The intricate motion arising from fluid-boundary interactions is visually compelling, yet notoriously difficult and computationally expensive to simulate in the presence of complex boundaries. Accurately resolving boundary geometry requires body-fitted grids constructed via cut-cell methods, which often leads to poorly conditioned linear systems in the pressure projection stage and, consequently, prohibitive computational cost. We present FastVEM, an efficient boundary-conforming fluid simulation framework that enables high-fidelity flow-boundary interaction at substantially reduced cost. Computational efficiency is achieved through a coordinated, top-down design spanning numerical discretization, grid construction, and linear solvers. FastVEM adopts a Virtual Element Method (VEM) discretization to robustly enforce incompressibility and boundary conditions on irregular body-fitted grids, and employs a VEM polynomial-space Particle-in-Cell scheme for advection. Complementing this discretization, a convexity-preserving cut-cell strategy is introduced to construct simulation-friendly body-fitted grids. To accelerate pressure projection, we develop a Galerkin geometric multi-grid solver featuring a diffusion-free prolongation operator that prevents coarse-level matrix densification, along with a nested, boundary-aware grid hierarchy that ensures well-posed placement of coarse-level degrees of freedom. Compared to prior cut-cell-based fluid simulators, FastVEM speeds up the computationally dominant pressure projection stage by up to 100×, while robustly handling even more challenging boundary geometries.
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We developed a new data structure for the efficient representation of spatial data, called SCom DAG — Similarity Compressed Directed Acyclic Graph. It subdivides space with an octree and utilizes local data similarities and topology for compact encoding. Our method exploits the fact that many surface and volume areas are similar to each other up to a transformation. We store spatial transformations on the edges of the graph and data transformations on terminal links pointing to data blocks. Compression is achieved mainly by reducing the number of graph nodes and data blocks while maintaining the same number of paths in the graph. Spatial transformations are compact due to the use of hyper-octahedral groups that are relatively small even in 4D space. SCom DAG works with data of different dimensionality, such as 2D textures, 3D meshes and 4D time-varying volumetric data. Thus, it is well suited for volumetric data visualization and rendering large scenes. The proposed algorithm performs lossy compression, creating a compact representation of various data with controlled quality, which is especially valuable for low-end devices and convenient browser use. It provides a balance of compression and quality comparable to state-of-the-art technologies in various domains, such as compact texture and geometry representation, volumetric data, radiance fields, and precomputed 4D volume animations. At the same time, our data structure enables fast sampling and real-time ray tracing, and its hierarchical nature allows for rendering with a continuous level of detail.
Spherical Harmonics (SH) are fundamental mathematical tools for compactly representing low-frequency spherical functions in computer graphics. Evaluating products of SH-represented functions is a core operation in many rendering algorithms and often becomes a major computational bottleneck. Existing SH product methods face two key challenges: insufficient computational efficiency, and the inflexible requirement that all input functions share the same SH order. To overcome these limitations, we introduce the Generalized Spherical Harmonics Product, a novel formulation that supports inputs with different SH orders and allows flexible truncation of the output. We further propose an efficient and practical computation approach based on Spherical Grids (SphGrid). We establish explicit bidirectional conversions between SphGrid representations and SH coefficients, thus enabling SphGrid to serve as an intermediate representation. Under this framework, SH product computation is reduced to simple point-wise multiplications on the grid. We then derive sufficient conditions on the grid resolution to guarantee exact computation. Using lower resolutions yields an approximate variant that provides a favorable trade-off between accuracy and efficiency. Our approach is not only more general but also demonstrates superior performance even for the specialized case of identical input orders. In particular, our accurate method achieves a 3.5–6.0× speedup over the state-of-the-art method in a practical setting for graphics, while our approximate variant yields lower errors and a 2.5–6.5× speedup over the state-of-the-art approximate method. We rigorously analyze the correctness and efficiency of our method and demonstrate its effectiveness in real-time rendering applications.
Gaussian-based representations have enabled efficient physically-based volume rendering at a fraction of the memory cost of regular, discrete, voxel-based distributions. One of the remaining advantages of classic voxel grids, however, is the ease of constructing hierarchical representations by either storing volumetric mipmaps or selectively pruning branches of an already hierarchical voxel grid. Such strategies reduce rendering time and eliminate aliasing when lower levels of detail are required. Constructing similar strategies for Gaussian-based volumes is not trivial. Straightforward solutions, such as prefiltering or computing mipmap-style representations, lead to increased memory requirements or expensive re-fitting of each level separately. Additionally, such solutions do not guarantee a smooth transition between different hierarchy levels. To address these limitations, we propose Gabor Fields, a mixture of Gabor kernels that enables continuous, orientation-selective frequency filtering at no cost. The frequency content of the asset is reduced by selectively pruning primitives, directly benefiting rendering performance, without refitting or extra storage. Beyond filtering, we demonstrate that stochastically sampling from different frequencies and orientations at each ray recursion enables masking substantial portions of the volume, accelerating ray traversal time in single- and multiple-scattering settings. Furthermore, inspired by procedural volumes, we present an application for efficient design and rendering of procedural clouds as Gabor-noise-modulated Gaussians.
Following the success of deep neural networks in 2D pose estimation, reconstruction-based approaches have significantly advanced multi-person 3D pose estimation from sparse multi-view images. These methods typically detect 2D poses independently in each view and then associate them for 3D reconstruction. However, despite strong progress, recent state-of-the-art methods still face critical limitations: 1) They often depend on global optimization over a large and complex set of multi-view 2D joints to jointly infer 3D poses for all individuals, making the process highly complex and prone to suboptimal solutions; 2) Their tight coupling with the bottom-up detector OpenPose hinders the use of more advanced top-down or single-stage 2D pose estimators and restricts the integration of richer instance-level cues learned by these models. To address these limitations, we propose TwinPose, a novel framework that alleviates the complexity of global pose inference by optimizing within person-specific 3D pose subspaces, while fully supporting diverse 2D pose detectors and effectively leveraging pose-instance cues. The key idea is to introduce a twin pose — a 3D counterpart of each 2D pose — that inherits its instance representation and aggregates geometrically consistent 2D joints from other views. All twin poses are unified in a common 3D space, where those belonging to the same individual naturally share a number of bones. This structural property enables association by counting shared bones, forming person-specific subspaces from which each individual's 3D pose can be inferred independently in an efficient and robust manner. Extensive experiments demonstrate that TwinPose achieves state-of-the-art performance in both accuracy and efficiency across multiple public and proprietary datasets. Importantly, it is fully detector-agnostic, allowing seamless integration with current and future advances in 2D pose estimation while remaining highly robust to noisy or imperfect 2D predictions. Project page with code and additional resources: https://github.com/zgspose/TwinPose
We present an analytical framework for exploring the design space of hinged kirigami structures that deploy rigidly and uniformly. A hinged kirigami structure consists of rigid planar faces connected by hinges, and is deployable if the faces can rotate about the hinges without deformation. Such deployability depends on both the topology and the geometry, i.e., the combinatorial connectivity of the faces and their spatial embedding. Prior work studies geometric constraints for uniform deployability in restricted settings, most notably quadrilateral kirigami patterns and structures derived from 2-colorable planar graphs. However, existing analysis does not readily generalize to arbitrary kirigami structures, nor does it provide a systematic approach for constructing deployable kirigami from non-2-colorable planar graphs (e.g., graphs with non-manifold embeddings). Moreover, while geometric conditions for deployability have been partially investigated, the structure of the full deployable design space and its associated degrees of freedom remain largely unexplored. In this work, we propose a new framework that enables the derivation of hinged kirigami structures from arbitrary planar graphs, with the key feature that multiple distinct kirigami structures can be generated from the same graph. We derive geometric constraints that ensure uniform rigid deployability and analytically characterize the full design space of deployable embeddings, including its associated degrees of freedom. This characterization allows continuous navigation of the design space and provides a systematic foundation for the design of kirigami-based mechanical metamaterials.
Cloaking objects with metamaterials has been extensively studied to hide internal objects across various physical properties, including optical, acoustic, and thermal. We explore a new direction in mechanical cloaking: halftoning an image using a porous structure that behaves like a uniform, linear, isotropic material and visually matches a target image. For an external observer, this creates the surprising effect where the object appears mechanically isotropic and homogeneous while its porous structure resembles a target image. We introduce a parametric class of porous structures suitable for this problem, as demonstrated by numerical experiments. The structures we define offer a wide range of visual contrasts, enabling effective halftoning while maintaining near isotropic effective mechanical properties.
Multi-axis fused filament fabrication (FFF) reduces staircase artifacts and support material by adapting nozzle orientation. However, reliable and highly customizable printing requires layers and toolpaths combining a number of challenging properties: following prescribed fields, preserving constant bead geometry, avoiding stops, retractions, and collisions. We present AtomSlicer, which takes a 3D tool-orientation field and perlayer 2-RoSy tangent direction fields, to generate field-aligned non-planar layers of near-constant thickness. It then computes collision-free deposition toolpaths that are continuous within each layer, and as continuous as possible across layers. AtomSlicer encodes geometry with three orthogonal phase fields sampled into oriented atoms, partitions them into fabricable layers, reconstructs layer meshes, and synthesizes 2-RoSy-aligned toolpaths. Unlike prior methods it treats user- or optimizer-defined fields as constraints, producing a feasible toolpath or reporting non-fabricability rather than modifying the specification. We validate on varied shapes, including a large Thingi10k study, and 13 printed models using constant extrusion per unit path length under a fixed bead profile. AtomSlicer reduces non-extruding travel to a few percent, cuts travel moves by one to two orders of magnitude versus planar and Atomizer baselines, and is 9×-60× faster than Atomizer.
We describe a method for recovering a manifold, intersection-free triangle mesh from the points where edges of a tetrahedral grid pierce a continuous surface. Unlike classic marching cubes or tets, our subgrid marching scheme allows arbitrarily many surface patches within a single cell, capturing fine features and thin sheets. Moreover, it requires neither a well-defined inside/outside (allowing surfaces with boundary), nor consistently-oriented input geometry. Yet we retain the local, parallel nature of classic marching: reconstruction is performed independently per tet, yielding a conforming mesh across tet boundaries. Our key innovation is a generalization of normal coordinates from geometric topology, which encode surface connectivity via arbitrary integer intersection counts along each grid edge. This encoding sidesteps the usual Nyquist-Shannon limit, putting no lower bound on the size of features that can be resolved on a fixed grid. In practice, for similar compute time and equal grid resolution—or even an equal number of output triangles—meshes produced by subgrid marching are far more accurate than those from classic marching. Beyond standard contouring, our method can be used to convert polygon soup into a manifold, intersection-free mesh.
Recent work in 3D deep learning has demonstrated that unsigned distance functions (UDFs) are a useful representation for 3D reconstruction and shape generation because they can represent surfaces with arbitrary topology. However, extracting meshes that preserve the intended topology, especially in the presence of non-manifold structures, remains challenging. We present DCx, an extension of the standard Dual Contouring (DC) method which was originally proposed for isosurface extraction from signed distance functions (SDFs). Standard DC operates on individual voxels and inserts one vertex per active cube, where activation is determined by detecting sign changes. To address the lack of sign information in UDFs, DCx adopts an optimization-based strategy for determining active cubes. It operates on each 2 × 2 × 2 voxel block, referred to as an expanded cube, and introduces a voxel-to-mesh lookup table that stores connectivity patterns based on local voxel configurations. This enables efficient triangle extraction using predefined templates. These changes improve upon DC by avoiding failure cases caused by unreliable active-cube detection in UDFs and by correcting mesh connections in non-manifold regions. As a result, DCx supports the extraction of both manifold and non-manifold surfaces from neural UDFs. DCx is conceptually simple and easy to implement. Experimental results show that DCx produces meshes with higher accuracy in a more robust way than existing methods, particularly on shapes with complex geometry or non-manifold structures. The source code is available at http://github.com/jjjkkyz/DCx.
We introduce the PhaseTree, a novel hierarchical construction-tree representation for compactly modeling volumetric objects composed of multiple phases or materials across scales. An object is defined as a single construction tree that combines phase-aware primitives through composition and warping operators, yielding a unified multiphase signed distance representation that naturally supports complex topologies and interfaces between phases. The PhaseTree is compatible with standard signed distance field workflows: single-phase algorithms can be directly promoted to a PhaseTree, and conversely reduced without loss of information. As a result, our model integrates seamlessly with existing algorithms and rendering pipelines. We extend classical Sphere Tracing to robustly handle multiphase configurations and show that, despite the additional expressiveness, our implementation preserves the compactness and resolution independence of signed distance fields and incurs less than a 25% runtime overhead compared to single-phase Sphere Tracing.
Implicit neural representations are powerful for geometric modeling, but their practical use is often limited by the high computational cost of network evaluations. We observe that implicit representations require progressively lower accuracy as query points move farther from the target surface, and that even within the same iso-surface, representation difficulty varies spatially with local geometric complexity. However, conventional neural implicit models evaluate all query points with the same network depth and computational cost, ignoring this spatial variation and thereby incurring substantial computational waste. Motivated by this observation, we propose an efficient neural implicit geometry representation framework with spatially adaptive network depth (SAND). SAND leverages a volumetric network-depth map together with a tailed multi-layer perceptron (T-MLP) to model implicit representation. The volumetric depth map records, for each spatial region, the network depth required to achieve sufficient accuracy, while the T-MLP is a modified MLP designed to learn implicit functions such as signed distance functions, where an output branch, referred to as a tail, is attached to each hidden layer. This design allows network evaluation to terminate adaptively without traversing the full network and directs computational resources to geometrically important and complex regions, improving efficiency while preserving high-fidelity representations. Extensive experimental results demonstrate that our approach can significantly improve the inference-time query speed of implicit neural representations.
We describe a method for computing signed distance to point clouds that allows fast pointwise evaluation at arbitrary spatial resolution. As input, our method takes a point cloud with normals; as output, it provides an analytical parameterization that allows queries of signed distance to the approximate underlying surface at arbitrary points — simultaneously providing reconstruction and distance. Our key idea is to reconstruct shapes by locally fitting point clouds with tori, which have closed-form signed distance functions. Tori are fitted in a feed-forward manner, using a pre-trained network to output per-point curvature and shift parameters. Importantly, our method does not require costly global optimization or spatial discretization, and is easily parallelizable. Underlying our method is a new theory that unifies signed distance with the classic reconstruction methods of winding numbers and Poisson surface reconstruction. We use our method to compute signed distance to point clouds arising from photogrammetry, meshes, 3D Gaussians, and neural implicits. Our method allows point clouds to be used directly in applications, without explicit surface reconstruction: as examples, we take offsets of point clouds, apply morphological and Boolean operations, and directly visualize offset surfaces using sphere tracing.
Generating high-quality stereo videos requires consistent depth perception and temporal coherence across frames. Despite advances in image and video synthesis using diffusion models, producing high-quality stereo videos remains a challenging task due to the difficulty of maintaining consistent temporal and spatial coherence between left and right views. We introduce DissolveStereo, a novel framework for zero-shot stereo video generation that leverages video diffusion priors without requiring paired training data. Our key innovations include a noisy restart strategy to initialize stereo-aware latent representations and an iterative refinement process that progressively harmonizes the latent space, addressing issues like temporal flickering and view inconsistencies. Importantly, we propose the use of dissolved depth maps to streamline latent space operations by reducing high-frequency depth information. Our comprehensive evaluations, including quantitative metrics and user studies, demonstrate that DissolveStereo produces high-quality stereo videos with enhanced depth consistency and temporal smoothness. In terms of epipolar consistency, our method achieves an 11.7% improvement in MEt3R score over the current state-of-the-art. Furthermore, user studies indicate strong perceptual gains over the previous arts, with an 8.0% higher perceived frame quality and 10.9% higher perceived temporal coherence. Our code is in https://github.com/shijianjian/DissolveStereo.
Recent progress has shown that video diffusion models (VDMs) can be repurposed to solve various multimodal graphics tasks. However, existing approaches predominantly train separate models for each specific problem setting. This practice locks models into fixed input-output mappings, and typically ignores the joint correlations across modalities. In this paper, we present UniVidX, a unified multimodal framework designed to leverage VDM priors to enable versatile video generation. Our goal is to (i) master diverse pixel-aligned tasks by formulating them as conditional generation problems within multimodal space, (ii) adapt to modality-specific distributions without compromising the backbone's native priors, and (iii) ensure cross-modal consistency during synthesis. Concretely, we propose three key designs: 1) Stochastic Condition Masking (SCM): by randomly partitioning modalities into clean conditions and noisy targets during training, we enable the model to learn omni-directional conditional generation rather than fixed mappings. 2) Decoupled Gated LoRA (DGL): we attach per-modality LoRAs and activate them when a modality serves as a generation target, thereby preserving the VDM's strong priors. 3) Cross-Modal Self-Attention (CMSA): we explicitly share keys/values across modalities while maintaining modality-specific queries, facilitating information exchange and inter-modal alignment. We validate our framework by instantiating it in two domains: 1) UniVid-Intrinsic for RGB videos and their intrinsic maps (albedo, irradiance, normal), and 2) UniVid-Alpha for blended RGB videos and their constituent RGBA layers. Experimental results demonstrate that both models achieve performance competitive with state-of-the-art methods across distinct tasks. Notably, they exhibit robust generalization capabilities in in-the-wild scenarios, even when trained on limited datasets of fewer than 1k videos.
We present a GPU-based system for automatic differentiation (AD) of functions defined on triangle meshes, designed to exploit the locality and sparsity in mesh-based computation. Our system evaluates derivatives using perelement forward-mode AD, confining all computation to registers and shared memory and assembling global gradients, sparse Jacobians, and sparse Hessians directly on the GPU. By avoiding global computation graphs, intermediate buffers, and device-host synchronization, our approach minimizes memory traffic and enables efficient differentiation under both static and dynamically changing sparsity. Our programming model lets users express energy terms over mesh neighborhoods, while our system automatically manages parallel execution, derivative propagation, sparse assembly, and matrix-free operations such as Hessian-vector products. Our system supports both scalar- and vector-valued objectives, dynamic interaction-driven sparsity updates, and seamless integration with external GPU sparse linear solvers. We evaluate our system on applications including elastic and cloth simulation, surface parameterization, mesh smoothing, frame field design, ARAP deformation, and spherical manifold optimization. Across these tasks, our system consistently outperforms state-of-the-art differentiation frameworks, including PyTorch, JAX, Warp, Dr.JIT, EnzymeAD, and Thallo. We demonstrate speedups across a range of solver types, from Newton and Gauss-Newton for nonlinear least squares to L-BFGS and gradient descent, and across different derivative usage modes, including Hessian-vector products as well as full sparse Hessian and Jacobian construction. Our system is available as open source at https://github.com/owensgroup/RXMesh.
k-nearest neighbor (k-NN) search is a fundamental primitive in geometry processing and computer graphics. While spatial partitioning structures such as kd-trees are standard, they are often manifold-blind, failing to exploit the intrinsic low-dimensional structure of points sampled from 2-manifolds. Recent advances in dynamic programming-based nearest neighbor search (DP-NNS) leverage incrementally constructed Voronoi diagrams to accelerate queries, where each site p maintains a list of successors that progressively refine its Voronoi cell. However, DP-NNS is restricted to single nearest neighbor (k = 1) searches, precluding their adoption in applications that require local neighborhood statistics. In this paper, we generalize the DP-NNS framework to support arbitrary k-NN queries for manifold-aligned data. Our approach is founded on the geometric observation that if pi is the nearest neighbor of a query q in P, then the second nearest neighbor of q must reside either within the prefix set P1:i-1 = [p1, ..., pi-1} or within pi's successor list. By recursively extending this principle, we introduce Manifold k-NN, a recursive algorithmic scheme that significantly outperforms conventional kd-trees for manifold-aligned data. Our method achieves a 1×-10× speedup in volume-to-surface query scenarios and inherently supports dynamic prefix queries—enabling k-NN searches within any subset P1:m (m ≤ n) with zero overhead. Furthermore, we extend the framework to support point deletion via local Delaunay updates, providing a complete suite of dynamic operations for point set modification. Comprehensive experiments on diverse geometric datasets demonstrate the efficiency and broad applicability of our approach for modern graphics pipelines. Source code is available at https://github.com/sssomeone/manifold-knn.
Computing the Hausdorff distance between triangle meshes with guaranteed accuracy is a computationally intensive task. Conventional Branch-and-Bound (B&B) approaches are fundamentally ill-suited for massive parallelism. Their reliance on a global priority queue (PQ) for both best-first scheduling and global termination checks creates a serial bottleneck that prevents scalable performance. We introduce PQ-Free HD, a parallel B&B framework that eliminates this dependency by decoupling the algorithm's termination logic from its scheduling order. This is achieved by relaxing the culling criterion, thereby replacing the priority queue with a contention-free ring buffer, which transforms the execution model from a state-dependent serial search into a high-throughput, asynchronous batch-processing paradigm. The framework consists of four key components: (1) a parallel priority-queue-free B&B paradigm; (2) a hierarchical GPU execution architecture combining batched depth-first scheduling with fused collaborative kernels; (3) a geometrically robust seven-stage culling pipeline featuring novel tests for challenging geometries; and (4) a compact 29-byte procedural task descriptor that achieves an 83.9% memory reduction. Evaluations demonstrate substantial speedups: a median of 71.7× over the state-of-the-art CPU algorithm on general benchmarks, and exceeding 10,000× on challenging CAD models with dense planar structures. The throughput advantage scales super-linearly with problem complexity. We showcase practical value by building a strictly Hausdorff-distance-bounded mesh simplification tool entirely on the GPU. Our work provides a new method for high-throughput, tolerance-controllable B&B-based geometric queries on GPUs. Code and data are available at https://github.com/huzhihao2001/pqfree-hd.
Computing the directed Hausdorff distance between two triangle meshes is a fundamental operation in geometry processing and simulation. While existing certified branch-and-bound (B&B) methods are efficient for well-separated geometry, they can become prohibitively expensive on large models under tight tolerances and near-zero distance configurations where pruning is limited. We present a GPU-accelerated certified B&B algorithm that explicitly maintains enclosing lower and upper bounds on the directed Hausdorff distance and terminates once their normalized gap, measured with respect to the bounding-box diagonal of the source mesh, meets a user-prescribed tolerance. To map the inherently prioritized search to SIMT (single-instruction, multiple-thread) hardware, we replace priority queues and recursion with a sorted, double-buffered wavefront pipeline built from bulk-parallel worklists for bound evaluation, culling, subdivision, and compaction. To mitigate loose bounds on thin primitives while preserving predictable stream behavior, we introduce a fixed-cardinality adaptive subdivision scheme that selectively applies double longest-edge bisection. To remain robust in deep-refinement regimes, we add a resource-aware deferral mechanism that enforces a device-capacity invariant by prioritizing candidates likely to be culled while postponing expensive ones. Finally, we improve numerical robustness under FP32 (single precision) via triangle-local coordinate transforms and other conservative numerical safeguards, and enhance coherence by spatially ordering the active set and traversing the BVH (bounding volume hierarchy) in triangle packets. Under the same stopping tolerance, experiments on an NVIDIA RTX 5090 show that our GPU solver remains numerically consistent with the FP64 CPU baseline, with normalized cross-platform deviation below 0.01% in over 99.9% of cases. Our method achieves millisecond-scale runtimes capable of supporting interactive frame rates, even on models with millions of triangles. Across the comparison set, it delivers throughput speedups of 836× on the Thingi10K/TetWild benchmark (A → B) and 709× on the Thingi10K/Decimation benchmark. Code and data for this paper are available at https://github.com/fhp-transient/gpu-hausdorff.
High-quality facial appearance capture has traditionally required costly studio recording. Recent works consider an in-the-wild smartphone-based setup; however, their model-based inverse rendering paradigm struggles with the complex disentanglement of reflectance from unknown illumination. To bridge this gap, we propose to shift the paradigm into training a powerful delighting network as a prior to constrain the optimization. We leverage the OLAT dataset and the rendered Light Stage scans for training, and propose Dataset Latent Modulation (DLM) to seamlessly integrate these heterogeneous data sources. Specifically, by conditioning the core network on learnable source-aware tokens, we decouple dataset-specific styles from physical delighting principles, enabling the emergence of a delighting prior that outperforms existing proprietary models. This powerful delighting prior enables a simple and automatic appearance capture pipeline that achieves high-quality reflectance estimation from casual video inputs, outperforming prior arts by a large margin. Furthermore, we leverage our appearance capture method to transform the multi-view NeRSemble dataset into NeRSemble-Scan, a large-scale collection of 4K-resolution relightable scans. By open-sourcing our model and the NeRSemble-Scan dataset, we democratize high-end facial capture and provide a new foundation for the research community to build photorealistic digital humans.