spatial deformation methods struggle to model covariate-driven nonstationary spatial dependencies and exhibit limited generalization. This work proposes a covariate-driven diffeomorphic spatial deformation framework that represents the deformation as a function of covariates, generating smooth and invertible mappings via velocity fields in a Lie algebra. To enhance stability and generalizability, the method incorporates a physics-informed truncation strategy for high-order interaction terms. It is the first approach to enable nonstationary Gaussian process extrapolation under covariate conditioning, demonstrating superior small-sample predictive performance on both synthetic data and real-world applications in manufacturing and geostatistics.

This work addresses the challenges of unnatural transitions and poor preservation of temporal motion characteristics in motion clip stitching by proposing a learning-free, parameter-free optimization method based on Rodrigues vectors. By representing joint rotations as continuous Rodrigues vectors and formulating the stitching process as a Laplacian smoothing problem in the time domain, the approach effectively enforces rotational continuity and numerical stability—leveraging the observation that rotation axis flips are rare in real human motion. The method supports both intra-class replacement and cross-category motion stitching, producing visually coherent and temporally faithful transitions even between highly dissimilar motions, while enabling efficient interactive editing.

This work proposes the first differentiable geometry processing system that seamlessly integrates with modern machine learning frameworks, addressing the longstanding challenge of combining geometric algorithms—typically non-differentiable and reliant on complex control flow—with gradient-based optimization. By unifying the adjoint method with a scatter-gather mesh processing paradigm, the system enables efficient gradient computation for existing geometric algorithms without requiring algorithmic reimplementation. It supports state-of-the-art solvers such as local-global and ADMM schemes and provides native differentiability for classical operations including curvature flows and conformal parameterizations. Evaluated on multiple inverse geometry problems, the approach significantly reduces both memory consumption and computational overhead, outperforming general-purpose differentiable optimization tools in runtime efficiency while dramatically lowering implementation effort.

This study addresses the challenge of reusing contact-rich dexterous manipulation demonstrations, which is complicated by constraints such as intermediate waypoints, environmental obstacles, and temporal misalignments. To overcome these issues, this work proposes an object-centric nonlinear spatiotemporal trajectory warping framework. By leveraging hand and object trajectory inputs alongside contact distribution modeling, the method reliably computes high-dimensional dexterous hand trajectories, enabling complex nonlinear adaptation to novel target scenarios. The proposed approach demonstrates strong generalization capabilities, significantly outperforming baselines across twelve variants in public benchmarks, and successfully transfers to diverse robotic arm platforms, highlighting its cross-platform applicability.

本文解决了刚体运动插值问题，通过将Park-Ravani构造扩展到正交对偶张量群，并利用对偶空间扭曲的高阶刚体运动学确保物理加速度场连续。