While cages provide a powerful reduction model to simulate elastic deformations, interactive real-time cutting of cages has been a longstanding challenge. Traditional solvers require costly volumetric re-meshing and global matrix updates after each modification. For a mesh-free harmonic weight computation using walk on spheres (WoS), we make a key observation: only a small fraction of walks (5-10%) is invalidated by the local cut in most practical cases. We propose a novel reuse pipeline to efficiently update only weights subject to a topological modification. Our approach leverages walk on spheres as an output sensitive and mesh-free Monte Carlo method for solving Laplacian equations, to enable localized updates of harmonic weights. By identifying and reusing unaffected walks, we minimize our re-walking updates. Our method achieves speedups of 10 × -40 × while being statistically identical to a complete WoS weight recomputation. This enables a real time simulation of interactive cutting on complex 2D and 3D cages, and is easily generalizable to other local cage editing operations.
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Walk on Spheres algorithms leverage properties of Brownian Motion to create Monte Carlo estimates of solutions to elliptic partial differential equations. We propose a new caching strategy that leverages the continuity of paths of Brownian Motion. Until recently, estimates were constructed pointwise and did not use the relationship between solutions at nearby points within a domain. In the case of Laplace’s equation with Dirichlet boundary conditions, our algorithm has improved asymptotic runtime compared to previous approaches. Our results are achieved by information reuse from a cache of fixed size. We also provide bounds on the performance of our algorithm and demonstrate our approach on example problems of increasing complexity.
Augmenting the surface of 3D objects with capacitive sensing is particularly challenging when their volumes cannot be modified. In this paper, we present a computational fabrication pipeline that retrofits surface-only sensor layouts to 3D geometries for multi-touch interaction. Our system scans real-world objects to obtain their 3D mesh, generates and optimizes a 3D sensor design of drive and sense lines for mutual-capacitance sensing that complies with physical and hardware sensing constraints, and unfolds them into individual 2D stencils that can be cut from conductive material. Our fabrication pipeline cuts these from thin copper foil with a vinyl cutter and then assists manual sensor attachment by projecting the sensor design onto the dynamically registered real-world object. We connect the resulting electrode mesh to a mutual-capacitance scanning controller and resolve touch interaction in real time. We demonstrate our approach with four 3D geometries and evaluate our method and fabrication pipeline on them.
Existing haptic interfaces remain predominantly contact-centric, relying on localized mechanical actuation to convey discrete events while neglecting continuous atmospheric stimuli—airflow and thermal cues—that fundamentally shape human environmental perception. This paper introduces Atmospheric Haptics, a paradigm treating air and temperature as programmable, non-contact haptic fields authored through four perceptual primitives: Intensity, Temperature, Spatiality, and Dynamics. We develop a three-layer rendering architecture that decouples perceptual authoring from hardware actuation via intensity linearization and thermo-aerodynamic coupling compensation. To validate this paradigm, we present AtmosTouch, a handheld prototype integrating high-static-pressure centrifugal airflow with liquid-cooled thermal management for sustained bidirectional thermal rendering. Our user study (N=14) demonstrates that atmospheric haptics significantly improved navigation precision (lower RMSE), enhanced environmental realism, and enabled novel sensory illusions including wetness perception without liquid contact. Participants unanimously preferred atmospheric haptics over vibrotactile haptics, highlighting its potential as a foundational component for next-generation embodied virtual experiences.
Developments in display technology mean that it may soon be possible to create stereoscopic 3-D imagery that cannot be distinguished from its real-world counterpart, i.e., it could pass the so-called Visual Turing Test. To measure how far current display technologies are from this ultimate goal, we built a custom ultra-realistic display — a high dynamic range (HDR) stereoscope, with accurate color and geometric calibration. Then, we used the display to measure how the reduction of display resolution and dynamic range (contrast) affects the sense of realism, relative to a real scene. These two display capabilities have improved greatly in recent years, and it is useful to understand what benefits further development might bring. The display resolution measurements showed that the realism of presented scenes starts dropping rapidly below ∼ 60 pixels per degree, and the gains diminish above that resolution. Our contrast measurement showed a linear reduction in realism as the contrast was reduced. Furthermore, we found that the observers could discriminate between real and virtual scenes in less than half of the trials (when adjusted for the guess rate), demonstrating the ultra-realistic capabilities of our display. Our results provide a clear guide to potential gains in realism, and can inform display design and HDR tone mapping.
In human vision, the inputs perceived by each eye do not contribute equally to the final percept. Instead, visual dominance influences how these inputs are fused, giving more weight to one eye view over the other. While eye dominance has been traditionally treated as a static, eye-fixed property, recent evidence suggests that dominance can vary with viewing conditions. In this work, we systematically characterize dynamic visual dominance across the visual field, with a particular focus on peripheral vision, where perceptual asymmetries are most relevant for stereoscopic rendering. Through two complementary psychophysical experiments, we first show that tolerance to eye-asymmetric blur at the fovea under binocular viewing depends on gaze direction, confirming that eye dominance is not spatially invariant. We then show that peripheral dominance is primarily governed by retinal eccentricity, with consistent naso-temporal asymmetries and dominance reversals around the blind spots. We leverage our insights in a dominance-contingent rendering application, where additional blur is selectively applied to the perceptually non-dominant eye regions under binocular viewing. Compared to static dominance approaches, our method enables stronger localized quality reductions, illustrating the practical relevance of dynamic peripheral dominance for stereoscopic foveated rendering. Thus, our goal through this work is to show how visual dominance behaves dynamically in both the fovea and the periphery, indicating how foveation techniques could benefit from it.
Interocular differences in visual perception can induce a variety of effects when fused by the brain. For example, prior works have found that carefully crafted binocular differences in local detail can improve contrast. It has also been found that when the frequency content of two stimuli are slightly different, blur suppression leads to a fused percept that is typically dominated by the sharper image. In this paper, we develop a psychophysical framework to measure the perception of natural image stimuli with interocular frequency differences across the visual field. To this end, we study the effect of dichoptic foveation, which we define as the application of blur to one eye and a simultaneous sharpening filter to the other. Stimuli were viewed in a virtual reality (VR) head-mounted display (HMD) and placed at different retinal eccentricities. Study data were scaled to a perceptual just objectionable difference (JOD) scale, and a 4D model was fit to it; our results suggest that interocular frequency differences can be well described by a simple computational model. We applied the model in a realistic VR scenario with free exploration of 360° videos to improve a base foveated rendering system by enhancing high frequency information dichoptically.
Computing injective, flip-free embeddings of simplicial meshes is a fundamental challenge in geometry processing. While the Total Lifted Content (TLC) energy provides a smooth functional with theoretically guaranteed injective global minima, its non-convex nature presents significant optimization hurdles. In this work, we propose a Nonlinear Multigrid (MG/Opt) framework specifically tailored for efficient TLC energy minimization. Our approach leverages a topology-preserving mesh hierarchy to rapidly eliminate low-frequency errors on coarse scales while maintaining rigorous gradient consistency between hierarchical levels through linear correction terms. To address the persistent challenge of local inversions, we introduce a targeted smoothing strategy and an adaptive parameter scheduling mechanism that balances global convergence speed with local injectivity precision. Experimental evaluations across extensive 2D and 3D benchmark datasets demonstrate the robustness of our approach. Our method achieves a 100% convergence success rate across all tested 2D cases and all but one 3D dataset (the VOLMAP benchmark). Furthermore, our MG/Opt framework delivers substantial performance gains, achieving up to 63 × speedup on high-resolution subdivided datasets compared to traditional solvers. These results confirm that our multigrid strategy provides a scalable and reliable solution for large-scale injective mapping problems. Code and data for this paper are at https://github.com/distmeshM/MGOpt_TLC
Geometry optimization often encounters sparse gradients from limited observations, which can cause optimization to drift toward unnatural shapes. Prior work stabilizes this process by exploiting spatial structure encoded by the Laplacian operator within a single shape, enforcing spatial smoothness on gradients. However, such smoothness alone propagates gradients to unobserved regions without any prior knowledge of how shapes typically deform in a given domain. We introduce statistical gradient filtering, which leverages statistical structure across a shape collection by learning shape variations via principal component analysis (PCA) and guiding geometry updates along directions consistent with this learned prior. Unlike previous PCA-based methods that constrain solutions to a linear subspace or modify the objective with regularization terms, we filter gradients at each iteration to steer the optimization path toward plausible shapes, without restricting the solution space or altering the original objective. We validate our approach across a range of shape optimization tasks, demonstrating robust convergence even under challenging conditions.
We present a fast sparse matrix permutation algorithm tailored to linear systems arising from triangle meshes. Our approach produces nested-dissection-style permutations while significantly reducing permutation runtime overhead. Rather than enforcing strict balance and separator optimality, the algorithm deliberately relaxes these design decisions to favor fast partitioning and efficient elimination-tree construction. Our method decomposes permutation into patch-level local orderings and a compact quotient-graph ordering of separators, preserving the essential structure required by sparse Cholesky factorization while avoiding its most expensive components. We integrate our algorithm into vendor-maintained sparse Cholesky solvers on both CPUs and GPUs. Across a range of graphics applications, including single factorizations and repeated factorizations, our method reduces permutation time and improves the sparse Cholesky solve performance by up to 6.27 ×. Our code is available at https://github.com/BehroozZare/fast-permute.
Gaussian Process Implicit Surfaces (GPIS) represent geometry as a distribution over implicit functions. Modeling an object’s appearance as the expected rendering of a GPIS yields a unified framework that captures diverse light-transport effects including microfacet-like reflections and volumetric scattering. Despite this generality, computing GPIS–ray intersections requires sampling conditional multivariate Gaussian distributions along each ray and remains prohibitively expensive. We introduce an online sampling algorithm that draws these distributions incrementally, and an adaptive marching scheme that takes large steps where the surface is provably absent, minimizing the probability of missed intersections. Together, these ideas reduce rendering MSE by up to 46 × at equal time compared to existing methods.
Photorealistic volume rendering suffers from slow convergence with traditional path tracing algorithms and poses significant challenges for real-time applications. In this paper, we present Multi-feature Radiance Baking Neural Networks (MRBNN), a neural volumetric rendering method that achieves real-time performance by leveraging analytic decomposition of scattering with an efficient learned representation. Our method reformulates in-scattering integral in Volumetric Radiance Transfer Equation to diagonal scaling operator in spherical harmonics spectrum. Building on this formulation, we propose a compact factorized representation with low-rank compression in latent space that replaces costly integration. We then introduce efficient dual-pattern feature sampling and a lightweight neural decoder for fast radiance prediction. With these dedicated designs, MRBNN achieves 4 ∼ 5 × speedup over the state-of-the-art while maintaining high visual fidelity. Moreover, our method addresses key limitations of prior work, including over-illumination artifacts and inability to handle volumes with spatially varying albedo or heterogeneous phase parameters. Extensive experiments demonstrate that our neural baking method can synthesize photorealistic images for complex volumes in a few milliseconds.
We present a training algorithm to mitigate optimization instabilities in small neural networks, like those used in real-time neural shading applications. While large, overparameterized models exhibit predictable convergence, smaller architectures often suffer from high optimization variance: differently initialized models converge to disparate local minima. To reduce these training instabilities, we introduce an optimization approach that utilizes an ensemble of network instances during training. We prune underperforming instances and dynamically resize training batches to maintain wall-clock timings comparable to—or faster than—single-instance training. This strategy allows efficiently exploring the weight space yielding a well-performing model with significantly higher likelihood than optimizing a single instance only. We develop and analyze the algorithm in the context of learning reflectance functions for neural shading. This is a challenging task for small neural models due to the high dynamic range of the target function. In addition to our multi-instance training method, we also revisit the choices of loss functions, activation functions, and input parameterization to further improve quality and training robustness.
This work introduces FilmGPT, an autoregressive transformer designed to address the challenge of video montage – turning a collection of raw, “unwatchable” footage into coherent cinematic sequences. Inspired by language learning in modern LLMs, we train a long-context autoregressive transformer on a large corpus of movies. The aim is to implicitly capture the “grammar” of film directly from data rather than from hand-coded rules. Unlike other generative models, FilmGPT does not generate any new video frames. Instead, at inference time, we introduce a footage-constrained decoding algorithm to select the best next shot from the input raw footage according to the statistical patterns learned from films. We first evaluate these learned statistics directly by using the FilmGPT autoregressive model for next shot prediction on a standard benchmark of shot sequence ordering, outperforming the previous state of the art. We then evaluate our footage-constrained decoding algorithm on the full film editing task via a user study, and find that our FilmGPT-based editing significantly outperforms previous approaches. Finally, we demonstrate the applicability of FilmGPT to a wide range of applications in video montage, from automatic video segment trimming to human-in-the-loop film editing. Please see our supplementary material for qualitative results.
Recovering high-quality video from sparse event streams is a challenging task. Regression methods often blur textures, while existing generative models struggle with long-term stability. We propose LongE2V, a novel approach that leverages pre-trained video diffusion priors to jointly handle event-based video reconstruction, prediction, and frame interpolation. By fine-tuning a foundational video model, our approach achieves high data efficiency and superior perceptual quality. We introduce Autoregressive Unrolling and Adaptive Context Switching to mitigate temporal drift in extremely long sequences. We also propose Reencoding Alignment with Cross Residual Correction to ensure precise bidirectional consistency during frame interpolation. Furthermore, Event Voxel Density Augmentation ensures robustness across varying sensor resolutions. Extensive experiments on real-world benchmarks demonstrate that LongE2V outperforms state-of-the-art methods across all three tasks, exhibiting exceptional temporal coherence and zero-shot generalization.