Neutron transport simulation plays a central role in nuclear engineering, yet its inverse problems—such as shielding design and sensitivity analysis—remain extremely challenging. The governing transport equation shares a common mathematical foundation with the volume rendering equation used for participating media in computer graphics. Recent advances in differentiable rendering have demonstrated that inverse problems—such as recovering scene properties from observations—can be efficiently solved through gradient-based optimization, where the gradients are estimated through Monte Carlo methods. Inspired by these developments, we extend differentiable rendering techniques to neutron transport problems, enabling inverse design and sensitivity analysis in nuclear systems. To adapt these methods to the neutron transport problem, we generalize the automatic differentiation of Monte Carlo light transport simulation to multi-energy neutron transport; propose a new simplified way to handle moving geometric discontinuities; and propose new estimators for derivatives of volume integrals. We demonstrate the effectiveness of the proposed framework on several model inverse problems, including gradient-based optimization of multi-group neutron moderation, sensitivity analysis of material properties, and diagnostic sensor shape optimization. These results show that differentiable Monte Carlo neutron transport can support optimization and analysis tasks, opening new opportunities for inverse design in nuclear shielding and related applications.

Implicit neural fields have made remarkable progress in reconstructing 3D surfaces from multiple images; however, they encounter challenges when it comes to separating individual objects within a scene. Previous approaches to this problem require ground-truth segmentation masks and introduce floating artifacts in occluded parts of the scene. We address these challenges with ObjectCarver. Object-Carver requires no ground-truth segmentation; all it needs is just a few user clicks in a single view. ObjectCarver also introduces a new loss function that prevents floaters and avoids inappropriate carving-out due to occlusion. Finally, ObjectCarver uses a simple initialization technique that significantly speeds up the process while preserving geometric details. We demonstrate qualitatively and quantitatively on multiple datasets (including a new dataset and benchmark with complete ground-truth) that ObjectCarver produces more accurate reconstructions of each object while minimizing artifacts.

Neural fields have become widely used in various fields, from shape representation to neural rendering, and for solving partial differential equations (PDEs). With the advent of hybrid neural field representations like Instant NGP that leverage small MLPs and explicit representations, these models train quickly and can fit large scenes. Yet in many applications like rendering and simulation, hybrid neural fields can cause noticeable and unreasonable artifacts. This is because they do not yield accurate spatial derivatives needed for these downstream applications. In this work, we propose two ways to circumvent these challenges. Our first approach is a post hoc operator that uses local polynomial fitting to obtain more accurate derivatives from pre-trained hybrid neural fields. Additionally, we also propose a self-supervised fine-tuning approach that refines the hybrid neural field to yield accurate derivatives directly while preserving the initial signal. We show applications of our method to rendering, collision simulation, and solving PDEs. We observe that using our approach yields more accurate derivatives, reducing artifacts and leading to more accurate simulations in downstream applications.

In this paper, we present a self-calibrating framework that jointly optimizes camera parameters, lens distortion and 3D Gaussian representations, enabling accurate and efficient scene reconstruction. In particular, our technique enables high-quality scene reconstruction from Large field-of-view (FOV) imagery taken with wide-angle lenses, allowing the scene to be modeled from a smaller number of images. Our approach introduces a novel method for modeling complex lens distortions using a hybrid network that combines invertible residual networks with explicit grids. This design effectively regularizes the optimization process, achieving greater accuracy than conventional camera models. Additionally, we propose a cubemap-based resampling strategy to support large FOV images without sacrificing resolution or introducing distortion artifacts. Our method is compatible with the fast rasterization of Gaussian Splatting, adaptable to a wide variety of camera lens distortion, and demonstrates state-of-the-art performance on both synthetic and real-world datasets.

Physically based differentiable rendering has established itself as key to inverse rendering, in which scenes are recovered from images through gradient-based optimization. Taking the derivative of the rendering equation is made difficult by the presence of discontinuities in the integrand at object silhouettes. To obtain correct derivatives w.r.t. changing geometry, accounting e.g. for changing penumbras or silhouettes in glossy reflections, differentiable renderers must compute an integral over these silhouettes. Prior work proposed importance sampling of silhouette edges for a given shading point. The main challenge is to efficiently reject parts of the mesh without silhouettes during sampling, which has been done using top-down traversal of a tree. Inaccuracies of this existing rejection procedure result in many samples with zero contribution. Thus, variance remains high and subsequent work has focused on alternatives such as area sampling or path space differentiable rendering. We propose an improved rejection test. It reduces variance substantially, which makes edge sampling in a unidirectional path tracer competitive again. Our rejection test relies on two approximations to the triangle planes of a mesh patch: A bounding box in dual space and dual quadrics. Additionally, we improve the heuristics used for stochastic traversal of the tree. We evaluate our method in a unidirectional path tracer and achieve drastic improvements over the original edge sampling and outperform methods based on area sampling.

Realistic fabric rendering is still a significant challenge due to their complex structures and varying fiber properties. We present a new fabric shading technique, which models both reflection and transmission using a hybrid of ray and wave optics methods, grounded in simulation data. We target fabrics woven from yarns, each formed by twisting together one or more plies, which further contain twisted fibers. Our model is based on simulations that predict the scattering of a narrow Gaussian beam by a single ply. Comparing results from full-wave simulations and path tracing, we found that ray optics can accurately simulate the average far field scattering from an ensemble of plies, but not the variation among individual ply instances, and ray tracing overlooks important diffraction effects. Following these observations, our model is built from ray simulations performed for many ply instances, with simulation data fitted by Gaussian mixtures to be used during rendering. Wave simulations are used to calibrate noise functions that account for instance-to-instance variation, and an aperture diffraction model is used to handle light passing between plies and yarns. The result is a hybrid model capable of producing realistic appearance and highlight structure in fabrics, while capturing spatial break-ups and irregularities and simulating the subtle color shifts and blurriness that occur in transmission. We validate our results by comparing rendered images with photographs, demonstrating the effectiveness of our approach in achieving realistic cloth rendering.

We present a simple algorithm for differentiable rendering of surfaces represented by Signed Distance Fields (SDF), which makes it easy to integrate rendering into gradient-based optimization pipelines.To tackle visibilityrelated derivatives that make rendering non-differentiable, existing physically based differentiable rendering methods often rely on elaborate guiding data structures or reparameterization with a global impact on variance.In this article, we investigate an alternative that embraces nonzero bias in exchange for low variance and architectural simplicity.Our method expands the lower-dimensional boundary integral into a thin band that is easy to sample when the underlying surface is represented by an SDF.We demonstrate the performance and robustness of our formulation in end-to-end inverse rendering tasks, where it obtains results that are competitive with or superior to existing work.

Many animals exhibit structural colors, which are often iridescent, meaning that the perceived colors change with illumination conditions and viewing perspectives. Biological iridescence is usually caused by multilayers or other periodic structures in animal tissues, which selectively reflect light of certain wavelengths and often result in a shiny appearance---which almost always comes with spatially varying highlights, thanks to randomness and irregularities in the structures. Previous models for biological iridescence tend to each target one specific structure, and most models only compute large-area averages, overlooking spatial variation in iridescent appearance. In this work, we build appearance models for biological iridescence using bird feathers as our case study, investigating different types of feathers with a variety of structural coloration mechanisms. We propose an approximate wave simulation method that takes advantage of quasi-regular structures while efficiently modeling the effects of natural structural irregularities. We further propose a method to distill our simulation results into distributions of BRDFs, generated using noise functions, that preserve relevant statistical properties of the simulated BRDFs. This allows us to model the spatially varying, glittery appearance commonly seen on feathers. Our BRDFs are practical and efficient, and we present renderings of multiple types of iridescent feathers with comparisons to photographic images.

This paper presents a method that uses neural networks as a caching mechanism to reduce the variance of Monte Carlo Partial Differential Equation solvers, such as the Walk-on-Spheres algorithm [Sawhney and Crane 2020]. While these Monte Carlo PDE solvers have the merits of being unbiased and discretization-free, their high variance often hinders real-time applications. On the other hand, neural networks can approximate the PDE solution, and evaluating these networks at inference time can be very fast. However, neural-network-based solutions may suffer from convergence difficulties and high bias. Our hybrid system aims to combine these two potentially complementary solutions by training a neural field to approximate the PDE solution using supervision from a WoS solver. This neural field is then used as a cache in the WoS solver to reduce variance during inference. We demonstrate that our neural field training procedure is better than the commonly used self-supervised objectives in the literature. We also show that our hybrid solver exhibits lower variance than WoS with the same computational budget: it is significantly better for small compute budgets and provides smaller improvements for larger budgets, reaching the same performance as WoS in the limit.

Abstract Looking at a cup of hot tea, an observer can see color patterns and granular textures both on the water surface and in the steam. Motivated by this example, we model the appearance of iridescent water droplets. Mie scattering describes the scattering of light waves by individual spherical particles and is the building block for both effects, but we show that other mechanisms must also be considered in order to faithfully reproduce the appearance. Iridescence on the water surface is caused by droplets levitating above the surface, and interference between light scattered by drops and reflected by the water surface, known as Quetelet scattering, is essential to producing the color. We propose a model, new to computer graphics, for rendering this phenomenon, which we validate against photographs. For iridescent steam, we show that variation in droplet size is essential to the characteristic color patterns. We build a droplet growth model and apply it as a post‐processing step to an existing computer graphics fluid simulation to compute collections of particles for rendering. We significantly accelerate the rendering of sparse particles with motion blur by intersecting rays with particle trajectories, blending contributions along viewing rays. Our model reproduces the distinctive color patterns correlated with the steam flow. For both effects, we instantiate individual droplets and render them explicitly, since the granularity of droplets is readily observed in reality, and demonstrate that Mie scattering alone cannot reproduce the visual appearance.

Traditional fiber scattering models, based on ray optics, are missing some important visual aspects of fiber appearance. Previous work [Xia et al. 2020] on wave scattering from ideal extrusions demonstrated that diffraction produces strong forward scattering and colorful effects that are missing from ray-based models. However, that work was unable to include some important surface characteristics such as surface roughness and tilted cuticle scales, which are known to be important for fiber appearance. In this work, we take an important step to study wave effects from rough fibers with arbitrary 3D microgeometry. While the full-wave simulation of realistic 3D fibers remains intractable, we developed a 3D wave optics simulator based on a physical optics approximation, using a GPU-based hierarchical algorithm to greatly accelerate the calculation. It simulates surface reflection and diffractive scattering, which are present in all fibers and typically dominate for darkly pigmented fibers. The simulation provides a detailed picture of first order scattering, but it is not practical to use for production rendering as this would require tabulation per fiber geometry. To practically handle geometry variations in the scene, we propose a model based on wavelet noise, capturing the important statistical features in the simulation results that are relevant for rendering. Both our simulation and practical model show similar granular patterns to those observed in optical measurement. Our compact noise model can be easily combined with existing scattering models to render hair and fur of various colors, introducing visually important colorful glints that were missing from all previous models.

Computing light reflection from rough surfaces is an important topic in computer graphics. Reflection models developed based on geometric optics fail to capture wave effects such as diffraction and interference, while existing models based on physical optics approximations give erroneous predictions under many circumstances (e.g. when multiple scattering from the surface cannot be ignored). We present a scalable 3D full-wave simulator for computing reference solutions to surface scattering problems, which can be used to evaluate and guide the development of approximate models for rendering. We investigate the range of validity for some existing wave optics based reflection models; our results confirm these models for low-roughness surfaces but also show that prior rendering methods do not accurately predict the scattering behavior of some types of surfaces. Our simulator is based on the boundary element method (BEM) and accelerated using the adaptive integral method (AIM), and is implemented to execute on modern GPUs. We demonstrate the simulator on domains up to 60 × 60 × 10 wavelengths, involving surface samples with significant height variations. Furthermore, we propose a new system for efficiently computing BRDF values for large numbers of incident and outgoing directions at once, by combining small simulations to characterize larger areas. Our simulator will be released as an open-source toolkit for computing surface scattering.

Digitally reproducing the appearance of woven fabrics is important in many applications of realistic rendering, from interior scenes to virtual characters. However, designing realistic shading models and capturing real fabric samples are both challenging tasks. Previous work ranges from applying generic shading models not meant for fabrics, to data-driven approaches scanning fabrics requiring expensive setups and large data. In this paper, we propose a woven fabric material model and a parameter estimation approach for it. Our lightweight forward shading model treats yarns as bent and twisted cylinders, shading these using a microflake-based bidirectional reflectance distribution function (BRDF) model. We propose a simple fabric capture configuration, wrapping the fabric sample on a cylinder of known radius and capturing a single image under known camera and light positions. Our inverse rendering pipeline consists of a neural network to estimate initial fabric parameters and an optimization based on differentiable rendering to refine the results. Our fabric parameter estimation achieves high-quality recovery of measured woven fabric samples, which can be used for efficient rendering and further edited.

To render higher quality images from the samples generated by path tracing with a low sample count, we propose a novel path reuse approach that processes a fixed collection of paths to iteratively refine and improve radiance estimates throughout the scene. Our method operates on a path graph consisting of the union of the traced paths with additional neighbor edges inserted among clustered nearby vertices. Our approach refines the initial noisy radiance estimates via an aggregation operator, treating vertices within clusters as independent sampling techniques that can be combined using MIS. In a novel step, we also introduce a propagation operator to forward the refined estimates along the paths to successive bounces. We apply the aggregation and propagation operations to the graph iteratively, progressively refining the radiance values, converging to fixed-point radiance estimates with lower variance than the original ones. We also introduce a decorrelation (final gather) step, which uses information already in the graph and is cheap to compute, allowing us to combine the method with standard denoisers. Our approach is lightweight, in the sense that it can be easily plugged into any standard path tracer and neural final image denoiser. Furthermore, it is independent of scene complexity, as the graph size only depends on image resolution and average path depth. We demonstrate that our technique leads to realistic rendering results starting from as low as 1 path per pixel, even in complex indoor scenes dominated by multi-bounce indirect illumination.

Abstract To increase diversity and realism, surface bidirectional scattering distribution functions (BSDFs) are often modelled as consisting of multiple layers, but accurately evaluating layered BSDFs while accounting for all light transport paths is a challenging problem. Recently, Guo et al. [GHZ18] proposed an accurate and general position‐free Monte Carlo method, but this method introduces variance that leads to longer render time compared to non‐stochastic layered models. We improve the previous work by presenting two new sampling strategies, pair‐product sampling and multiple‐product sampling. Our new methods better take advantage of the layered structure and reduce variance compared to the conventional approach of sequentially sampling one BSDF at a time. Our pair‐product sampling strategy importance samples the product of two BSDFs from a pair of adjacent layers. We further generalize this to multiple‐product sampling, which importance samples the product of a chain of three or more BSDFs. In order to compute these products, we developed a new approximate Gaussian representation of individual layer BSDFs. This representation incorporates spatially varying material properties as parameters so that our techniques can support an arbitrary number of textured layers. Compared to previous Monte Carlo layering approaches, our results demonstrate substantial variance reduction in rendering isotropic layered surfaces.

3D weaving is a manufacturing technique that creates multilayer textiles with substantial thickness. Currently, the primary use for these materials is in regularly structured carbon-polymer or glass-polymer composites, but in principle a wide range of complex shapes can be achieved, providing the opportunity to customize the fiber structure for individual parts and also making 3D weaving appealing in many soft-goods applications. The primary obstacle to broader use is the need to design intricate weave structures, involving tens to hundreds of thousands of yarn crossings, which are different for every shape to be produced. The goal of this research is to make 3D weaving as readily usable as CNC machining or 3D printing, by providing an algorithm to convert an arbitrary 3D solid model into machine instructions to weave the corresponding shape. We propose a method to generate 3D weaving patterns for height fields by slicing the shape along intersecting arrays of parallel planes and then computing the paths for all the warp and weft yarns, which travel in these planes. We demonstrate the method by generating weave structures for different shapes and fabricating a number of examples in polyester yarn using a Jacquard loom.

3D weaving is an emerging technology for manufacturing multilayer woven textiles. In this work, we present Weavecraft: an interactive, simulation-based design tool for 3D weaving. Unlike existing textile software that uses 2D representations for design patterns, we propose a novel weave block representation that helps the user to understand 3D woven structures and to create complex multi-layered patterns. With Weavecraft, users can create blocks either from scratch or by loading traditional weaves, compose the blocks into large structures, and edit the pattern at various scales. Furthermore, users can verify the design with a physically based simulator, which predicts and visualizes the geometric structure of the woven material and reveals potential defects at an interactive rate. We demonstrate a range of results created with our tool, from simple two-layer cloth and well known 3D structures to a more sophisticated design of a 3D woven shoe, and we evaluate the effectiveness of our system via a formative user study.

Existing fiber scattering models in rendering are all based on tracing rays through fiber geometry, but for small fibers diffraction and interference are non-negligible, so relying on ray optics can result in appearance errors. This paper presents the first wave optics based fiber scattering model, introducing an azimuthal scattering function that comes from a full wave simulation. Solving Maxwell's equations for a straight fiber of constant cross section illuminated by a plane wave reduces to solving for a 3D electromagnetic field in a 2D domain, and our fiber scattering simulator solves this 2.5D problem efficiently using the boundary element method (BEM). From the resulting fields we compute extinction, absorption, and far-field scattering distributions, which we use to simulate shadowing and scattering by fibers in a path tracer. We validate our path tracer against the wave simulation and the simulation against a measurement of diffraction from a single textile fiber. Our results show that our approach can reproduce a wide range of fibers with different sizes, cross sections, and material properties, including textile fibers, animal fur, and human hair. The renderings include color effects, softening of sharp features, and strong forward scattering that are not predicted by traditional ray-based models, though the two approaches produce similar appearance for complex fiber assemblies under many conditions.

Rendering specular material appearance is a core problem of computer graphics. While smooth analytical material models are widely used, the high-frequency structure of real specular highlights requires considering discrete, finite microgeometry. Instead of explicit modeling and simulation of the surface microstructure (which was explored in previous work), we propose a novel direction: learning the high-frequency directional patterns from synthetic or measured examples, by training a generative adversarial network (GAN). A key challenge in applying GAN synthesis to spatially varying BRDFs is evaluating the reflectance for a single location and direction without the cost of evaluating the whole hemisphere. We resolve this using a novel method for partial evaluation of the generator network. We are also able to control large-scale spatial texture using a conditional GAN approach. The benefits of our approach include the ability to synthesize spatially large results without repetition, support for learning from measured data, and evaluation performance independent of the complexity of the dataset synthesis or measurement.

Extended stochastic sources, like falling rain or a flowing waterway, provide an immersive ambience in virtual environments. In complex scenes, the rendered sound should vary naturally with listener position, differing not only in overall loudness but also in texture, to capture the indistinct murmur of a faraway brook versus the bright babbling of one up close. Modeling an ambient sound as a collection of random events such as individual raindrop impacts or water bubble oscillations, this variation can be seen as a change in the statistical distribution of events heard by the listener: the arrival rate of nearby, louder events relative to more distant or occluded, quieter ones. Reverberation and edge diffraction from scene geometry multiply and mix events more extensively compared to an empty scene and introduce salient spatial variation in texture. We formalize the notion of acoustic texture by introducing the event loudness density (ELD), which relates the rapidity of received events to their loudness. To model spatial variation in texture, the ELD is made a function of listener location in the scene. We show that this ELD field can be extracted from a single wave simulation for each extended source and rendered flexibly using a granular synthesis pipeline, with grains derived procedurally or from recordings. Our system yields believable, realtime changes in acoustic texture as the listener moves, driven by sound propagation in the scene.

We develop a new theory of volumetric light transport for media with non-exponential free-flight distributions. Recent insights from atmospheric sciences and neutron transport demonstrate that such distributions arise in the presence of correlated scatterers, which are naturally produced by processes such as cloud condensation and fractal-pattern formation. Our theory formulates a non-exponential path integral as the result of averaging stochastic classical media, and we introduce practical models to solve the resulting averaging problem efficiently. Our theory results in a generalized path integral which allows us to handle non-exponential media using the full range of Monte Carlo rendering algorithms while enriching the range of achievable appearance. We propose parametric models for controlling the statistical correlations by leveraging work on stochastic processes, and we develop a method to combine such unresolved correlations (and the resulting non-exponential free-flight behavior) with explicitly modeled macroscopic heterogeneity. This provides a powerful authoring approach where artists can freely design the shape of the attenuation profile separately from the macroscopic heterogeneous density, while our theory provides a physically consistent interpretation in terms of a path space integral. We address important considerations for graphics including reciprocity and bidirectional rendering algorithms, all in the presence of surfaces and correlated media.

We describe an interactive design tool for authoring, simulating, and adjusting yarn-level patterns for knitted and woven cloth. To achieve interactive performance for notoriously slow yarn-level simulations, we propose two acceleration schemes: (a) yarn-level periodic boundary conditions that enable the restricted simulation of only small periodic patches, thereby exploiting the spatial repetition of many cloth patterns in cardinal directions, and (b) a highly parallel GPU solver for efficient yarn-level simulation of the small patch. Our system supports interactive pattern editing and simulation, and runtime modification of parameters. To adjust the amount of material used (yarn take-up) we support "on the fly" modification of (a) local yarn rest-length adjustments for pattern specific edits, e.g., to tighten slip stitches, and (b) global yarn length by way of a novel yarn-radius similarity transformation. We demonstrate the tool's ability to support interactive modeling, by novice users, of a wide variety of yarn-level knit and woven patterns. Finally, to validate our approach, we compare dozens of generated patterns against reference images of actual woven or knitted cloth samples, and we release this corpus of digital patterns and simulated models as a public dataset to support future comparisons.

We propose a comprehensive approach to characterizing the mechanical properties of structured sheet materials, i.e., planar rod networks whose mechanics and aesthetics are inextricably linked. We establish a connection between the complex mesoscopic deformation behavior of such structures and their macroscopic elastic properties through numerical homogenization. Our approach leverages 3D Kirchhoff rod simulation in order to capture nonlinear effects for both in-plane and bending deformations. We apply our method to different families of structures based on isohedral tilings---a simple yet extensive and aesthetically interesting group of space-filling patterns. We show that these tilings admit a wide range of material properties, and our homogenization approach allows us to create concise and intuitive descriptions of a material's direction-dependent macromechanical behavior that are easy to communicate even to non-experts. We perform this characterization for an extensive set of structures and organize these data in a material browser to enable efficient forward exploration of the aesthetic-mechanical space of structured sheet materials. We also propose an inverse design method to automatically find structure parameters that best approximate a user-specified target behavior.

Recreating the appearance of humans in virtual environments for the purpose of movie, video game, or other types of production involves the acquisition of a geometric representation of the human body and its scattering parameters which express the interaction between the geometry and light propagated throughout the scene. Teeth appearance is defined not only by the light and surface interaction, but also by its internal geometry and the intra-oral environment, posing its own unique set of challenges. Therefore, we present a system specifically designed for capturing the optical properties of live human teeth such that they can be realistically re-rendered in computer graphics. We acquire our data in vivo in a conventional multiple camera and light source setup and use exact geometry segmented from intra-oral scans. To simulate the complex interaction of light in the oral cavity during inverse rendering we employ a novel pipeline based on derivative path tracing with respect to both optical properties and geometry of the inner dentin surface. The resulting estimates of the global derivatives are used to extract parameters in a joint numerical optimization. The final appearance faithfully recreates the acquired data and can be directly used in conventional path tracing frameworks for rendering virtual humans.

Simulation of light reflection from specular surfaces is a core problem of computer graphics. Existing solutions either make the approximation of providing only a large-area average solution in terms of a fixed BRDF (ignoring spatial detail), or are specialized for specific microgeometry (e.g. 1D scratches), or are based only on geometric optics (which is an approximation to more accurate wave optics). We design the first rendering algorithm based on a wave optics model that is also able to compute spatially-varying specular highlights with high-resolution detail on general surface microgeometry. We compute a wave optics reflection integral over the coherence area; our solution is based on approximating the phase-delay grating representation of a micron-resolution surface heightfield using Gabor kernels. We found that the appearance difference between the geometric and wave solution is more dramatic when spatial detail is taken into account. The visualizations of the corresponding BRDF lobes differ significantly. Moreover, the wave optics solution varies as a function of wavelength, predicting noticeable color effects in the highlights. Our results show both single-wavelength and spectral solution to reflection from common everyday objects, such as brushed, scratched and bumpy metals.

Ambient sounds arise from a massive superposition of chaotic events distributed over a large area or volume, such as waves breaking on a beach or rain hitting the ground. The directionality and loudness of these sounds as they propagate in complex 3D scenes vary with listener location, providing cues that distinguish indoors from outdoors and reveal portals and occluders. We show that ambient sources can be approximated using an ideal notion of spatio-temporal incoherence and develop a lightweight technique to capture their global propagation effects. Our approach precomputes a single FDTD simulation using a sustained source signal whose phase is randomized over frequency and source extent. It then extracts a spherical harmonic encoding of the resulting steady-state distribution of power over direction and position in the scene using an efficient flux density formulation. The resulting parameter fields are smooth and compressible, requiring only a few MB of memory per extended source. We also present a fast binaural rendering technique that exploits phase incoherence to reduce filtering cost.

The appearance of hair follows from the small-scale geometry of hair fibers, with the cross-sectional shape determining the azimuthal distribution of scattered light. Although previous research has described some of the effects of non-circular cross sections, no accurate scattering models for non-circular fibers exist. This article presents a scattering model for elliptical fibers, which predicts that even small deviations from circularity produce important changes in the scattering distribution and which disagrees with previous approximations for the effects of eccentricity. To confirm the model’s predictions, new scattering measurements of fibers from a wide range of hair types were made, using a new measurement device that provides a more complete and detailed picture of the light scattered by fibers than was previously possible. The measurements show features that conclusively match the model’s predictions, but they also contain an ideal-specular forward-scattering behavior that is not predicted and has not been fully described before. The results of this article indicate that an accurate and efficient method for computing scattering in elliptical cylinders—something not provided in this article—is the correct model to use for realistic hair in the future and that the new specular behavior should be included as well.

Rendering fabrics using micro-appearance models---fiber-level microgeometry coupled with a fiber scattering model---can take hours per frame. We present a fast, precomputation-based algorithm for rendering both single and multiple scattering in fabrics with repeating structure illuminated by directional and spherical Gaussian lights. Precomputed light transport (PRT) is well established but challenging to apply directly to cloth. This paper shows how to decompose the problem and pick the right approximations to achieve very high accuracy, with significant performance gains over path tracing. We treat single and multiple scattering separately and approximate local multiple scattering using precomputed transfer functions represented in spherical harmonics. We handle shadowing between fibers with precomputed per-fiber-segment visibility functions, using two different representations to separately deal with low and high frequency spherical Gaussian lights. Our algorithm is designed for GPU performance and high visual quality. Compared to existing PRT methods, it is more accurate. In tens of seconds on a commodity GPU, it renders high-quality supersampled images that take path tracing tens of minutes on a compute cluster.

The ability to fabricate surfaces with fine control over bidirectional reflectance (BRDF) is a long-standing goal in appearance research, with applications in product design and manufacturing. We propose a technique that embeds magnetic flakes in a photo-cured resin, allowing the orientation distribution of those flakes to be controlled at printing time using a magnetic field. We show that time-varying magnetic fields allow us to control off-specular lobe direction, anisotropy, and lobe width, while using multiple spatial masks displayed by a UV projector allows for spatial variation. We demonstrate optical effects including bump maps: fat surfaces with spatially-varying specular lobe direction.

Sound generation methods, such as linear modal synthesis, can sonify a wide range of physics-based animation of solid objects, resolving vibrations and sound radiation from various structures. However, elastic rods are an important computer animation primitive for which prior sound synthesis methods, such as modal synthesis, are ill-suited for several reasons: large displacements, nonlinear vibrations, dispersion effects, and the geometrically singular nature of rods. In this paper, we present physically based methods for simultaneous generation of animation and sound for deformable rods. We draw on Kirchhoff theory to simplify the representation of rod dynamics and introduce a generalized dipole model to calculate the spatially varying acoustic radiation. In doing so, we drastically decrease the amount of precomputation required (in some cases eliminating it completely), while being able to resolve sound radiation for arbitrary body deformations encountered in computer animation. We present several examples, including challenging scenes involving thousands of highly coupled frictional contacts.

Current interactive fabrication tools offer tangible feedback by allowing users to work directly on the physical model, but they are slow because users need to participate in the physical instantiation of their designs. In contrast, CAD software offers powerful tools for 3D modeling but delays access to the physical workpiece until the end of the design process. In this paper we propose On-the-Fly Print: a 3D modeling approach that allows the user to design 3D models digitally while having a low-fidelity physical wireframe model printed in parallel. Our software starts printing features as soon as they are created and updates the physical model as needed. Users can quickly check the design in a real usage context by removing the partial physical print from the printer and replacing it afterwards to continue printing. Digital content modification can be updated with quick physical correction using a retractable cutting blade. We present the detailed description of On-the-Fly Print and showcase several examples designed and printed with our system.

Specular BRDF rendering traditionally approximates surface microstructure using a smooth normal distribution, but this ignores glinty effects, easily observable in the real world. While modeling the actual surface microstructure is possible, the resulting rendering problem is prohibitively expensive. Recently, Yan et al. [2014] and Jakob et al. [2014] made progress on this problem, but their approaches are still expensive and lack full generality in their material and illumination support. We introduce an efficient and general method that can be easily integrated in a standard rendering system. We treat a specular surface as a four-dimensional position-normal distribution , and fit this distribution using millions of 4D Gaussians, which we call elements. This leads to closed-form solutions to the required BRDF evaluation and sampling queries, enabling the first practical solution to rendering specular microstructure.

Wood is an important decorative material prized for its unique appearance. It is commonly rendered using artistically authored 2D color and bump textures, which reproduces color patterns on flat surfaces well. But the dramatic anisotropic specular figure caused by wood fibers, common in curly maple and other species, is harder to achieve. While suitable BRDF models exist, the texture parameter maps for these wood BRDFs are difficult to author---good results have been shown with elaborate measurements for small flat samples, but these models are not much used in practice. Furthermore, mapping 2D image textures onto 3D objects leads to distortion and inconsistencies. Procedural volumetric textures solve these geometric problems, but existing methods produce much lower quality than image textures. This paper aims to bring the best of all these techniques together: we present a comprehensive volumetric simulation of wood appearance, including growth rings, color variation, pores, rays, and growth distortions. The fiber directions required for anisotropic specular figure follow naturally from the distortions. Our results rival the quality of textures based on photographs, but with the consistency and convenience of a volumetric model. Our model is modular, with components that are intuitive to control, fast to compute, and require minimal storage.

Traditional 3D printers fabricate objects by depositing material to build up the model layer by layer. Instead printing only wireframes can reduce printing time and the cost of material while producing effective depictions of shape. However, wireframe printing requires the printer to undergo arbitrary 3D motions, rather than slice-wise 2D motions, which can lead to collisions with already-printed parts of the model. Previous work has either limited itself to restricted meshes that are collision free by construction, or simply dropped unreachable parts of the model, but in this paper we present a method to print arbitrary meshes on a 5DOF wireframe printer. We formalize the collision avoidance problem using a directed graph, and propose an algorithm that finds a locally minimal set of constraints on the order of edges that guarantees there will be no collisions. Then a second algorithm orders the edges so that the printing progresses smoothly. Though meshes do exist that still cannot be printed, our method prints a wide range of models that previous methods cannot, and it provides a fundamental enabling algorithm for future development of wireframe printing.

The visual appearance of many materials is created by micro-scale details of their surface geometry. In this article, we investigate a new approach to capturing the appearance of metal surfaces without reflectance measurements, by deriving microfacet distributions directly from measured surface topography. Modern profilometers are capable of measuring surfaces with subwavelength resolution at increasingly rapid rates. We consider both wave- and geometric-optics methods for predicting BRDFs of measured surfaces and compare the results to optical measurements from a gonioreflectometer for five rough metal samples. Surface measurements are also used to predict spatial variation, or texture, which is especially important for the appearance of our anisotropic brushed metal samples. Profilometer-based BRDF acquisition offers many potential advantages over traditional techniques, including speed and easy handling of anisotropic, highly directional materials. We also introduce a new generalized normal distribution function, the ellipsoidal NDF, to compactly represent nonsymmetric features in our measured data and texture synthesis.

Micro-appearance models explicitly model the interaction of light with microgeometry at the fiber scale to produce realistic appearance. To effectively match them to real fabrics, we introduce a new appearance matching framework to determine their parameters. Given a micro-appearance model and photographs of the fabric under many different lighting conditions, we optimize for parameters that best match the photographs using a method based on calculating derivatives during rendering. This highly applicable framework, we believe, is a useful research tool because it simplifies development and testing of new models. Using the framework, we systematically compare several types of micro-appearance models. We acquired computed microtomography (micro CT) scans of several fabrics, photographed the fabrics under many viewing/illumination conditions, and matched several appearance models to this data. We compare a new fiber-based light scattering model to the previously used microflake model. We also compare representing cloth microgeometry using volumes derived directly from the micro CT data to using explicit fibers reconstructed from the volumes. From our comparisons, we make the following conclusions: (1) given a fiber-based scattering model, volume- and fiber-based microgeometry representations are capable of very similar quality, and (2) using a fiber-specific scattering model is crucial to good results as it achieves considerably higher accuracy than prior work.

We address the problem of modeling and rendering granular materials---such as large structures made of sand, snow, or sugar---where an aggregate object is composed of many randomly oriented, but discernible grains. These materials pose a particular challenge as the complex scattering properties of individual grains, and their packing arrangement, can have a dramatic effect on the large-scale appearance of the aggregate object. We propose a multi-scale modeling and rendering framework that adapts to the structure of scattered light at different scales. We rely on path tracing the individual grains only at the finest scale, and---by decoupling individual grains from their arrangement---we develop a modular approach for simulating longer-scale light transport. We model light interactions within and across grains as separate processes and leverage this decomposition to derive parameters for classical radiative transport, including standard volumetric path tracing and a diffusion method that can quickly summarize the large scale transport due to many grain interactions. We require only a one-time precomputation per exemplar grain, which we can then reuse for arbitrary aggregate shapes and a continuum of different packing rates and scales of grains. We demonstrate our method on scenes containing mixtures of tens of millions of individual, complex, specular grains that would be otherwise infeasible to render with standard techniques.

We propose a method for fabricating deformable objects with spatially varying elasticity using 3D printing. Using a single, relatively stiff printer material, our method designs an assembly of small-scale microstructures that have the effect of a softer material at the object scale, with properties depending on the microstructure used in each part of the object. We build on work in the area of metamaterials, using numerical optimization to design tiled microstructures with desired properties, but with the key difference that our method designs families of related structures that can be interpolated to smoothly vary the material properties over a wide range. To create an object with spatially varying elastic properties, we tile the object's interior with microstructures drawn from these families, generating a different microstructure for each cell using an efficient algorithm to select compatible structures for neighboring cells. We show results computed for both 2D and 3D objects, validating several 2D and 3D printed structures using standard material tests as well as demonstrating various example applications.

This paper investigates rendering glittery surfaces, ones which exhibit shifting random patterns of glints as the surface or viewer moves. It applies both to dramatically glittery surfaces that contain mirror-like flakes and also to rough surfaces that exhibit more subtle small scale glitter, without which most glossy surfaces appear too smooth in close-up. These phenomena can in principle be simulated by high-resolution normal maps, but maps with tiny features create severe aliasing problems under narrow-angle illumination. In this paper we present a stochastic model for the effects of random subpixel structures that generates glitter and spatial noise that behave correctly under different illumination conditions and viewing distances, while also being temporally coherent so that they look right in motion. The model is based on microfacet theory, but it replaces the usual continuous microfacet distribution with a discrete distribution of scattering particles on the surface. A novel stochastic hierarchy allows efficient evaluation in the presence of large numbers of random particles, without ever having to consider the particles individually. This leads to a multiscale procedural BRDF that is readily implemented in standard rendering systems, and which converges back to the smooth case in the limit.

We present a general and practical method for computing BSDFs of layered materials. Its ingredients are transport-theoretical models of isotropic or anisotropic scattering layers and smooth or rough boundaries of conductors and dielectrics. Following expansion into a directional basis that supports arbitrary composition, we are able to efficiently and accurately synthesize BSDFs for a great variety of layered structures. Reflectance models created by our system correctly account for multiple scattering within and between layers, and in the context of a rendering system they are efficient to evaluate and support texturing and exact importance sampling. Although our approach essentially involves tabulating reflectance functions in a Fourier basis, the generated models are compact to store due to the inherent sparsity of our representation, and are accurate even for narrowly peaked functions. While methods for rendering general layered surfaces have been investigated in the past, ours is the first system that supports arbitrary layer structures while remaining both efficient and accurate. We validate our model by comparing to measurements of real-world examples of layered materials, and we demonstrate an interactive visual design tool that enables easy exploration of the space of layered materials. We provide a fully practical, high-performance implementation in an open-source rendering system.

Complex specular surfaces under sharp point lighting show a fascinating glinty appearance, but rendering it is an unsolved problem. Using Monte Carlo pixel sampling for this purpose is impractical: the energy is concentrated in tiny highlights that take up a minuscule fraction of the pixel. We instead compute an accurate solution using a completely different deterministic approach. Our method considers the true distribution of normals on a surface patch seen through a single pixel, which can be highly complex. We show how to evaluate this distribution efficiently, assuming a Gaussian pixel footprint and Gaussian intrinsic roughness. We also take advantage of hierarchical pruning of position-normal space to rapidly find texels that might contribute to a given normal distribution evaluation. Our results show complex, temporally varying glints from materials such as bumpy plastics, brushed and scratched metals, metallic paint and ocean waves.

Force-deformation measurements of cloth exhibit significant hysteresis, and many researchers have identified internal friction as the source of this effect. However, it has not been incorporated into computer animation models of cloth. In this paper, we propose a model of internal friction based on an augmented reparameterization of Dahl's model, and we show that this model provides a good match to several important features of cloth hysteresis even with a minimal set of parameters. We also propose novel parameter estimation procedures that are based on simple and inexpensive setups and need only sparse data, as opposed to the complex hardware and dense data acquisition of previous methods. Finally, we provide an algorithm for the efficient simulation of internal friction, and we demonstrate it on simulation examples that show disparate behavior with and without internal friction.

We present a method for practical physical reproduction and design of homogeneous materials with desired subsurface scattering. Our process uses a collection of different pigments that can be suspended in a clear base material. Our goal is to determine pigment concentrations that best reproduce the appearance and subsurface scattering of a given target material. In order to achieve this task we first fabricate a collection of material samples composed of known mixtures of the available pigments with the base material. We then acquire their reflectance profiles using a custom-built measurement device. We use the same device to measure the reflectance profile of a target material. Based on the database of mappings from pigment concentrations to reflectance profiles, we use an optimization process to compute the concentration of pigments to best replicate the target material appearance. We demonstrate the practicality of our method by reproducing a variety of different translucent materials. We also present a tool that allows the user to explore the range of achievable appearances for a given set of pigments.

Abstract Progress in cloth simulation for computer animation and apparel design has led to a multitude of deformation models, each with its own way of relating geometry, deformation, and forces. As simulators improve, differences between these models become more important, but it is difficult to choose a model and a set of parameters to match a given real material simply by looking at simulation results. This paper provides measurement and fitting methods that allow nonlinear models to be fit to the observed deformation of a particular cloth sample. Unlike standard textile testing, our system measures complex 3D deformations of a sheet of cloth, not just one‐dimensional force‐displacement curves, so it works under a wider range of deformation conditions. The fitted models are then evaluated by comparison to measured deformations with motions very different from those used for fitting.

We present a practical data-driven method for automatically synthesizing plausible soundtracks for physics-based cloth animations running at graphics rates. Given a cloth animation, we analyze the deformations and use motion events to drive crumpling and friction sound models estimated from cloth measurements. We synthesize a low-quality sound signal, which is then used as a target signal for a concatenative sound synthesis (CSS) process. CSS selects a sequence of microsound units, very short segments, from a database of recorded cloth sounds, which best match the synthesized target sound in a low-dimensional feature-space after applying a hand-tuned warping function. The selected microsound units are concatenated together to produce the final cloth sound with minimal filtering. Our approach avoids expensive physics-based synthesis of cloth sound, instead relying on cloth recordings and our motion-driven CSS approach for realism. We demonstrate its effectiveness on a variety of cloth animations involving various materials and character motions, including first-person virtual clothing with binaural sound.

Although facial hair plays an important role in individual expression, facial-hair reconstruction is not addressed by current face-capture systems. Our research addresses this limitation with an algorithm that treats hair and skin surface capture together in a coupled fashion so that a high-quality representation of hair fibers as well as the underlying skin surface can be reconstructed. We propose a passive, camera-based system that is robust against arbitrary motion since all data is acquired within the time period of a single exposure. Our reconstruction algorithm detects and traces hairs in the captured images and reconstructs them in 3D using a multiview stereo approach. Our coupled skin-reconstruction algorithm uses information about the detected hairs to deliver a skin surface that lies underneath all hairs irrespective of occlusions. In dense regions like eyebrows, we employ a hair-synthesis method to create hair fibers that plausibly match the image data. We demonstrate our scanning system on a number of individuals and show that it can successfully reconstruct a variety of facial-hair styles together with the underlying skin surface.

We propose a complete process for designing, simulating, and fabricating synthetic skin for an animatronics character that mimics the face of a given subject and its expressions. The process starts with measuring the elastic properties of a material used to manufacture synthetic soft tissue. Given these measurements we use physics-based simulation to predict the behavior of a face when it is driven by the underlying robotic actuation. Next, we capture 3D facial expressions for a given target subject. As the key component of our process, we present a novel optimization scheme that determines the shape of the synthetic skin as well as the actuation parameters that provide the best match to the target expressions. We demonstrate this computational skin design by physically cloning a real human face onto an animatronics figure.

The appearance of a particular fabric is produced by variations in both large-scale reflectance and small-scale texture as the viewing and illumination angles change across the surface. This article presents a study of the reflectance and texture of woven cloth that aims to identify and model important optical features of cloth appearance. New measurements are reported for a range of fabrics including natural and synthetic fibers as well as staple and filament yarns. A new scattering model for woven cloth is introduced that describes the reflectance and the texture based on an analysis of specular reflection from the fibers. Unlike data-based models, our procedural model doesn't require image data. It can handle a wide range of fabrics using a small set of physically meaningful parameters that describe the characteristics of the fibers, the geometry of the yarns, and the pattern of the weave. The model is validated against the measurements and evaluated by comparisons to high-resolution video of the real fabrics and to BTF models of two of the fabrics.

It is a long-standing problem in unbiased Monte Carlo methods for rendering that certain difficult types of light transport paths, particularly those involving viewing and illumination along paths containing specular or glossy surfaces, cause unusably slow convergence. In this paper we introduce Manifold Exploration, a new way of handling specular paths in rendering. It is based on the idea that sets of paths contributing to the image naturally form manifolds in path space, which can be explored locally by a simple equation-solving iteration. This paper shows how to formulate and solve the required equations using only geometric information that is already generally available in ray tracing systems, and how to use this method in in two different Markov Chain Monte Carlo frameworks to accurately compute illumination from general families of paths. The resulting rendering algorithms handle specular, near-specular, glossy, and diffuse surface interactions as well as isotropic or highly anisotropic volume scattering interactions, all using the same fundamental algorithm. An implementation is demonstrated on a range of challenging scenes and evaluated against previous methods.

Recent yarn-based simulation techniques permit realistic and efficient dynamic simulation of knitted clothing, but producing the required yarn-level models remains a challenge. The lack of practical modeling techniques significantly limits the diversity and complexity of knitted garments that can be simulated. We propose a new modeling technique that builds yarn-level models of complex knitted garments for virtual characters. We start with a polygonal model that represents the large-scale surface of the knitted cloth. Using this mesh as an input, our interactive modeling tool produces a finer mesh representing the layout of stitches in the garment, which we call the stitch mesh . By manipulating this mesh and assigning stitch types to its faces, the user can replicate a variety of complicated knitting patterns. The curve model representing the yarn is generated from the stitch mesh, then the final shape is computed by a yarn-level physical simulation that locally relaxes the yarn into realistic shape while preserving global shape of the garment and avoiding "yarn pull-through," thereby producing valid yarn geometry suitable for dynamic simulation. Using our system, we can efficiently create yarn-level models of knitted clothing with a rich variety of patterns that would be completely impractical to model using traditional techniques. We show a variety of example knitting patterns and full-scale garments produced using our system.

Woven fabrics have a wide range of appearance determined by their small-scale 3D structure. Accurately modeling this structural detail can produce highly realistic renderings of fabrics and is critical for predictive rendering of fabric appearance. But building these yarn-level volumetric models is challenging. Procedural techniques are manually intensive, and fail to capture the naturally arising irregularities which contribute significantly to the overall appearance of cloth. Techniques that acquire the detailed 3D structure of real fabric samples are constrained only to model the scanned samples and cannot represent different fabric designs. This paper presents a new approach to creating volumetric models of woven cloth, which starts with user-specified fabric designs and produces models that correctly capture the yarn-level structural details of cloth. We create a small database of volumetric exemplars by scanning fabric samples with simple weave structures. To build an output model, our method synthesizes a new volume by copying data from the exemplars at each yarn crossing to match a weave pattern that specifies the desired output structure. Our results demonstrate that our approach generalizes well to complex designs and can produce highly realistic results at both large and small scales.

This paper introduces a rapid appearance capture method suited for a variety of common indoor surfaces, in which a single photograph of the reflection of a step edge is used to estimate both a BRDF and a statistical model for visible surface geometry, or mesostructure. It is applicable to surfaces with statistically stationary variation in surface height, even when these variations are large enough to produce visible texture in the image. Results are shown from a prototype system using a separate camera and LCD, demonstrating good visual matches for a range of man-made indoor materials.

The appearance of complex, thick materials like textiles is determined by their 3D structure, and they are incompletely described by surface reflection models alone. While volume scattering can produce highly realistic images of such materials, creating the required volume density models is difficult. Procedural approaches require significant programmer effort and intuition to design specialpurpose algorithms for each material. Further, the resulting models lack the visual complexity of real materials with their naturally-arising irregularities. This paper proposes a new approach to acquiring volume models, based on density data from X-ray computed tomography (CT) scans and appearance data from photographs under uncontrolled illumination. To model a material, a CT scan is made, resulting in a scalar density volume. This 3D data is processed to extract orientation information and remove noise. The resulting density and orientation fields are used in an appearance matching procedure to define scattering properties in the volume that, when rendered, produce images with texture statistics that match the photographs. As our results show, this approach can easily produce volume appearance models with extreme detail, and at larger scales the distinctive textures and highlights of a range of very different fabrics like satin and velvet emerge automatically---all based simply on having accurate mesoscale geometry.

The radiative transfer framework that underlies all current rendering of volumes is limited to scattering media whose properties are invariant to rotation. Many systems allow for "anisotropic scattering," in the sense that scattered intensity depends on the scattering angle, but the standard equation assumes that the structure of the medium is isotropic. This limitation impedes physics-based rendering of volume models of cloth, hair, skin, and other important volumetric or translucent materials that do have anisotropic structure. This paper presents an end-to-end formulation of physics-based volume rendering of anisotropic scattering structures, allowing these materials to become full participants in global illumination simulations. We begin with a generalized radiative transfer equation, derived from scattering by oriented non-spherical particles. Within this framework, we propose a new volume scattering model analogous to the well-known family of microfacet surface reflection models; we derive an anisotropic diffusion approximation, including the weak form required for finite element solution and a way to compute the diffusion matrix from the parameters of the scattering model; and we also derive a new anisotropic dipole BSSRDF for anisotropic translucent materials. We demonstrate results from Monte Carlo, finite element, and dipole simulations. All these contributions are readily implemented in existing rendering systems for volumes and translucent materials, and they all reduce to the standard practice in the isotropic case.

Yarn-based cloth simulation can improve visual quality but at high computational costs due to the reliance on numerous persistent yarn-yarn contacts to generate material behavior. Finding so many contacts in densely interlinked geometry is a pathological case for traditional collision detection, and the sheer number of contact interactions makes contact processing the simulation bottleneck. In this paper, we propose a method for approximating penalty-based contact forces in yarn-yarn collisions by computing the exact contact response at one time step, then using a rotated linear force model to approximate forces in nearby deformed configurations. Because contacts internal to the cloth exhibit good temporal coherence, sufficient accuracy can be obtained with infrequent updates to the approximation, which are done adaptively in space and time. Furthermore, by tracking contact models we reduce the time to detect new contacts. The end result is a 7- to 9-fold speedup in contact processing and a 4- to 5-fold overall speedup, enabling simulation of character-scale garments.

Hair models for computer graphics consist of many curves representing individual hair fibers. In current practice these curves are generated by ad hoc random processes, and in close-up views their arrangement appears plainly different from real hair. To begin improving this situation, this paper presents a new method for measuring the detailed arrangement of fibers in a hair assembly. Many macrophotographs with shallow depth of field are taken of a sample of hair, sweeping the plane of focus through the hair's volume. The shallow depth of field helps isolate the fibers and reduces occlusion. Several sweeps are performed with the hair at different orientations, resulting in multiple observations of most of the clearly visible fibers. The images are filtered to detect the fibers, and the resulting feature data from all images is used jointly in a hair growing process to construct smooth curves along the observed fibers. Finally, additional hairs are generated to fill in the unseen volume inside the hair. The method is demonstrated on both straight and wavy hair, with results suitable for realistic close-up renderings. These models provide the first views we know of into the 3D arrangement of hair fibers in real hair assemblies.

Knitted fabric is widely used in clothing because of its unique and stretchy behavior, which is fundamentally different from the behavior of woven cloth. The properties of knits come from the nonlinear, three-dimensional kinematics of long, inter-looping yarns, and despite significant advances in cloth animation we still do not know how to simulate knitted fabric faithfully. Existing cloth simulators mainly adopt elastic-sheet mechanical models inspired by woven materials, focusing less on the model itself than on important simulation challenges such as efficiency, stability, and robustness. We define a new computational model for knits in terms of the motion of yarns, rather than the motion of a sheet. Each yarn is modeled as an inextensible, yet otherwise flexible, B-spline tube. To simulate complex knitted garments, we propose an implicit-explicit integrator, with yarn inextensibility constraints imposed using efficient projections. Friction among yarns is approximated using rigid-body velocity filters, and key yarn-yarn interactions are mediated by stiff penalty forces. Our results show that this simple model predicts the key mechanical properties of different knits, as demonstrated by qualitative comparisons to observed deformations of actual samples in the laboratory, and that the simulator can scale up to substantial animations with complex dynamic motion.

Previous research has shown that a global multiple scattering simulation is needed to achieve physically realistic renderings of hair, particularly light-colored hair with low absorption. However, previous methods have either sacrificed accuracy or have been too computationally expensive for practical use. In this paper we describe a physically based, volumetric rendering method that computes multiple scattering solutions, including directional effects, much faster than previous accurate methods. Our two-pass method first traces light paths through a volumetric representation of the hair, contributing power to a 3D grid of spherical harmonic coefficients that store the directional distribution of scattered radiance everywhere in the hair volume. Then, in a ray tracing pass, multiple scattering is computed by integrating the stored radiance against the scattering functions of visible fibers using an efficient matrix multiplication. Single scattering is computed using conventional direct illumination methods. In our comparisons the new method produces quality similar to that of the best previous methods, but computes multiple scattering more than 10 times faster.

Realistic hair modeling is a fundamental part of creating virtual humans in computer graphics. This paper surveys the state of the art in the major topics of hair modeling: hairstyling, hair simulation, and hair rendering. Because of the difficult, often unsolved problems that arise in all these areas, a broad diversity of approaches are used, each with strengths that make it appropriate for particular applications. We discuss each of these major topics in turn, presenting the unique challenges facing each area and describing solutions that have been presented over the years to handle these complex issues. Finally, we outline some of the remaining computational challenges in hair modeling.

Simulating multiple scattering correctly is important for accurate rendering of hair. However, a volume of hair is a difficult scene to simulate because scattering from an individual fiber is very structured and forward directed, and because the radiance distributions that arise from many such scattering events remain quite directional. For these reasons, previous methods cannot compute accurate images substantially faster than Monte Carlo path tracing.This paper proposes a new physically accurate method for rendering hair that is based on previous volumetric photon mapping methods. The first pass generates a photon map by tracing particles through the hair geometry, depositing them along paths rather than at scattering events. The second pass ray traces the hair, computing direct illumination and looking up indirect radiance in the photon map. Photons are stored and looked up in 5D position-direction space to allow for the very directional radiance distributions that occur in hair. Together with a new radiance caching method for fibers, our method simulates difficult scattering problems in hair efficiently and with low noise.The new algorithm is validated against path tracing and also compared with a photograph of light scattering in real hair.

Wood coated with transparent finish has a beautiful and distinctive appearance that is familiar to everyone. Woods with unusual grain patterns. such as tiger, burl, and birdseye figures, have a strikingly unusual directional reflectance that is prized for decorative applications. With new, high resolution measurements of spatially varying BRDFs. we show that this distinctive appearance is due to light scattering that does not conform to the usual notion of anisotropic surface reflection. The behavior can be explained by scattering from the matrix of wood fibers below the surface, resulting in a subsurface highlight that occurs on a cone with an out-of-plane axis. We propose a new shading model component to handle reflection from subsurface fibers, which is combined with the standard diffuse and specular components to make a complete shading model. Rendered results from fits of our model to the measurement data demonstrate that this new model captures the distinctive appearance of wood.

We present a novel photographic technique called dual photography, which exploits Helmholtz reciprocity to interchange the lights and cameras in a scene. With a video projector providing structured illumination, reciprocity permits us to generate pictures from the viewpoint of the projector, even though no camera was present at that location. The technique is completely image-based, requiring no knowledge of scene geometry or surface properties, and by its nature automatically includes all transport paths, including shadows, inter-reflections and caustics. In its simplest form, the technique can be used to take photographs without a camera; we demonstrate this by capturing a photograph using a projector and a photo-resistor. If the photo-resistor is replaced by a camera, we can produce a 4D dataset that allows for relighting with 2D incident illumination. Using an array of cameras we can produce a 6D slice of the 8D reflectance field that allows for relighting with arbitrary light fields. Since an array of cameras can operate in parallel without interference, whereas an array of light sources cannot, dual photography is fundamentally a more efficient way to capture such a 6D dataset than a system based on multiple projectors and one camera. As an example, we show how dual photography can be used to capture and relight scenes.

Light scattering from hair is normally simulated in computer graphics using Kajiya and Kay's classic phenomenological model. We have made new measurements of scattering from individual hair fibers that exhibit visually significant effects not predicted by Kajiya and Kay's model. Our measurements go beyond previous hair measurements by examining out-of-plane scattering, and together with this previous work they show a multiple specular highlight and variation in scattering with rotation about the fiber axis. We explain the sources of these effects using a model of a hair fiber as a transparent elliptical cylinder with an absorbing interior and a surface covered with tilted scales. Based on an analytical scattering function for a circular cylinder, we propose a practical shading model for hair that qualitatively matches the scattering behavior shown in the measurements. In a comparison between a photograph and rendered images, we demonstrate the new model's ability to match the appearance of real hair.

We present a new method for the animation and rendering of photo-realistic water effects. Our method is designed to produce visually plausible three dimensional effects, for example the pouring of water into a glass (see figure 1) and the breaking of an ocean wave, in a manner which can be used in a computer animation environment. In order to better obtain photorealism in the behavior of the simulated water surface, we introduce a new "thickened" front tracking technique to accurately represent the water surface and a new velocity extrapolation method to move the surface in a smooth, water-like manner. The velocity extrapolation method allows us to provide a degree of control to the surface motion, e.g. to generate a windblown look or to force the water to settle quickly. To ensure that the photorealism of the simulation carries over to the final images, we have integrated our method with an advanced physically based rendering system.

This paper introduces a simple model for subsurface light transport in translucent materials. The model enables efficient simulation of effects that BRDF models cannot capture, such as color bleeding within materials and diffusion of light across shadow boundaries. The technique is efficient even for anisotropic, highly scattering media that are expensive to simulate using existing methods. The model combines an exact solution for single scattering with a dipole point source diffusion approximation for multiple scattering. We also have designed a new, rapid image-based measurement technique for determining the optical properties of translucent materials. We validate the model by comparing predicted and measured values and show how the technique can be used to recover the optical properties of a variety of materials, including milk, marble, and skin. Finally, we describe sampling techniques that allow the model to be used within a conventional ray tracer.

To render images from a three-dimensional array of sample values, it is necessary to interpolate between the samples. This paper is concerned with interpolation methods that are equivalent to convolving the samples with a reconstruction filter; this covers all commonly used schemes, including trilinear and cubic interpolation. We first outline the formal basis of interpolation in three-dimensional signal processing theory. We then propose numerical metrics that can be used to measure filter characteristics that are relevant to the appearance of images generated using that filter. We apply those metrics to several previously used filters and relate the results to isosurface images of the interpolations. We show that the choice of interpolation scheme can have a dramatic effect on image quality, and we discuss the cost/benefit tradeoff inherent in choosing a filter.>