Global Illumination Using Well‐Separated Pair Decomposition

Instant radiosity methods rely on using a large number of virtual point lights (VPLs) to approximate global illumination. Efficiency considerations require grouping the VPLs into a small number of clusters that are treated as individual lights with respect to each point to be shaded. Two examples of clustering algorithms are Lightcuts [WFA*05] and LightSlice [OP11]. In this work, we use the notion of geometric separatedness of point sets as a basis for a data structure for pre‐computing and compactly storing a set of candidate VPL clusterings. Our data structure is created prior to rendering, is view‐independent and relies only on geometric and radiometric information. For any point to be shaded, we show that a suitable clustering of the VPLs can be efficiently extracted from this data structure. We develop the above framework into an accurate and efficient clustering algorithm based on well‐separated pair decompositions which outperforms earlier work in speed and/or quality for diffuse scenes.     

Virtual Spherical Gaussian Lights for Real‐time Glossy Indirect Illumination

Virtual point lights (VPLs) are well established for real‐time global illumination. However, this method suffers from spiky artifacts and flickering caused by singularities of VPLs, highly glossy materials, high‐frequency textures, and discontinuous geometries. To avoid these artifacts, this paper introduces a virtual spherical Gaussian light (VSGL) which roughly represents a set of VPLs. For a VSGL, the total radiant intensity and positional distribution of VPLs are approximated using spherical Gaussians and a Gaussian distribution, respectively. Since this approximation can be computed using summations of VPL parameters, VSGLs can be dynamically generated using mipmapped reflective shadow maps. Our VSGL generation is simple and independent from any scene geometries. In addition, reflected radiance for a VSGL is calculated using an analytic formula. Hence, we are able to render one‐bounce glossy interreflections at real‐time frame rates with smaller artifacts.     

Approximate Bias Compensation for Rendering Scenes with Heterogeneous Participating Media

In this paper we present a novel method for high‐quality rendering of scenes with participating media. Our technique is based on instant radiosity, which is used to approximate indirect illumination between surfaces by gathering light from a set of virtual point lights (VPLs). It has been shown that this principle can be applied to participating media as well, so that the combined single scattering contribution of VPLs within the medium yields full multiple scattering. As in the surface case, VPL methods for participating media are prone to singularities, which appear as bright “splotches” in the image. These artifacts are usually countered by clamping the VPLs' contribution, but this leads to energy loss within the short‐distance light transport. Bias compensation recovers the missing energy, but previous approaches are prohibitively costly. We investigate VPL‐based methods for rendering scenes with participating media, and propose a novel and efficient approximate bias compensation technique. We evaluate our technique using various test scenes, showing it to be visually indistinguishable from ground truth.     

An Error Estimation Framework for Many‐Light Rendering

The popularity of many‐light rendering, which converts complex global illumination computations into a simple sum of the illumination from virtual point lights (VPLs), for predictive rendering has increased in recent years. A huge number of VPLs are usually required for predictive rendering at the cost of extensive computational time. While previous methods can achieve significant speedup by clustering VPLs, none of these previous methods can estimate the total errors due to clustering. This drawback imposes on users tedious trial and error processes to obtain rendered images with reliable accuracy. In this paper, we propose an error estimation framework for many‐light rendering. Our method transforms VPL clustering into stratified sampling combined with confidence intervals, which enables the user to estimate the error due to clustering without the costly computing required to sum the illumination from all the VPLs. Our estimation framework is capable of handling arbitrary BRDFs and is accelerated by using visibility caching, both of which make our method more practical. The experimental results demonstrate that our method can estimate the error much more accurately than the previous clustering method.     

Stochastic Light Culling for VPLs on GGX Microsurfaces

This paper introduces a real‐time rendering method for single‐bounce glossy caustics created by GGX microsurfaces. Our method is based on stochastic light culling of virtual point lights (VPLs), which is an unbiased culling method that randomly determines the range of influence of light for each VPL. While the original stochastic light culling method uses a bounding sphere defined by that light range for coarse culling (e.g., tiled culling), we have further extended the method by calculating a tighter bounding ellipsoid for glossy VPLs. Such bounding ellipsoids can be calculated analytically under the classic Phong reflection model which cannot be applied to physically plausible materials used in modern computer graphics productions. In order to use stochastic light culling for such modern materials, this paper derives a simple analytical solution to generate a tighter bounding ellipsoid for VPLs on GGX microsurfaces. This paper also presents an efficient implementation for culling bounding ellipsoids in the context of tiled culling. When stochastic light culling is combined with interleaved sampling for a scene with tens of thousands of VPLs, this tiled culling is faster than conservative rasterization‐based clustered shading which is a state‐of‐the‐art culling technique that supports bounding ellipsoids. Using these techniques, VPLs are culled efficiently for completely dynamic single‐bounce glossy caustics reflected from GGX microsurfaces.     

Hierarchical Image-Space Radiosity for Interactive Global Illumination

We introduce image-space radiosity and a hierarchical variant as a method for interactively approximating diffuse indirect illumination in fully dynamic scenes. As oft observed, diffuse indirect illumination contains mainly low-frequency details that do not require independent computations at every pixel. Prior work leverages this to reduce computation costs by clustering and caching samples in world or object space. This often involves scene preprocessing, complex data structures for caching, or wasted computations outside the view frustum. We instead propose clustering computations in image space, allowing the use of cheap hardware mipmapping and implicit quadtrees to allow coarser illumination computations. We build on a recently introduced multiresolution splatting technique combined with an image-space lightcut algorithm to intelligently choose virtual point lights for an interactive, one-bounce instant radiosity solution. Intelligently selecting point lights from our reflective shadow map enables temporally coherent illumination similar to results using more than 4096 regularly-sampled VPLs.     

Temporally Coherent Adaptive Sampling for Imperfect Shadow Maps

We propose a new adaptive algorithm for determining virtual point lights (VPL) in the scope of real‐time instant radiosity methods, which use a limited number of VPLs. The proposed method is based on Metropolis‐Hastings sampling and exhibits better temporal coherence of VPLs, which is particularly important for real‐time applications dealing with dynamic scenes. We evaluate the properties of the proposed method in the context of the algorithm based on imperfect shadow maps and compare it with the commonly used inverse transform method. The results indicate that the proposed technique can significantly reduce the temporal flickering artifacts even for scenes with complex materials and textures. Further, we propose a novel splatting scheme for imperfect shadow maps using hardware tessellation. This scheme significantly improves the rendering performance particularly for complex and deformable scenes. We thoroughly analyze the performance of the proposed techniques on test scenes with detailed materials, moving camera, and deforming geometry.     

Realtime Rendering Glossy to Glossy Reflections in Screen Space

Glossy to glossy reflections are lights bounced between glossy surfaces. Such directional light transports are important for humans to perceive glossy materials, but difficult to simulate. This paper proposes a new method for rendering screen‐space glossy to glossy reflections in realtime. We use spherical von Mises‐Fisher (vMF) distributions to model glossy BRDFs at surfaces, and employ screen space directional occlusion (SSDO) rendering framework to trace indirect light transports bounced in the screen space. As our main contributions, we derive a new parameterization of vMF distribution so as to convert the non‐linear fit of multiple vMF distributions into a linear sum in the new space. Then, we present a new linear filtering technique to build MIP‐maps on glossy BRDFs, which allows us to create filtered radiance transfer functions at runtime, and efficiently estimate indirect glossy to glossy reflections. We demonstrate our method in a realtime application for rendering scenes with dynamic glossy objects. Compared with screen space directional occlusion, our approach only requires one extra texture and has a negligible overhead, 3% ～ 6% loss at frame rate, but enables glossy to glossy reflections.     

Rich‐VPLs for Improving the Versatility of Many‐Light Methods

Many‐light methods approximate the light transport in a scene by computing the direct illumination from many virtual point light sources (VPLs), and render low‐noise images covering a wide range of performance and quality goals. However, they are very inefficient at representing glossy light transport. This is because a VPL on a glossy surface illuminates a small fraction of the scene only, and a tremendous number of VPLs might be necessary to render acceptable images. In this paper, we introduce Rich‐VPLs which, in contrast to standard VPLs, represent a multitude of light paths and thus have a more widespread emission profile on glossy surfaces and in scenes with multiple primary light sources. By this, a single Rich‐VPL contributes to larger portions of a scene with negligible additional shading cost. Our second contribution is a placement strategy for (Rich‐)VPLs proportional to sensor importance times radiance. Although both Rich‐VPLs and improved placement can be used individually, they complement each other ideally and share interim computation. Furthermore, both complement existing many‐light methods, e.g. Lightcuts or the Virtual Spherical Lights method, and can improve their efficiency as well as their application for scenes with glossy materials and many primary light sources.     

LOCAL++: A C++ framework for local search algorithms

Local search is an emerging paradigm for combinatorial search which has recently been shown to be very effective for a large number of combinatorial problems. It is based on the idea of navigating the search space by iteratively stepping from one solution to one of its neighbors, which are obtained by applying a simple local change to it. In this paper we present LOCAL++, an object‐oriented framework to be used as a general tool for the development and implementation of local search algorithms in C++. The framework comprises a hierarchy of abstract template classes, one for each local search technique taken into account (i.e. hill‐climbing, simulated annealing and tabu search). Each class specifies and implements the invariant part of the algorithm built according to the technique, and is supposed to be specialized by a concrete class once a given search problem is considered, so as to implement the problem‐dependent part of the algorithm. LOCAL++ comprises also a set of abstract classes for creating new techniques by combining different search techniques and different neighborhood relations. The architecture of LOCAL++ provides a principled modularization for the solution of combinatorial search problems, and helps the designer deriving a neat conceptual scheme of the application, thus facilitating the development and debugging phases. LOCAL++ proved to be flexible enough for the implementation of the algorithms solving various scheduling problems. Copyright © 2000 John Wiley & Sons, Ltd.     

Efficient Image‐Based Proximity Queries with Object‐Space Precision

We present an efficient algorithm for object‐space proximity queries between multiple deformable triangular meshes. Our approach uses the rasterization capabilities of the GPU to produce an image‐space representation of the vertices. Using this image‐space representation, inter‐object vertex‐triangle distances and closest points lying under a user‐defined threshold are computed in parallel by conservative rasterization of bounding primitives and sorted using atomic operations. We additionally introduce a similar technique to detect penetrating vertices. We show how mechanisms of modern GPUs such as mipmapping, Early‐Z and Early‐Stencil culling can optimize the performance of our method. Our algorithm is able to compute dense proximity information for complex scenes made of more than a hundred thousand triangles in real time, outperforming a CPU implementation based on bounding volume hierarchies by more than an order of magnitude.     

Stochastic Soft Shadow Mapping

In this paper, we extend the concept of pre‐filtered shadow mapping to stochastic rasterization, enabling real‐time rendering of soft shadows from planar area lights. Most existing soft shadow mapping methods lose important visibility information by relying on pinhole renderings from an area light source, providing plausible results only for small light sources. Since we sample the entire 4D shadow light field stochastically, we are able to closely approximate shadows of large area lights as well. In order to efficiently reconstruct smooth shadows from this sparse data, we exploit the analogy of soft shadow computation to rendering defocus blur, and introduce a multiplane pre‐filtering algorithm. We demonstrate how existing pre‐filterable approximations of the visibility function, such as variance shadow mapping, can be extended to four dimensions within our framework.     

Metropolis Instant Radiosity

We present Metropolis Instant Radiosity (MIR), an unbiased algorithm to solve the Light Transport problem. MIR is a hybrid technique which consists in representing the incoming radiance field by a set of Virtual Point Lights (V PLs) and in computing the response of all sensors in the scene (i.e. camera captors) by accumulating their contributions. In contrast to other similar approaches, we propose to sample the VPLs with an innovative Multiple-try Metropolis-Hastings (MTMH) Algorithm: the goal is to build an efficient, aggressive, and unconditionally robust variance reduction method that works well regardless of the scene layout. Finally, we present a fast ray tracing implementation using MIR and show how our complete rendering pipeline can produce high-quality and high-resolution pictures in a few seconds.     

Accurate Translucent Material Rendering under Spherical Gaussian Lights

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.     

Uniformization and Density Adaptation for Point Cloud Data Via Graph Laplacian

Point cloud data is one of the most common types of input for geometric processing applications. In this paper, we study the point cloud density adaptation problem that underlies many pre‐processing tasks of points data. Specifically, given a (sparse) set of points Q sampling an unknown surface and a target density function, the goal is to adapt Q to match the target distribution. We propose a simple and robust framework that is effective at achieving both local uniformity and precise global density distribution control. Our approach relies on the Gaussian‐weighted graph Laplacian and works purely in the points setting. While it is well known that graph Laplacian is related to mean‐curvature flow and thus has denoising ability, our algorithm uses certain information encoded in the graph Laplacian that is orthogonal to the mean‐curvature flow. Furthermore, by leveraging the natural scale parameter contained in the Gaussian kernel and combining it with a simulated annealing idea, our algorithm moves points in a multi‐scale manner. The resulting algorithm relies much less on the input points to have a good initial distribution (neither uniform nor close to the target density distribution) than many previous refinement‐based methods. We demonstrate the simplicity and effectiveness of our algorithm with point clouds sampled from different underlying surfaces with various geometric and topological properties.     

Quaternion Julia Set Shape Optimization

We present the first 3D algorithm capable of answering the question: what would a Mandelbrot‐like set in the shape of a bunny look like? More concretely, can we find an iterated quaternion rational map whose potential field contains an isocontour with a desired shape? We show that it is possible to answer this question by casting it as a shape optimization that discovers novel, highly complex shapes. The problem can be written as an energy minimization, the optimization can be made practical by using an efficient method for gradient evaluation, and convergence can be accelerated by using a variety of multi‐resolution strategies. The resulting shapes are not invariant under common operations such as translation, and instead undergo intricate, non‐linear transformations.     

CageR: Cage‐Based Reverse Engineering of Animated 3D Shapes

We present CageR: A novel framework for converting animated 3D shape sequences into compact and stable cage‐based representations. Given a raw animated sequence with one‐to‐one point correspondences together with an initial cage embedding, our algorithm automatically generates smoothly varying cage embeddings which faithfully reconstruct the enclosed object deformation. Our technique is fast, automatic, oblivious to the cage coordinate system, provides controllable error and exploits a GPU implementation. At the core of our method, we introduce a new algebraic algorithm based on maximum volume sub‐matrices (maxvol) to speed up and stabilize the deformation inversion. We also present a new spectral regularization algorithm that can apply arbitrary regularization terms on selected subparts of the inversion spectrum. This step allows to enforce a highly localized cage regularization, guaranteeing its smooth variation along the sequence. We demonstrate the speed, accuracy and robustness of our framework on various synthetic and acquired data sets. The benefits of our approach are illustrated in applications such as animation compression and post‐editing.     

Pattern‐Based Quadrangulation for N‐Sided Patches

We propose an algorithm to quadrangulate an N‐sided patch (2 ≤ N ≤ 6) with prescribed numbers of edge subdivisions at its boundary. Our algorithm is guaranteed to succeed for arbitrary valid input, which is proved using a canonical simplification of the input and a small set of topological patterns that are sufficient for supporting all possible cases. Our algorithm produces solutions with minimal number of irregular vertices by default, but it also allows the user to choose other feasible solutions by solving a set of small integer linear programs. We demonstrate the effectiveness of our algorithm by integrating it into a sketch‐based quad remeshing system. A reference C++ implementation of our algorithm is provided as a supplementary material.     

Learning 3D Deformation of Animals from 2D Images

Understanding how an animal can deform and articulate is essential for a realistic modification of its 3D model. In this paper, we show that such information can be learned from user‐clicked 2D images and a template 3D model of the target animal. We present a volumetric deformation framework that produces a set of new 3D models by deforming a template 3D model according to a set of user‐clicked images. Our framework is based on a novel locally‐bounded deformation energy, where every local region has its own stiffness value that bounds how much distortion is allowed at that location. We jointly learn the local stiffness bounds as we deform the template 3D mesh to match each user‐clicked image. We show that this seemingly complex task can be solved as a sequence of convex optimization problems. We demonstrate the effectiveness of our approach on cats and horses, which are highly deformable and articulated animals. Our framework produces new 3D models of animals that are significantly more plausible than methods without learned stiffness.     

CARR: a scalable solution for network packet classification

Modern Internet routers have to handle a large number of packet classification rules, which requires classification schemes to be scalable both in time and space. In this paper, we present a scalable packet classification algorithm that is developed by combining two new concepts to the well‐known bit vector (BV) scheme. We propose a range search method based on a cache‐aware tree (CATree) which makes full use of processor's cache line to reduce the number of dynamic random access memory (DRAM) accesses. Theoretically, the number of DRAM accesses of CATree is about log(m+1) times lower than that of the widely used binary search algorithm, where m is the number of keys in a single cache line. Based on our computational results on a set of 1024 keys, the CATree algorithm is 36% faster than binary search algorithm and the performance is better when applied to a larger set of keys. In addition, we develop a rule re‐arrangement algorithm to reduce the bitmap space of BV. With this re‐arrangement, the rules for the same action may be assigned an identical priority. This reduces the number of priorities as well as the memory space of the bitmap. Furthermore, this also reduces the number of memory accesses and hence, increases the CPU cache utilization. With CATree and rule re‐arrangement, the cache‐aware bit vector with rule re‐arrangement algorithm achieves better performance in comparison with the regular BV scheme, both in space and time. In our experiments, the proposed algorithm reduces the bitmap memory space of a practical set of firewall rules by two orders of magnitude and is 91% faster than the regular BV.