3D Mesh Deformation

Cage-based deformation (CBD) parametrises 3D geometry through a small set of control handles, effectively enabling a variety of tasks from animation and interactive modelling to tool-based co-design, neural deformation transfer, and aerodynamic shape optimization. Many optimization approaches relying on CBD employ regularisation strategies to reduce the distortion of the deformed mesh by encouraging smooth, regular cage deformations. These techniques offer soft guidance to an optimization algorithm towards desirable deformations, but compete with the task objective rather than changing the deformation parameterization itself. In this work we introduce Structural Affinity for CBD, an explicit regularisation method which enables smooth deformations through control cages by exploiting a two-cage structure to couple cage-handle motion directly. Structural Affinity precomputes an affinity matrix using mean-value coordinates, binding the inner control-cage to a coarser outer-cage. This matrix defines how much a cage handle displacement propagates to neighbouring handles which substantially decreases and often eliminates cage self-intersections, reduces mesh distortion, and adds linear overhead at deformation time. Across robotic control--morphology co-design, source-to-target neural deformation transfer, and aerodynamic wing shape optimization, Structural Affinity produces more regular deformations and substantially reduces reliance on hand-designed structural loss terms. We report consistent gains on three complementary diagnostics: the cotangent Laplacian, a proxy for surface smoothness; cage distortion, capturing whether control handles move coherently; and surface roughness, which measures undesirable oscillation in wing geometry.

Deformable-object manipulation requires accurate modeling of highly localized contact while maintaining simulation speeds suitable for interactive use. Uniformly fine tetrahedral meshes can resolve these interactions, but they introduce unnecessary degrees of freedom throughout the object. Coarse meshes are more efficient, yet they may under-resolve contact-induced deformation. We present a contact-adaptive mesh refinement framework that introduces spatial resolution only where it is most useful. The method uses geometric, elastic, and contact quantities already available from the deformable-body solver to score candidate edges. A fully GPU-parallel procedure then selects a conflict-free subset and updates both mesh topology and physical state directly within the simulation loop. We evaluate the approach on real deformable-object manipulation sequences. Adaptive refinement reduces simulation-to-real error, improves agreement with a fine-mesh reference, and remains substantially more efficient than uniformly fine simulation. These results show that local refinement can improve physical fidelity without incurring the cost of a globally fine discretization. The framework provides a practical basis for contact-rich simulation in interactive manipulation, sim-to-real modeling, and online physical digital twins.

Mesh-agnostic facial animation retargeting transfers expressions across meshes with different structures, but preserving facial motion without surface artifacts remains challenging. To address this, we present PDB, Point-Based Deformation Blending for facial animation retargeting. PDB predicts a compact set of deformed control points from a source neutral-expression pair and blending weights from the target neutral mesh. The weights are computed once per target and reused across frames, while the control points vary with each source expression. ReLU enforces non-negative weights and permits exact zeros, followed by row-wise normalization. The target mesh is reconstructed directly by multiplying the weights and control points, without a predefined cage, precomputed coordinates, a learned per-element deformation decoder, or a global reconstruction solve. Trained only with self-retargeting reconstruction supervision, PDB supports cross-identity transfer without paired cross-identity training expressions. Experiments demonstrate accurate retargeting, fast inference, and localized support in the learned weights. Joint evaluation of expression accuracy and local surface preservation shows reduced surface artifacts relative to the evaluated dense displacement method while retaining the intended motion. Perceptual evaluations further support expression fidelity and visual quality in both self- and cross-retargeting.

This paper studies tetrahedral meshes as the body representation for differentiable simulation and computational design. Fixed-connectivity meshes degrade under large morphs, while remeshing from scratch discards node correspondence. We present JamTet, a physics-based sphere-packing framework for volumetric meshing and morphing. We contribute (i) a GPU-parallel mesher combining octree-hierarchical packing with constrained Delaunay tetrahedralization, producing more uniform element volumes than TetGen and fTetWild; (ii) Lagrangian mesh morphing that preserves interior-node identities by re-equilibrating the same spheres within changing shapes and rebuilding the boundary and connectivity, remaining inversion-free where fixed-connectivity and TetSphere meshes invert; and (iii) a differentiable GPU simulator in JAX, with mass-spring edges and a volumetric Neo-Hookean term, integrated with mesh morphing in a design pipeline. In soft-robot morphology design experiments, interior-node gradients improve swimming fitness by 0.73-1.07 over a matched surface-only variant, while voxelized versions of the same designs yield 32-63% lower fitness. These results establish sphere packing as a practical volumetric mesh representation for gradient-based shape optimization. Code and media: under review.

We present DiT-Garment to model dynamic 3D clothing over human body models in arbitrary motion. Unlike existing methods, DiT-Garment can animate garments with unseen designs and physical materials, while allowing for direct inference of deformations for any target pose. To achieve this, we leverage a 2D diffusion transformer architecture to learn 3D deformations in a 2D UV-space. As the result is non-deterministic, our generative model learns the distribution of possible outcomes. The template garment is represented as a 3D triangle mesh spatially aligned with a 3D human body model in a standardized pose. To work with different garment designs without the need of a common template or complex graph convolution operations, the diffusion transformer is conditioned on a 3D position map of the template, represented in UV-space, which allows to implicitly learn a deformation of the 3D space around the body in standard pose. Further conditioning on body motion and physical parameters allows to physically ground the model. We quantitatively and qualitatively evaluate DiT-Garment on both synthetic and real data. While only trained on synthetic simulations of automatically generated cloth designs, our method generalizes to captured and artist-made garment designs. Code and data are available for research purposes at https://dumoulina.github.io/dit-garment/.

Estimating deformable object states remains a fundamental challenge in robotics and simulation. We propose a novel factor graph-based framework for probabilistic mesh state estimation of deformable objects. The method directly updates a tetrahedral mesh, a rich and physically-grounded representation of an environment, by combining physics priors, noisy sensor measurements, and temporal smoothness constraints within a unified probabilistic formulation. The estimation problem is posed as a nonlinear least-squares optimization and solved using Levenberg-Marquardt. Ex vivo central-airway obstruction experiments and simulations on deforming cube models demonstrate reliable and accurate reconstruction under both rigid motion and deformation, highlighting the potential of this probabilistic approach for principled, measurement-driven mesh state estimation in deformable object reconstruction.

We propose a remeshing-enhanced method for generatively deforming shapes with visual losses. It is intuitive that sufficiently drastic deformations of a mesh without changing its triangulation can easily compromise element quality, even if such large geometry changes may be semantically desired. Shape deformation methods could thus benefit from changing the triangulation; however, this is not done by most generative, text-based, visually-supervised mesh deformation methods. Remeshing is a discrete operation, proven to be especially challenging to couple with the notoriously noisy supervision signal provided by visual losses. We propose a vertex-based deformation optimization quantity capable of large deformations and robustness to such noise; we periodically remesh using an isotropic remesher that interpolates and carries forward the deformation optimization state. This enables continuous, geometry-informed progress in coarse-to-fine addition of resolution. The resulting shapes' triangulations fit their optimized geometry and have neat isotropic elements. Further, our method is localizable, able to grow new features on a base shape with expressive detail, leaving the rest unchanged. We showcase the effectiveness of our method on a variety of shapes and prompts, both local and global deformations, and demonstrate its superior visual quality and triangle efficiency. Our project page is at https://threedle.github.io/radmesh.

Different shape representations facilitate different computations. Surface representations, in particular meshes, are often used for modeling, whereas volume representations are useful for spatial queries such as intersection or containment. Optimizing a surface representation based on a volumetric properties by gradient descent requires the derivatives of the volume relative to its bounding surface. We derive this gradient for winding numbers and show that it can be efficiently computed for volumetric values sampled on a regular grid (voxel representation) and surface parameters based on vertex sets (triangle meshes). This enables an efficient solution for a variety of optimization problems. We demonstrate the practical use of this approach at the examples of deforming meshes to resolve intersections, being manufacturable by cutting with a bandsaw from three directions, and creating shapes that are close to tiling 3D space.

We introduce cut-cell skinning, a geometric prior designed to augment data-driven skinning weight generation. While data-driven methods show promise in producing high-quality skinning weights, they often lack the generalizability of classic geometric approaches. To bridge this gap, we propose a geometric prior that can be robustly computed for in-the-wild meshes and is efficient for large-scale machine learning workflows. The key idea of our cut-cell skinning is a fast graph-based approximation of the volumetric geodesics distances, motivated by their importance in classic skinning weight computation. Our method achieves orders of magnitude speedup compared to optimization-based solvers and remains resilient to topological artifacts common in cage- or voxel-based alternatives. We demonstrate the efficacy of the cut-cell skinning prior by integrating it into recent neural skinning models, showing consistent improvements across existing methods and achieving state-of-the-art results. Project page: https://wenchao-m.github.io/CutCell.github.io/

Mesh deformation, the process of altering the vertex positions of a 3D mesh while preserving its topological structure, is a cornerstone of computer graphics. Despite the recent emergence of numerous text-guided 3D mesh deformation methods, deforming an initial mesh into one that both adheres to text prompts and preserves its pose remains challenging. This paper proposes PoseAlign, which decomposes text-guided mesh deformation into two stages: global pose scaling and local detail sculpting. Specifically, in the first stage, we introduce the Laplacian as a differentiable mesh representation to enable more efficient yet smoother global deformation. Then, we propose a novel pose-aligned SDS loss by adapting score distillation sampling (SDS) with an attention-sharing mechanism, which sculptures fine-grained geometric details for the deformed mesh while preserving its original pose. PoseAlign significantly enhances the controllability of the overall deformation process, achieving a favorable balance between pose preservation and text alignment. Experiments demonstrate the competitive advantages of our method in text alignment and mesh quality. Code is available at: https://cousingrade6.github.io/PoseAlign

We present MeshLoom, a feed-forward registration network that directly reconstructs vertex deformations across mesh sequences. Our approach advances non-rigid registration beyond existing models, which are typically constrained by costly per-instance optimization, narrow object categories, pairwise-only inputs, or merely intermediate outputs. The network is simple and efficient, registering multiple meshes within seconds. At its core lies a topology-aware encoder--decoder design. Specifically, we first introduce a topology-aware point representation that encodes the anchor (reference) mesh's topology into its per-vertex features. This representation strengthens the network's understanding of the anchor-mesh geometry and disambiguates points that are Euclidean-close yet geodesically distant. We then propose a multi-modal encoder that fuses this anchor-mesh representation with complementary cues from each frame, such as shape latents and image features. These multi-source signals are compressed into a compact global motion embedding that captures dense inter-frame correspondence. A lightweight decoder then queries this global embedding with the anchor-mesh point representation, retrieving per-vertex deformations at target timestamps. Through extensive experiments across diverse motions and object categories, we show that MeshLoom achieves state-of-the-art results on non-rigid registration. In addition, we find that our global embedding-then-query paradigm naturally enables the network to generate deformations at intermediate timestamps, which extends MeshLoom to motion interpolation and mesh morphing. Project page: https://meshloom.github.io/ .

Large-scale controllable 3D assets are critical for computer graphics, embodied AI, robotics, and interactive content creation, yet creating diverse 3D assets remains challenging due to the high cost of manual modeling and rigging. Shape deformation offers a natural way to generate variations from existing meshes, but existing data-driven methods often rely on sparse user inputs, while parametric editing frameworks require manually designed control structures and category-specific configurations. Inspired by natural creatures, where a central spine governs global shape and cross-sectional ribs control local variation, we introduce Fishbone, a unified rib-spine representation for general shapes that supports controllable parametric mesh deformation, reduced-space dynamics, and animation. Given an input mesh, Fishbone computes a geodesic scalar field with an adaptive heat method, extracts iso-contours as cross-sectional ribs, constructs a smooth geometry-aware spine through rib centers, and associates surface vertices with nearby rib and spine structures using Gaussian-weighted skinning. The resulting representation enables real-time and predictable deformation: ribs control local profiles such as thickness, orientation, and cross-sectional variation, while the spine controls global bending, twisting, and stretching. The same structure also supports reduced-space simulation and keyframe animation. We further construct Fishbone-136K by augmenting Hunyuan3D with rib-spine structures, and demonstrate applications in controllable 3D generation, deformation-based data augmentation for robot learning, interactive mesh editing, and agentic generation. Experiments demonstrate the effectiveness, efficiency, and versatility of the proposed framework.

Recent generative models can create visually plausible 3D representations of objects. However, the generation process often allows for implicit control signals, such as contextual descriptions, and rarely supports bold geometric distortions beyond existing data distributions. We propose a geometric stylization framework that deforms a 3D mesh, allowing it to express the style of an image. While style is inherently ambiguous, we utilize pre-trained diffusion models to extract an abstract representation of the provided image. Our coarse-to-fine stylization pipeline can drastically deform the input 3D model to express a diverse range of geometric variations while retaining the valid topology of the original mesh and part-level semantics. We also propose an approximate VAE encoder that provides efficient and reliable gradients from mesh renderings. Extensive experiments demonstrate that our method can create stylized 3D meshes that reflect unique geometric features of the pictured assets, such as expressive poses and silhouettes, thereby supporting the creation of distinctive artistic 3D creations. Project page: https://changwoonchoi.github.io/GeoStyle

Deep learning-based approaches, particularly graph neural networks (GNNs), have gained prominence in simulating flexible deformations and contacts of solids, due to their ability to handle unstructured physical fields and nonlinear regression on graph structures. However, existing GNNs commonly represent meshes with graphs built solely from vertices and edges. These approaches tend to overlook higher-dimensional spatial features, e.g., 2D facets and 3D cells, from the original geometry. As a result, it is challenging to accurately capture boundary representations and volumetric characteristics, though this information is critically important for modeling contact interactions and internal physical quantity propagation, particularly under sparse mesh discretization. In this paper, we introduce MAVEN, a mesh-aware volumetric encoding network for simulating 3D flexible deformation, which explicitly models geometric mesh elements of higher dimension to achieve a more accurate and natural physical simulation. MAVEN establishes learnable mappings among 3D cells, 2D facets, and vertices, enabling flexible mutual transformations. Explicit geometric features are incorporated into the model to alleviate the burden of implicitly learning geometric patterns. Experimental results show that MAVEN consistently achieves state-of-the-art performance across established datasets and a novel metal stretch-bending task featuring large deformations and prolonged contacts.

Speech-driven 3D facial animation has advanced rapidly, yet most approaches remain tied to registered template meshes, preventing effective deployment on raw 3D scans with arbitrary topology. At the same time, modeling controllable emotional dynamics beyond lip articulation remains challenging, and is often tied to template-based parameterizations. We address these challenges by proposing FreeTalk, a two-stage framework for emotion-conditioned 3D talking-head animation that generalizes to unregistered face meshes with arbitrary vertex count and connectivity. First, Audio-To-Sparse (ATS) predicts a temporally coherent sequence of 3D landmark displacements from speech audio, conditioned on an emotion category and intensity. This sparse representation captures both articulatory and affective motion while remaining independent of mesh topology. Second, Sparse-To-Mesh (STM) transfers the predicted landmark motion to a target mesh by combining intrinsic surface features with landmark-to-vertex conditioning, producing dense per-vertex deformations without template fitting or correspondence supervision at test time. Extensive experiments show that FreeTalk matches specialized baselines when trained in-domain, while providing substantially improved robustness to unseen identities and mesh topologies. Code and pre-trained models will be made publicly available.

Posing 3D characters is a fundamental task in computer graphics. However, existing paradigms, ranging from traditional auto-rigging to recent pose-conditioned generative models, frequently struggle with inaccurate skinning weights, fixed mesh topologies, and poor pose conformance. These challenges have become particularly pronounced with the recent explosion of AI-generated 3D assets, which often exhibit flawed structures and fused geometry. To address these issues, we introduce Make-It-Poseable, a novel feed-forward framework that reformulates character posing as a skinning-free latent-space transformation problem. By decoupling shape deformation from the constraints of fixed mesh connectivity, our method directly operates on compact latent representations to reconstruct characters in target poses. To achieve this, our framework integrates a latent posing transformer for shape manipulation, a dense pose representation for fine-grained control, and an adaptive completion module optimized via a bipartite-matched latent loss to robustly handle topological changes. Extensive experiments demonstrate that our method significantly outperforms existing baselines in posing quality. Furthermore, our design shows promising generalization to diverse morphologies such as quadrupeds in our qualitative tests, and supports various 3D authoring applications such as part replacement and refinement.