Free-space diffractions are an optical phenomenon where light appears to "bend" around the geometric edges and corners of scene objects. In this paper we present an efficient method to simulate such effects. We derive an edge-based formulation of Fraunhofer diffraction, which is well suited to the common (triangular) geometric meshes used in computer graphics. Our method dynamically constructs a free-space diffraction BSDF by considering the geometry around the intersection point of a ray of light with an object, and we present an importance sampling strategy for these BSDFs. Our method is unique in requiring only ray tracing to produce free-space diffractions, works with general meshes, requires no geometry preprocessing, and is designed to work with path tracers with a linear rendering equation. We show that we are able to reproduce accurate diffraction lobes, and, in contrast to any existing method, are able to handle complex, real-world geometry. This work serves to connect free-space diffractions to the efficient path tracing tools from computer graphics.
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Stochastic geometry models have enjoyed immense success in graphics for modeling interactions of light with complex phenomena such as participating media, rough surfaces, fibers, and more. Although each of these models operates on the same principle of replacing intricate geometry by a random process and deriving the average light transport across all instances thereof, they are each tailored to one specific application and are fundamentally distinct. Each type of stochastic geometry present in the scene is firmly encapsulated in its own appearance model, with its own statistics and light transport average, and no cross-talk between different models or deterministic and stochastic geometry is possible. In this paper, we derive a theory of light transport on stochastic implicit surfaces, a geometry model capable of expressing deterministic geometry, microfacet surfaces, participating media, and an exciting new continuum in between containing aggregate appearance, non-classical media, and more. Our model naturally supports spatial correlations, missing from most existing stochastic models. Our theory paves the way for tractable rendering of scenes in which all geometry is described by the same stochastic model, while leaving ample future work for developing efficient sampling and rendering algorithms.
We introduce an improved version of the micrograin BSDF model [Lucas et al. 2023] for the rendering of anisotropic porous layers. Our approach leverages the properties of micrograins to take into account the correlation between their height and normal, as well as the correlation between the light and view directions. This allows us to derive an exact analytical expression for the Geometrical Attenuation Factor (GAF), summarizing shadowing and masking inside the porous layer. This fully-correlated GAF is then used to define appropriate mixing weights to blend the BSDFs of the porous and base layers. Furthermore, by generalizing the micrograins shape to anisotropy, combined with their fully-correlated GAF, our improved BSDF model produces effects specific to porous layers such as retro-reflection visible on dust layers at grazing angles or height and color correlation that can be found on rusty materials. Finally, we demonstrate very close matches between our BSDF model and light transport simulations realized with explicit instances of micrograins, thus validating our model.
Implicit Swept Volume SDF: Enabling Continuous Collision-Free Trajectory Generation for Arbitrary Shapes
PDF ↗In the field of trajectory generation for objects, ensuring continuous collision-free motion remains a huge challenge, especially for non-convex geometries and complex environments. Previous methods either oversimplify object shapes, which results in a sacrifice of feasible space or rely on discrete sampling, which suffers from the "tunnel effect". To address these limitations, we propose a novel hierarchical trajectory generation pipeline, which utilizes the Swept Volume Signed Distance Field (SVSDF) to guide trajectory optimization for Continuous Collision Avoidance (CCA). Our interdisciplinary approach, blending techniques from graphics and robotics, exhibits outstanding effectiveness in solving this problem. We formulate the computation of the SVSDF as a Generalized Semi-Infinite Programming model, and we solve for the numerical solutions at query points implicitly, thereby eliminating the need for explicit reconstruction of the surface. Our algorithm has been validated in a variety of complex scenarios and applies to robots of various dynamics, including both rigid and deformable shapes. It demonstrates exceptional universality and superior CCA performance compared to typical algorithms. The code will be released at https://github.com/ZJU-FAST-Lab/Implicit-SVSDF-Planner for the benefit of the community.
Across many scientific disciplines, the pursuit of even higher grid resolutions leads to a severe scalability problem in scientific computing. Feature extraction is a commonly chosen approach to reduce the amount of information from dense fields down to geometric primitives that further enable a quantitative analysis. Examples of common features are isolines, extremal lines, or vortex corelines. Due to the rising complexity of the observed phenomena, or in the event of discretization issues with the data, a straightforward application of textbook feature definitions is unfortunately insufficient. Thus, feature extraction from spatial data often requires substantial pre- or post-processing to either clean up the results or to include additional domain knowledge about the feature in question. Such a separate pre- or post-processing of features not only leads to suboptimal and incomparable solutions, it also results in many specialized feature extraction algorithms arising in the different application domains. In this paper, we establish a mathematical language that not only encompasses commonly used feature definitions, it also provides a set of regularizers that can be applied across the bounds of individual application domains. By using the language of variational calculus, we treat features as variational minimizers, which can be combined and regularized as needed. Our formulation not only encompasses existing feature definitions as special case, it also opens the path to novel feature definitions. This work lays the foundations for many new research directions regarding formal definitions, data representations, and numerical extraction algorithms.
We introduce a novel method for acquiring boundary representations (B-Reps) of 3D CAD models which involves a two-step process: it first applies a spatial partitioning, referred to as the "split", followed by a "fit" operation to derive a single primitive within each partition. Specifically, our partitioning aims to produce the classical Voronoi diagram of the set of ground-truth (GT) B-Rep primitives. In contrast to prior B-Rep constructions which were bottom-up, either via direct primitive fitting or point clustering, our Split-and-Fit approach is top-down and structure-aware, since a Voronoi partition explicitly reveals both the number of and the connections between the primitives. We design a neural network to predict the Voronoi diagram from an input point cloud or distance field via a binary classification. We show that our network, coined NVD-Net for neural Voronoi diagrams, can effectively learn Voronoi partitions for CAD models from training data and exhibits superior generalization capabilities. Extensive experiments and evaluation demonstrate that the resulting B-Reps, consisting of parametric surfaces, curves, and vertices, are more plausible than those obtained by existing alternatives, with significant improvements in reconstruction quality. Code will be released on https://github.com/yilinliu77/NVDNet.
While free-hand sketching has long served as an efficient representation to convey characteristics of an object, they are often subjective, deviating significantly from realistic representations. Moreover, sketches are not consistent for arbitrary viewpoints, making it hard to catch 3D shapes. We propose 3Dooole, generating descriptive and view-consistent sketch images given multi-view images of the target object. Our method is based on the idea that a set of 3D strokes can efficiently represent 3D structural information and render view-consistent 2D sketches. We express 2D sketches as a union of view-independent and view-dependent components. 3D cubic Bézier curves indicate view-independent 3D feature lines, while contours of superquadrics express a smooth outline of the volume of varying viewpoints. Our pipeline directly optimizes the parameters of 3D stroke primitives to minimize perceptual losses in a fully differentiable manner. The resulting sparse set of 3D strokes can be rendered as abstract sketches containing essential 3D characteristic shapes of various objects. We demonstrate that 3Doodle can faithfully express concepts of the original images compared with recent sketch generation approaches.1
Perceiving 3D structures from RGB images based on CAD model primitives can enable an effective, efficient 3D object-based representation of scenes. However, current approaches rely on supervision from expensive yet imperfect annotations of CAD models associated with real images, and encounter challenges due to the inherent ambiguities in the task - both in depth-scale ambiguity in monocular perception, as well as inexact matches of CAD database models to real observations. We thus propose DiffCAD, the first weakly-supervised probabilistic approach to CAD retrieval and alignment from an RGB image. We learn a probabilistic model through diffusion, modeling likely distributions of shape, pose, and scale of CAD objects in an image. This enables multi-hypothesis generation of different plausible CAD reconstructions, requiring only a few hypotheses to characterize ambiguities in depth/scale and inexact shape matches. Our approach is trained only on synthetic data, leveraging monocular depth and mask estimates to enable robust zero-shot adaptation to various real target domains. Despite being trained solely on synthetic data, our multi-hypothesis approach can even surpass the supervised state-of-the-art on the Scan2CAD dataset by 5.9% with 8 hypotheses.
Creating super-resolution cloth animations, which refine coarse cloth meshes with fine wrinkle details, faces challenges in preserving spatial consistency and temporal coherence across frames. In this paper, we introduce a general framework to address these issues, leveraging two core modules. The first module interleaves a simulator and a corrector. The simulator handles cloth dynamics, while the corrector rectifies differences in low-frequency features across various resolutions. This interleaving ensures prompt correction of spatial errors from the coarse simulation, effectively preventing their temporal propagation. The second module performs mesh-based super-resolution for detailed wrinkle enhancements. We decompose garment meshes into overlapping patches for adaptability to various styles and geometric continuity. Our method achieves an 8× improvement in resolution for cloth animations. We showcase the effectiveness of our method through diverse animation examples, including simple cloth pieces and intricate garments.
We propose Progressive Dynamics, a coarse-to-fine, level-of-detail simulation method for the physics-based animation of complex frictionally contacting thin shell and cloth dynamics. Progressive Dynamics provides tight-matching consistency and progressive improvement across levels, with comparable quality and realism to high-fidelity, IPC-based shell simulations [Li et al. 2021] at finest resolutions. Together these features enable an efficient animation-design pipeline with predictive coarse-resolution previews providing rapid design iterations for a final, to-be-generated, high-resolution animation. In contrast, previously, to design such scenes with comparable dynamics would require prohibitively slow design iterations via repeated direct simulations on high-resolution meshes. We evaluate and demonstrate Progressive Dynamics's features over a wide range of challenging stress-tests, benchmarks, and animation design tasks. Here Progressive Dynamics efficiently computes consistent previews at costs comparable to coarsest-level direct simulations. Its matching progressive refinements across levels then generate rich, high-resolution animations with high-speed dynamics, impacts, and the complex detailing of the dynamic wrinkling, folding, and sliding of frictionally contacting thin shells and fabrics.
Mutual-capacitive sensing is the most common technology for detecting multi-touch, especially on flat and simple curvature surfaces. Its extension to a more complex shape is still challenging, as a uniform distribution of sensing electrodes is required for consistent touch sensitivity across the surface. To overcome this problem, we propose a method to adapt the sensor layout of common capacitive multi-touch sensors to more complex 3D surfaces, ensuring high-resolution, robust multi-touch detection. The method automatically computes a grid of transmitter and receiver electrodes with as regular distribution as possible over a general 3D shape. It starts with the computation of a proxy geometry by quad meshing used to place the electrodes through the dual-edge graph. It then arranges electrodes on the surface to minimize the number of touch controllers required for capacitive sensing and the number of input/output pins to connect the electrodes with the controllers. We reach these objectives using a new simplification and clustering algorithm for a regular quad-patch layout. The reduced patch layout is used to optimize the routing of all the structures (surface grooves and internal pipes) needed to host all electrodes on the surface and inside the object's volume, considering the geometric constraints of the 3D shape. Finally, we print the 3D object prototype ready to be equipped with the electrodes. We analyze the performance of the proposed quad layout simplification and clustering algorithm using different quad meshing and characterize the signal quality and accuracy of the capacitive touch sensor for different non-planar geometries. The tested prototypes show precise and robust multi-touch detection with good Signal-to-Noise Ratio and spatial accuracy of about 1mm.
NICER: A New and Improved Consumed Endurance and Recovery Metric to Quantify Muscle Fatigue of Mid-Air Interactions
PDF ↗Natural gestures are crucial for mid-air interaction, but predicting and managing muscle fatigue is challenging. Existing torque-based models are limited in their ability to model above-shoulder interactions and to account for fatigue recovery. We introduce a new hybrid model, NICER, which combines a torque-based approach with a new term derived from the empirical measurement of muscle contraction and a recovery factor to account for decreasing fatigue during rest. We evaluated NICER in a mid-air selection task using two interaction methods with different degrees of perceived fatigue. Results show that NICER can accurately model above-shoulder interactions as well as reflect fatigue recovery during rest periods. Moreover, both interaction methods show a stronger correlation with subjective fatigue measurement (ρ = 0.978/0.976) than a previous model, Cumulative Fatigue (ρ = 0.966/0.923), confirming that NICER is a powerful analytical tool to predict fatigue across a variety of gesture-based interactive applications.
The ability to represent artworks as stacks of layers is fundamental to modern graphics design, as it allows artists to easily separate visual elements, edit them in isolation, and blend them to achieve rich visual effects. Despite their ubiquity in 2D painting software, layers have not yet made their way to VR painting, where users paint strokes directly in 3D space by gesturing a 6-degrees-of-freedom controller. But while the concept of a stack of 2D layers was inspired by real-world layers in cell animation, what should 3D layers be? We propose to define 3D-Layers as groups of 3D strokes, and we distinguish the ones that represent 3D geometry from the ones that represent color modifications of the geometry. We call the former substrate layers and the latter appearance layers. Strokes in appearance layers modify the color of the substrate strokes they intersect. Thanks to this distinction, artists can define sequences of color modifications as stacks of appearance layers, and edit each layer independently to finely control the final color of the substrate. We have integrated 3D-Layers into a VR painting application and we evaluate its flexibility and expressiveness by conducting a usability study with experienced VR artists.
We present an approach enabling large-scale pretrained latent diffusion models to generate transparent images. The method allows generation of single transparent images or of multiple transparent layers. The method learns a "latent transparency" that encodes alpha channel transparency into the latent manifold of a pretrained latent diffusion model. It preserves the production-ready quality of the large diffusion model by regulating the added transparency as a latent offset with minimal changes to the original latent distribution of the pretrained model. In this way, any latent diffusion model can be converted into a transparent image generator by finetuning it with the adjusted latent space. We train the model with 1M transparent image layer pairs collected using a human-in-the-loop collection scheme. We show that latent transparency can be applied to different open source image generators, or be adapted to various conditional control systems to achieve applications like foreground/background-conditioned layer generation, joint layer generation, structural control of layer contents, etc. A user study finds that in most cases (97%) users prefer our natively generated transparent content over previous ad-hoc solutions such as generating and then matting. Users also report the quality of our generated transparent images is comparable to real commercial transparent assets like Adobe Stock.
Sphere tracing is a fast and high-quality method for visualizing surfaces encoded by signed distance functions (SDFs). We introduce a similar method for a completely different class of surfaces encoded by harmonic functions, opening up rich new possibilities for visual computing. Our starting point is similar in spirit to sphere tracing: using conservative Harnack bounds on the growth of harmonic functions, we develop a Harnack tracing algorithm for visualizing level sets of harmonic functions, including those that are angle-valued and exhibit singularities. The method takes much larger steps than naïve ray marching, avoids numerical issues common to generic root finding methods and, like sphere tracing, needs only perform pointwise evaluation of the function at each step. For many use cases, the method is fast enough to run real time in a shader program. We use it to visualize smooth surfaces directly from point clouds (via Poisson surface reconstruction) or polygon soup (via generalized winding numbers) without linear solves or mesh extraction. We also use it to visualize nonplanar polygons (possibly with holes), surfaces from architectural geometry, mesh "exoskeletons", and key mathematical objects including knots, links, spherical harmonics, and Riemann surfaces. Finally we show that, at least in theory, Harnack tracing provides an alternative mechanism for visualizing arbitrary implicit surfaces.
Recent advancements in spatiotemporal reservoir resampling (ReSTIR) leverage sample reuse from neighbors to efficiently evaluate the path integral. Like rasterization, ReSTIR methods implicitly assume a pinhole camera and evaluate the light arriving at a pixel through a single predetermined subpixel location at a time (e.g., the pixel center). This prevents efficient path reuse in and near pixels with high-frequency details. We introduce Area ReSTIR, extending ReSTIR reservoirs to also integrate each pixel's 4D ray space, including 2D areas on the film and lens. We design novel subpixel-tracking temporal reuse and shift mappings that maximize resampling quality in such regions. This robustifies ReSTIR against high-frequency content, letting us importance sample subpixel and lens coordinates and efficiently render antialiasing and depth of field.
Robust light transport algorithms, particularly bidirectional path tracing (BDPT), face significant challenges when dealing with specular or highly glossy involved paths. BDPT constructs the full path by connecting sub-paths traced individually from the light source and camera. However, it remains difficult to sample by connecting vertices on specular and glossy surfaces with narrow-lobed BSDF, as it poses severe constraints on sampling in the feasible direction. To address this issue, we propose a novel approach, called proxy sampling, that enables efficient sub-path connection of these challenging paths. When a low-contribution specular/glossy connection occurs, we drop out the problematic neighboring vertex next to this specular/glossy vertex from the original path, then retrace an alternative sub-path as a proxy to complement this incomplete path. This newly constructed complete path ensures that the connection adheres to the constraint of the narrow lobe within the BSDF of the specular/glossy surface. Unbiased reciprocal estimation is the key to our method to obtain a probability density function (PDF) reciprocal to ensure unbiased rendering. We derive the reciprocal estimation method and provide an efficiency-optimized setting for efficient sampling and connection. Our method provides a robust tool for substituting problematic paths with favorable alternatives while ensuring unbiasedness. We validate this approach in the probabilistic connections BDPT for addressing specular-involved difficult paths. Experimental results have proved the effectiveness and efficiency of our approach, showcasing high-performance rendering capabilities across diverse settings.
We propose a generalization of the rendering equation that captures both the realistic light transport of physically-based rendering (PBR) and a subset of non-photorealistic rendering (NPR) stylizations in a principled manner. The proposed formulation is based on the key observation that both classical transport and certain NPR stylizations can be modeled as a function of expectation. Given this observation, we generalize the recursive integrals of the rendering equation to recursive functions of expectation. As estimating functions of expectation can be challenging, especially recursive ones, we provide a toolkit for unbiased and biased estimation comprising prior work, general strategies, and a novel build-your-own strategy for constructing more complex unbiased estimators from simpler unbiased estimators. We then use this toolkit to construct a complete estimator for the proposed recursive formulation, and implement a sampling algorithm that is both conceptually simple and leverages many of the components of an ordinary path tracer. To demonstrate the practicality of the proposed method we showcase how it captures several existing stylizations like color mapping, cel shading, and cross-hatching, fuses NPR and PBR visuals, and allows us to explore visuals that were previously challenging under existing formulations.
Strand-based hair simulations have recently become increasingly popular for a range of real-time applications. However, accurately simulating the full number of hair strands remains challenging. A commonly employed technique involves simulating a subset of guide hairs to capture the overall behavior of the hairstyle. Details are then enriched by interpolation using linear skinning. Hair interpolation enables fast real-time simulations but frequently leads to various artifacts during runtime. As the skinning weights are often pre-computed, substantial variations between the initial and deformed shapes of the hair can cause severe deviations in fine hair geometry. Straight hairs may become kinked, and curly hairs may become zigzags. This work introduces a novel physical-driven hair interpolation scheme that utilizes existing simulated guide hair data. Instead of directly operating on positions, we interpolate the internal forces from the guide hairs before efficiently reconstructing the rendered hairs based on their material model. We formulate our problem as a constraint satisfaction problem for which we present an efficient solution. Further practical considerations are addressed using regularization terms that regulate penetration avoidance and drift correction. We have tested various hairstyles to illustrate that our approach can generate visually plausible rendered hairs with only a few guide hairs and minimal computational overhead, amounting to only about 20% of conventional linear hair interpolation. This efficiency underscores the practical viability of our method for real-time applications.
Physically-based simulation is a powerful approach for 3D facial animation as the resulting deformations are governed by physical constraints, allowing to easily resolve self-collisions, respond to external forces and perform realistic anatomy edits. Today's methods are data-driven, where the actuations for finite elements are inferred from captured skin geometry. Unfortunately, these approaches have not been widely adopted due to the complexity of initializing the material space and learning the deformation model for each character separately, which often requires a skilled artist followed by lengthy network training. In this work, we aim to make physics-based facial animation more accessible by proposing a generalized physical face model that we learn from a large 3D face dataset. Once trained, our model can be quickly fit to any unseen identity and produce a ready-to-animate physical face model automatically. Fitting is as easy as providing a single 3D face scan, or even a single face image. After fitting, we offer intuitive animation controls, as well as the ability to retarget animations across characters. All the while, the resulting animations allow for physical effects like collision avoidance, gravity, paralysis, bone reshaping and more.