Abstract We present PriFit, a semi‐supervised approach for label‐efficient learning of 3D point cloud segmentation networks. PriFit combines geometric primitive fitting with point‐based representation learning. Its key idea is to learn point representations whose clustering reveals shape regions that can be approximated well by basic geometric primitives, such as cuboids and ellipsoids. The learned point representations can then be re‐used in existing network architectures for 3D point cloud segmentation, and improves their performance in the few‐shot setting. According to our experiments on the widely used ShapeNet and PartNet benchmarks, PriFit outperforms several state‐of‐the‐art methods in this setting, suggesting that decomposability into primitives is a useful prior for learning representations predictive of semantic parts. We present a number of ablative experiments varying the choice of geometric primitives and downstream tasks to demonstrate the effectiveness of the method.

We present a generative model to synthesize 3D shapes as sets of handles -- lightweight proxies that approximate the original 3D shape -- for applications in interactive editing, shape parsing, and building compact 3D representations. Our model can generate handle sets with varying cardinality and different types of handles. Key to our approach is a deep architecture that predicts both the parameters and existence of shape handles and a novel similarity measure that can easily accommodate different types of handles, such as cuboids or sphere-meshes. We leverage the recent advances in semantic 3D annotation as well as automatic shape summarization techniques to supervise our approach. We show that the resulting shape representations are not only intuitive, but achieve superior quality than previous state-of-the-art. Finally, we demonstrate how our method can be used in applications such as interactive shape editing and completion, leveraging the latent space learned by our model to guide these tasks.

We investigate the problem of reconstructing shapes from noisy and incomplete projections in the presence of viewpoint uncertainities. The problem is cast as an optimization over the shape given measurements obtained by a projection operator and a prior. We present differentiable projection operators for a number of reconstruction problems which when combined with the deep image prior or shape prior allows efficient inference through gradient descent. We apply our method on a variety of reconstruction problems, such as tomographic reconstruction from a few samples, visual hull reconstruction incorporating view uncertainties, and 3D shape reconstruction from noisy depth maps. Experimental results show that our approach is effective for such shape reconstruction problems, without requiring any task-specific training.

In this work, we present SkinnyPower, a technology for Intra-Body Power Transfer (IBPT) that wirelessly transfers power through human skin to operate batteryless wearable sensors. We envision a scenario, in which batteryless sensors placed on small body parts (e.g., on-finger, in-ear, and in-mouth) can obtain operating power from another body-worn energy sources (e.g., already existing battery-powered wearable devices such as a smartwatch or a BandAid-like battery patch attached to the neck). The key technical challenges in realizing this vision include 1) providing a robust return path in the body channel - where the forward (power signal) and return (ground) paths are not explicitly defined - using implicit capacitances formed between the devices and earth ground, and 2) achieving reliable operation despite variations in capacitive coupling between the skin and devices, devices and earth ground, and conductance of the subdermal layer. We identify and optimize critical system design parameters to maximize the power transfer between a transmitter and a receiver with the capacitively coupled return path. To demonstrate and validate the concept of IBPT, we implemented a prototype consisting of 1) a wrist-worn, battery-equipped power transmitter that sends alternating current through the human body and 2) a finger-worn, batteryless sensor device that operates solely on body-transferred power. Evaluations on five subjects show that we can reliably support the power of approximately 1 mW, which can be used to operate an embedded system, continuously collect sensor (e.g. accelerometer) data, and wirelessly transfer the collected data in real-time using Bluetooth Low Energy. Moreover, we achieve a power transfer rate of 14.5% between the transmitter and receiver, which is significantly higher than other wireless power transfer techniques such as RFID. We believe that the proposed system has great potential to transform current architectures and designs for body-area networks, promoting the development of innovative on-body sensors that would otherwise not be possible with on-device batteries.

In this work, we present SkinnyPower, a concept of Intra-Body Power Transfer (IBPT) that wirelessly transfers power through human skin to operate batteryless wearable sensors. We envision a scenario, in which batteryless sensors placed on small body parts (e.g., on-finger, in-ear, and in-mouth) can obtain operating power from another body-worn energy sources (e.g., already existing battery-powered wearable devices such as a smartphone, smartwatch, or BandAid-like battery patch attached to the neck). To demonstrate and validate the concept of IBPT, we implemented a prototype consisting of 1) a wrist-worn, battery-powered power transmitter that sends alternating current through the human body and 2) a finger-worn, batteryless sensor device that operates solely on body-transferred power. Evaluations on five subjects show that we can reliably support the power of approximately 1 mW, which can be used to operate an embedded system, continuously collect sensor (accelerometer) data, and wirelessly transfer the collected data in real-time using Bluetooth Low Energy. We believe that the proposed system has great potential to transform current architectures and designs for body-area networks, promoting the development of innovative on-body sensors that would otherwise not be possible with on-device batteries.

In this paper we investigate the problem of inducing a distribution over three-dimensional structures given two-dimensional views of multiple objects taken from unknown viewpoints. Our approach called "projective generative adversarial networks" (PrGANs) trains a deep generative model of 3D shapes whose projections match the distributions of the input 2D views. The addition of a projection module allows us to infer the underlying 3D shape distribution without using any 3D, viewpoint information, or annotation during the learning phase. We show that our approach produces 3D shapes of comparable quality to GANs trained on 3D data for a number of shape categories including chairs, airplanes, and cars. Experiments also show that the disentangled representation of 2D shapes into geometry and viewpoint leads to a good generative model of 2D shapes. The key advantage is that our model allows us to predict 3D, viewpoint, and generate novel views from an input image in a completely unsupervised manner.

We propose a method for reconstructing 3D shapes from 2D sketches in the form of line drawings. Our method takes as input a single sketch, or multiple sketches, and outputs a dense point cloud representing a 3D reconstruction of the input sketch(es). The point cloud is then converted into a polygon mesh. At the heart of our method lies a deep, encoder-decoder network. The encoder converts the sketch into a compact representation encoding shape information. The decoder converts this representation into depth and normal maps capturing the underlying surface from several output viewpoints. The multi-view maps are then consolidated into a 3D point cloud by solving an optimization problem that fuses depth and normals across all viewpoints. Based on our experiments, compared to other methods, such as volumetric networks, our architecture offers several advantages, including more faithful reconstruction, higher output surface resolution, better preservation of topology and shape structure.

Abstract Recently there has been an increasing demand for software that can help designers create functional 3D objects with required physical strength. We introduce a generic and extensible method that directly optimizes a shape subject to physical and geometric constraints. Given an input shape, our method optimizes directly its input mesh representation until it can withstand specified external forces, while remaining similar to the original shape. Our method performs physics simulation and shape optimization together in a unified framework, where the physics simulator is an integral part of the optimizer. We employ geometric constraints to preserve surface details and shape symmetry, and adapt a second‐order method with analytic gradients to improve convergence and computation time. Our method provides several advantages over previous work, including the ability to handle general shape deformations, preservation of surface details, and incorporation of user‐defined constraints. We demonstrate the effectiveness of our method on a variety of prinTable 3D objects through detailed simulations as well as physical validations.

When geometric models with a desired combination of style and functionality are not available, they currently need to be created manually. We facilitate algorithmic synthesis of 3D models of man-made shapes which combines user-specified style, described via anexemplarshape, and functionality, encoded by a functionally differenttargetshape. Our method automatically transfers the style of the exemplar to the target, creating the desired combination. The main challenge in performing cross-functional style transfer is to implicitly separate an object's style from its function: while stylistically the output shapes should be as close as possible to the exemplar, their original functionality and structure, as encoded by the target, should be strictly preserved. Recent literature point to the presence of similarly shaped, salientgeometric elementsas a main indicator of stylistic similarity between 3D shapes. We therefore transfer the exemplar style to the target via a sequence of element-level operations. We allow onlycompatibleoperations, ones that do not affect the target functionality. To this end, we introduce a cross-structural element compatibility metric that estimates the impact of each operation on the edited shape. Our metric is based on the global context and coarse geometry of evaluated elements, and is trained on databases of 3D objects. We use this metric to cast style transfer as a tabu search, which incrementally updates the target shape using compatible operations, progressively increasing its style similarity to the exemplar while strictly maintaining its functionality at each step. We evaluate our framework across a range of man-made objects including furniture, light fixtures, and tableware, and perform a number of user studies confirming that it produces convincing outputs combining the desired style and function.

We propose a novel algorithm for blue noise sampling inspired by the Smoothed Particle Hydrodynamics (SPH) method. SPH is a well-known method in fluid simulation -- it computes particle distributions to minimize the internal pressure variance. We found that this results in sample points (i.e., particles) with a high quality blue-noise spectrum. Inspired by this, we tailor the SPH method for blue noise sampling. Our method achieves fast sampling in general dimensions for both surfaces and volumes. By varying a single parameter our method can generate a variety of blue noise samples with different distribution properties, ranging from Lloyd's relaxation to Capacity Constrained Voronoi Tessellations (CCVT). Our method is fast and supports adaptive sampling and multi-class sampling. We have also performed experimental studies of the SPH kernel and its influence on the distribution properties of samples. We demonstrate with examples that our method can generate a variety of controllable blue noise sample patterns, suitable for applications such as image stippling and re-meshing.

Abstract Style transfer aims to apply the style of an exemplar model to a target one, while retaining the target's structure. The main challenge in this process is to algorithmically distinguish style from structure, a high‐level, potentially ill‐posed cognitive task. Inspired by cognitive science research we recast style transfer in terms ofshape analogies. In IQ testing, shape analogy queries present the subject with three shapes:source, targetandexemplar, and ask them to select anoutputsuch that the transformation, oranalogy, from the exemplar to the output is similar to that from the source to the target. The logical process involved in identifying the source‐to‐target analogies implicitly detects the structural differences between the source and target and can be used effectively to facilitate style transfer. Since the exemplar has a similar structure to the source, applying the analogy to the exemplar will provide the output we seek. The main technical challenge we address is to compute the source to target analogies, consistent with human logic. We observe that the typical analogies we look for consist of a small set of simple transformations, which when applied to the exemplar generate a continuous, seamless output model. To assemble a shape analogy, we compute an optimal set of source‐to‐target transformations, such that the assembled analogy best fits these criteria. The assembled analogy is then applied to the exemplar shape to produce the desired output model. We use the proposed framework to seamlessly transfer a variety of style properties between 2D and 3D objects and demonstrate significant improvements over the state of the art in style transfer. We further show that our framework can be used to successfully complete partial scans with the help of a user provided structural template, coherently propagating scan style across the completed surfaces.

Algorithms for rendering interreflection (or indirect illumination) effects often make assumptions about the frequency range of the materials' reflectance properties. For example, methods based on Virtual Point Lights (VPLs) perform well for diffuse and semi-glossy materials but not so for highly glossy or specular materials; the situation is reversed for methods based on ray tracing. In this article, we present a practical algorithm for rendering interreflection effects with all-frequency BRDFs. Our method builds upon a spherical Gaussian representation of the BRDF, based on which a novel mathematical development of the interreflection equation is made. This allows us to efficiently compute one-bounce interreflection from a triangle to a shading point, by using an analytic formula combined with a piecewise linear approximation. We show through evaluation that this method is accurate for a wide range of BRDFs. We further introduce a hierarchical integration method to handle complex scenes (i.e., many triangles) with bounded errors. Finally, we have implemented the present algorithm on the GPU, achieving rendering performance ranging from near interactive to a few seconds per frame for various scenes with different complexity.

Recognizing text in natural photographs that contain specular highlights and focal blur is a challenging problem. In this paper we describe a new text segmentation method based on inverse rendering, i.e. decomposing an input image into basic rendering elements. Our technique uses iterative optimization to solve the rendering parameters, including light source, material properties (e.g. diffuse/specular reflectance and shininess) as well as blur kernel size. We combine our segmentation method with a recognition component and show that by accounting for the rendering parameters, our approach achieves higher text recognition accuracy than previous work, particularly in the presence of color changes and image blur. In addition, the derived rendering parameters can be used to synthesize new text images that imitate the appearance of an existing image.

Abstract We present a novel particle‐based method for stable simulation of elasto‐plastic materials. The main contribution of our method is an implicit numerical integrator, using a physically‐based model, for computing particles that undergo both elastic and plastic deformations. The main advantage of our implicit integrator is that it allows the use of large time steps while still preserving stable and physically plausible simulation results. As a key component of our algorithm, at each time step we compute the particle positions and velocities based on a sparse linear system, which we solve efficiently on the graphics hardware. Compared to existing techniques, our method allows for a much wider range of stiffness and plasticity settings. In addition, our method can significantly reduce the computation cost for certain range of material types. We demonstrate fast and stable simulations for a variety of elasto‐plastic materials, ranging from highly stiffelastic materials to highly plastic ones.

The papers in this special section includes extended versions of four of the best papers presented at the 2012 ACM SIGGRAPH Symposium on Interactive 3D Graphics and Games held from 9-11 March 2012 in Costa Mesa, California.

Abstract In this paper we present a new algorithm for accurate rendering of translucent materials under Spherical Gaussian (SG) lights. Our algorithm builds upon the quantized‐diffusion BSSRDF model recently introduced in [ dI11 ]. Our main contribution is an efficient algorithm for computing the integral of the BSSRDF with an SG light. We incorporate both single and multiple scattering components. Our model improves upon previous work by accounting for the incident angle of each individual SG light. This leads to more accurate rendering results, notably elliptical profiles from oblique illumination. In contrast, most existing models only consider the total irradiance received from all lights, hence can only generate circular profiles. Experimental results show that our method is suitable for rendering of translucent materials under finite‐area lights or environment lights that can be approximated by a small number of SGs.

Point samples with different spectral noise properties (often defined using color names such as white, blue, green, and red) are important for many science and engineering disciplines including computer graphics. While existing techniques can easily produce white and blue noise samples, relatively little is known for generating other noise patterns. In particular, no single algorithm is available to generate different noise patterns according to user-defined spectra. In this paper, we describe an algorithm for generating point samples that match a user-defined Fourier spectrum function. Such a spectrum function can be either obtained from a known sampling method, or completely constructed by the user. Our key idea is to convert the Fourier spectrum function into a differential distribution function that describes the samples' local spatial statistics; we then use a gradient descent solver to iteratively compute a sample set that matches the target differential distribution function. Our algorithm can be easily modified to achieve adaptive sampling, and we provide a GPU-based implementation. Finally, we present a variety of different sample patterns obtained using our algorithm, and demonstrate suitable applications.

Abstract Diffusion curves [ OBW*08 ] provide a flexible tool to create smooth‐shaded images from curves defined with colors. The resulting image is typically computed by solving a Poisson equation that diffuses the curve colors to the interior of the image. In this paper we present a new method for solving diffusion curves by using ray tracing. Our approach is analogous to final gathering in global illumination, where the curves define source radiance whose visible contribution will be integrated at a shading pixel to produce a color using stochastic ray tracing. Compared to previous work, the main benefit of our method is that it provides artists with extended flexibility in achieving desired image effects. Specifically, we introduce generalized curve colors called shaders that allow for the seamless integration of diffusion curves with classic 2D graphics including vector graphics (e.g. gradient fills) and raster graphics (e.g. patterns and textures). We also introduce several extended curve attributes to customize the contribution of each curve. In addition, our method allows any pixel in the image to be independently evaluated, without having to solve the entire image globally (as required by a Poisson‐based approach). Finally, we present a GPU‐based implementation that generates solution images at interactive rates, enabling dynamic curve editing. Results show that our method can easily produce a variety of desirable image effects.

Abstract Recent work in interactive global illumination addresses diffuse and moderately glossy indirect lighting effects, but high‐frequency effects such as multi‐bounce reflections on highly glossy surfaces are often ignored. Accurately simulating such effects is important to convey the realistic appearance of materials such as chrome and shiny metal. In this paper, we present an efficient method for visualizing multi‐bounce glossy reflections at interactive rates under environment lighting. Our main contribution is a pre‐computation–based method which efficiently gathers subsequent highly glossy reflection passes modelled with a non‐linear transfer function representation based on the von Mises–Fisher distribution. We show that our gathering method is superior to scattered sampling. To exploit the sparsity of the pre‐computed data, we apply perfect spatial hashing. As a result, we are able to visualize multi‐bounce glossy reflections at interactive rates at a low pre‐computation cost.

Abstract We present a practical importance‐driven method for GPU‐based final gathering. We take as input a point cloud representing directly illuminated scene geometry; we then project and splat the points to microbuffers, which store each shading pixel's occluded radiance field. We select points for projection based on importance, defined as each point's estimated contribution to a shading pixel. For each selected point, we calculate its splat size adaptively based on its importance value. The main advantage of our method is that it's simple and fast, and provides the capability to incorporate additional importance factors such as glossy reflection paths. We also introduce an image‐space adaptive sampling method, which combines adaptive image subdivision with joint bilateral upsampling to robustly preserve fine details. We have implemented our algorithm on the GPU, providing high‐quality rendering for dynamic scenes at near interactive rates.

Recent work demonstrates that interactive ray tracing is possible on desktop systems, but there is still much debate as to how to most efficiently support advanced visual effects such as soft shadows, smooth freeform surfaces, complex shading, and animated scenes. With these challenges in mind, we reconsider the options for designing a rendering system and present Razor , a new software rendering architecture for distribution ray tracing designed to produce high-quality images with high performance on future single-chip many-core hardware. Razor includes two noteworthy capabilities: a set of techniques for quickly building the kd-tree acceleration structure on demand every frame from a scene graph and a system design that allows for crack-free multiresolution geometry with each ray independently choosing its geometry resolution. Razor's per-frame kd-tree build is designed to robustly handle arbitrarily scene animation, while its per-ray multiresolution geometry provides continuous level of detail driven by ray and path differentials. Razor also decouples shading from visibility computations using a two-phase shading scheme inspired by the REYES system, and caches tessellated representations of freeform surfaces at multiple levels of detail. We present experimental results gathered from a prototype system implemented on eight CPU cores, and discuss which aspects of the system are most successful and which would benefit from further investigation.

Sampling is a core component for many graphics applications including rendering, imaging, animation, and geometry processing. The efficacy of these applications often crucially depends upon the distribution quality of the underlying samples. While uniform sampling can be analyzed by using existing spatial and spectral methods, these cannot be easily extended to general non-uniform settings, such as adaptive, anisotropic, or non-Euclidean domains. We present new methods for analyzing non-uniform sample distributions. Our key insight is that standard Fourier analysis, which depends on samples' spatial locations, can be reformulated into an equivalent form that depends only on the distribution of their location differentials . We call this differential domain analysis. The main benefit of this reformulation is that it bridges the fundamental connection between the samples' spatial statistics and their spectral properties. In addition, it allows us to generalize our method with different computation kernels and differential measurements. Using this analysis, we can quantitatively measure the spatial and spectral properties of various non-uniform sample distributions, including adaptive, anisotropic, and non-Euclidean domains.

We present an interactive algorithm for hair rendering and appearance editing under complex environment lighting represented as spherical radial basis functions (SRBFs). Our main contribution is to derive a compact 1D circular Gaussian representation that can accurately model the hair scattering function introduced by [Marschner et al. 2003]. The primary benefit of this representation is that it enables us to evaluate, at run-time, closed-form integrals of the scattering function with each SRBF light, resulting in efficient computation of both single and multiple scatterings. In contrast to previous work, our algorithm computes the rendering integrals entirely on the fly and does not depend on expensive pre-computation. Thus we allow the user to dynamically change the hair scattering parameters, which can vary spatially. Analyses show that our 1D circular Gaussian representation is both accurate and concise. In addition, our algorithm incorporates the eccentricity of the hair. We implement our algorithm on the GPU, achieving interactive hair rendering and simultaneous appearance editing under complex environment maps for the first time.

Abstract This paper proposes a method for efficiently rendering indirect highlights. Indirect highlights are caused by the primary light source reflecting off two or more glossy surfaces. Accurately simulating such highlights is important to convey the realistic appearance of materials such as chrome and shiny metal. Our method models the glossy BRDF at a surface point as a directional distribution, using a spherical von Mises‐Fisher (vMF) distribution. As our main contribution, we merge multiple vMFs into a combined multimodal distribution. This effectively creates a filtered radiance response function, allowing us to efficiently estimate indirect highlights. We demonstrate our method in a near‐interactive application for rendering scenes with highly glossy objects. Our results produce realistic reflections under both local and environment lighting.

Abstract We present a new algorithm for efficient rendering of high‐quality depth‐of‐field (DoF) effects. We start with a single rasterized view (reference view) of the scene, and sample the light field by warping the reference view to nearby views. We implement the algorithm using NVIDIA's CUDA to achieve parallel processing, and exploit the atomic operations to resolve visibility when multiple pixels warp to the same image location. We then directly synthesize DoF effects from the sampled light field. To reduce aliasing artifacts, we propose an image‐space filtering technique that compensates for spatial undersampling using MIP mapping. The main advantages of our algorithm are its simplicity and generality. We demonstrate interactive rendering of DoF effects in several complex scenes. Compared to existing methods, ours does not require ray tracing and hence scales well with scene complexity.

The ability to place surface samples with Poisson disk distribution can benefit a variety of graphics applications. Such a distribution satisfies the blue noise property, i.e. lack of low frequency noise and structural bias in the Fourier power spectrum. While many techniques are available for sampling the plane, challenges remain for sampling arbitrary surfaces. In this paper, we present new methods for Poisson disk sampling with spectrum analysis on arbitrary manifold surfaces. Our first contribution is a parallel dart throwing algorithm that generates high-quality surface samples at interactive rates. It is flexible and can be extended to adaptive sampling given a user-specified radius field. Our second contribution is a new method for analyzing the spectral quality of surface samples. Using the spectral mesh basis derived from the discrete mesh Laplacian operator, we extend standard concepts in power spectrum analysis such as radial means and anisotropy to arbitrary manifold surfaces. This provides a way to directly evaluate the spectral distribution quality of surface samples without requiring mesh parameterization. Finally, we implement our Poisson disk sampling algorithm on the GPU, and demonstrate practical applications involving interactive sampling and texturing on arbitrary surfaces.

Abstract Recent research in bidirectional importance sampling has focused primarily on structured illumination sources such as distant environment maps, while unstructured illumination has received little attention. In this paper, we present a method for bidirectional importance sampling of unstructured illumination, allowing us to use the same method for sampling both distant as well as local/indirect sources. Building upon recent work in [ WFA*05 ], we model complex illumination as a large set of point lights. The subsequent sampling process draws samples only from this point set. We start by constructing a piecewise constant approximation for the lighting using an illumination cut [ CPWAP08 ]. We show that this cut can be used directly for illumination importance sampling. We then use BRDF importance sampling followed by sample counting to update the cut, resulting in a bidirectional distribution that closely approximates the product of the illumination and BRDF. Drawing visibility samples from this new distribution significantly reduces the sampling variance. As a main advance over previous work, our method allows for unstructured sources, including arbitrary local direct lighting and one‐bounce of indirect lighting.

This paper presents a GPU-based method for interactive global illumination that integrates complex effects such as multi-bounce indirect lighting, glossy reflections, caustics, and arbitrary specular paths. Our method builds upon scattered data sampling and interpolation on the GPU. We start with raytraced shading points and partition them into coherent shading clusters using adaptive seeding followed by k-means. At each cluster center we apply final gather to evaluate its incident irradiance using GPU-based photon mapping. We approximate the entire photon tree as a compact illumination cut, thus reducing the final gather cost for each ray. The sampled irradiance values are then interpolated at all shading points to produce rendering. Our method exploits the spatial coherence of illumination to reduce sampling cost. We sample sparsely and the distribution of sample points conforms with the underlying illumination changes. Therefore our method is both fast and preserves high rendering quality. Although the same property has been exploited by previous caching and adaptive sampling methods, these methods typically require sequential computation of sample points, making them ill-suited for the GPU. In contrast, we select sample points adaptively in a single pass, enabling parallel computation. As a result, our algorithm runs entirely on the GPU, achieving interactive rates for scenes with complex illumination effects.

Abstract We present an interactive GPU‐based algorithm for accurately rendering high‐quality, dynamic glossy reflection effects from both HDR environment maps and local scene objects. Our method uses hardware rasterization to produce primary pixels, and GPU‐based BRDF importance sampling [ CK07 ] to quickly generate reflected rays. We utilize a fast GPU ray tracer proposed by Carr et al. [ CHCH06 ] to compute reflection hits. Our main contribution is an adaptive level‐of‐detail (LOD) control algorithm that greatly improves ray tracing performance during reflection shading. Specifically, we use the solid angle represented by each reflected ray to adaptively pick the level of termination in the BVH traversal step during ray tracing. This leads to 2 ∼ 3x speedup over an unmodified implementation of [ CHCH06 ]. Based on the same solid angle measure, we derive a texture filtering formula to reduce reflection aliasing artifacts, taking advantage of hardware MIP mapping. This extends the filtering algorithm presented in [ CK07 ] from environment mapping to local scene reflection. Using our algorithm, we demonstrate interactive rendering rates for several scenes featuring dynamic lighting and material changes, spatially varying BRDF parameters, and rigid‐body object movement.

We present an efficient computational algorithm for functions represented by a nonlinear piecewise constant approximation called cuts. Our main contribution is a single traversal algorithm for merging cuts that allows for arbitrary pointwise computation, such as addition, multiplication, linear interpolation, and multi-product integration. A theoretical error bound of this approach can be proved using a statistical interpretation of cuts. Our algorithm extends naturally to computation with many cuts and maps easily to modern GPUs, leading to significant advantages over existing methods based on wavelet approximation. We apply this technique to the problem of realistic lighting and material design under complex illumination with arbitrary BRDFs. Our system smoothly integrates all-frequency relighting of shadows and reflections with dynamic per-pixel shading effects, such as bump mapping and spatially varying BRDFs. This combination of capabilities is typically missing in current systems. We represent illumination and precomputed visibility as nonlinear sparse vectors; we then use our cut merging algorithm to simultaneously interpolate visibility cuts at each pixel, and compute the triple product integral of the illumination, interpolated visibility, and dynamic BRDF samples. Finally, we present a two-pass, data-driven approach that exploits pilot visibility samples to optimize the construction of the light tree, leading to more efficient cuts and reduced datasets.

This paper presents a novel PRT-based method that uses precomputed visibility cuts for interactive relighting with all-frequency environment maps and arbitrary dynamic BRDFs. Our method is inspired by the recent Lightcuts approach [24] and we parameterize distant environment lighting onto uniformly distributed sample points over the sphere. Using a binary tree structure of the points, we precompute and approximate each vertex's visibility function into clusters that we call the precomputed visibility cuts. These cuts are iteratively selected with bounded approximation error and confined cluster size. At run-time, a GPU-based relighting algorithm quickly computes the view-dependent shading color by accessing a dynamically built light tree, the precomputed visibility cuts, and a direct sampling of an arbitrary BRDF using each visibility cluster's average direction and the dynamic view direction. Compared to existing PRT techniques, our method guarantees uniform sampling of the lighting, requires no precomputed BRDF data, and can be easily extended to handle one-bounce glossy indirect transfer effects in real-time.

We present a technique for interactive rendering of glossy objects in complex and dynamic lighting environments that captures interreflections and all-frequency shadows. Our system is based on precomputed radiance transfer and separable BRDF approximation. We factor glossy BRDFs using a separable decomposition and keep only a few low-order approximation terms, each consisting of a purely view-dependent and a purely light-dependent component. In the precomputation step, for every vertex, we sample its visibility and compute a direct illumination transport vector corresponding to each BRDF term. We use modern graphics hardware to accelerate this step and further compress the data using a nonlinear wavelet approximation. The direct illumination pass is followed by one or more interreflection passes, each of which gathers compressed transport vectors from the previous pass to produce global illumination transport vectors. To render at run time, we dynamically sample the lighting to produce a light vector, also represented in a wavelet basis. We compute the inner product of the light vector with the precomputed transport vectors, and the results are further combined with the BRDF view-dependent components to produce vertex colors. We describe acceleration of the rendering algorithm using programmable graphics hardware and discuss the limitations and trade-offs imposed by the hardware.

We present a technique, based on precomputed light transport, for interactive rendering of translucent objects under all-frequency environment maps. We consider the complete BSSRDF model proposed by Jensen et al. [2001]. which includes both single and diffuse multiple scattering components. The challenge is how to efficiently precompute all-frequency light transport functions due to subsurface scattering. We apply the two-pass hierarchical technique by Jensen et al. [2002] in the space of non-linearly approximated transport vectors, which allows us to efficiently evaluate transport vectors due to diffuse multiple scattering. We then include an approximated single scattering term in the precomputation, which previous interactive systems have ignored. For an isotropic phase function, this approximation produces a diffuse transport vector per vertex, and is combined with the multiple scattering component. For a general phase function, we introduce a technique from BRDF rendering to factor the phase function using a separable decomposition to allow for view-dependent rendering. We show that our rendering results qualitatively match the appearance of translucent objects, achieving a high level of realism at interactive rates.