Fast Wavelet Radiosity Method

Wavelet analysis has been found [1] to be very useful for functional representation and accurate global solution of radiosity. In radiosity we deal with functions in 2D and 4D spaces. Under such conditions, the biggest bottleneck in applying this wavelet analysis seems to be the large number of multidimensional inner products. In this paper, we propose (i) the use of interpolating wavelets for fast inner product computation and consequently for faster wavelet radiosity solution (ii) the use of hierarchical decomposition technique for determining the smoothness of the radiosity function for optimal adaptive subdivision.     

Adaptive Wavelet Methods for Hyperbolic PDEs

We analyze how to solve hyperbolic PDEs with compactly supported orthonormal wavelets adaptively. We use thresholded wavelet expansions of signals and operators. A tree structure is used to represent the signal, and a multidimensional analogue of the fast wavelet transform is used to expand the operators. We solve the advection equation and Burgers' equation on a periodic domain.     

An Implementation of Fast Wavelet Galerkin Methods for Integral Equations of the Second Kind

We present a numerical implementation of the fast Galerkin method for Fredholm integral equations of the second kind using the piecewise polynomial wavelets. We focus on addressing critical issues for the numerical implementation of such a method. They include a choice of practical truncation strategy, numerical integration of weakly singular integrals and the error control of the numerical quadrature. We also implement a multiscale iteration method for solving the resulting compressed linear system. Numerical examples are given to demonstrate the proposed ideas and methods.     

Multiresolution B-spline Radiosity

This paper introduces a kind of new wavelet radiosity method called multiresolution B-spline radiosity, which uses B-splines of different scales to represent radiosity distribution functions. A set of techniques and algorithms, such as function extrapolation, adaptive quadrature, scale adjustment and octree, are proposed to implement it. This method sets up hierarchical structures on surfaces, keeps radiosity distribution continuous at element boundaries, does not need postprocessing, and does not prevent the use of any surface whose parameter domain is rectilinear.     

A Progressive Radiosity Algorithm for Scenes Containing Curved Surfaces

Based on the theory of light energy transfer between two differential diffuse surface areas, a generalized radiosity approach is presented. Unlike the conventional radiosity method, curved surfaces are subdivided into triangular surface patches, radiosity is assummed to be vary across each triangular surface patch. By adopting linear interpolation scheme over each triangular surface patch, we have established a complete set of approximated radiosity equations. Their unknowns are radiosities of differential surface areas located at all vertices of surface patches. The generalized radiosity equation has also been extended to non-diffuse environments. Theoretical analysis and experimental results demonstrate the great potential of this method,     

Radiosity: A method for computing global illumination

The radiosity method for computing the interreflection of light within diffuse environments is described. The development of the method for realistic image synthesis over the past three years is outlined. A short discussion of the underlying theory and implementation is followed by a real life example which illustrates the power and accuracy of the radiosity method and points out the different results from ray tracing procedures. Current and future developments of the radiosity method are outlined.     

可大规模应用的辐射度计算的自动网格化方法

合理地网格化场景是有效地进行辐射度计算的重要前提.现有的两种主要剖分方法是细分法和阴影边界计算法.前者是在必要时对大面片进行自动细分,后者是先解析地求出阴影的区域,然后根据阴影边界进行划分.前者存在的问题是无法检测出落在大面片中间的细节变化,绘制的质量得不到保证.后一种方法又局限于基本上只能处理纯多边形场景,而且计算时间长,实现复杂,难以在工程上进行应用.文章提出一种网格化方法,它面向大规模工程应用,简便易行,并能生成较高质量的图像.这种方法先将能量接受面划分成满足精度要求的细小面元,然后根据各面元对场景中各光源的可见性特征进行合并操作,以使能量变化情况不同的区域能以不同大小的尺寸进行剖分,这样,用于计算的面片大大减少,而图像质量没有明显的降低.实验结果和统计数据表明,此方法因其简单、高效,很适合大规模的工程应用.     

层次结构辐射度渲染中的可见性测试

在辐射度渲染等整体光照模型中，可见性测试是影响整体性能的关键，为了获得较好的可见性测试效果，在光线投射方法基础上，对可见性测试方法做了如下两方面的优化，一方面引入Shaft Culling算法，作首轮筛选，以提高线投射的效率，另一方面，在可见性测试和自适应分割时，进行基于可见性的分割，以保证只有完全可见和完全不可见两种情况，这两方面优化都被引入到层次结构辐射度渲染的实现中，实验结果表明，改进过的可见性测试，不仅减少了计算量和误差，还保证了阴影边界的质量。     

Hierarchical Radiosity for Dynamic Environments

This paper extends the hierarchical radiosity method to environments in which geometry and surface attributes can be changed dynamically. New algorithms are presented for maintaining an appropriately-sized mesh and speeding the construction of the corresponding linear system. Mesh folding, the unrefinement of a mesh, is used to optimize mesh size while maintaining a specified error tolerance. Two new interactions are introduced: shadow links guide local shadow clean up after a change in geometry and ghost links guide global mesh folding after a change in surface attributes. The algorithms stabilize the memory requirements of dynamic scenes. Different types of interactions are analyzed to determine how they are affected by changes in geometry. A dynamic scene-partitioning scheme called a motion volume, used in conjunction with a three-dimensional clipping algorithm, provides a fast way to cull interactions that do not need to be updated. The algorithms are demonstrated on several sample scenes.     

MAX渲染算法光线跟踪与光能传递的分析对比

光线跟踪(Raytracer)与光能传递(Radiosity)渲染是3D设计软件中常用的渲染方法,对场景使用光线跟踪与光能传递渲染可以生成十分逼真的光影效果。但两种渲染算法都需要进行大量复杂的运算,尤其是光能传递对计算机系统的性能要求很高,对硬件平台的运算速度和能力都有很苛刻的要求。     

MAX渲染算法光线跟踪与光能传递的分析对比

光线跟踪（Raytracer）与光能传递（Radiosity）渲染是3D设计软件中常用的渲染方法,时场景使用光线跟踪与光能传递渲染可以生成十分逼真的光影效果。但两种渲染算法都需要进行大量复杂的运算,尤其是光能传递时计算机系统的性能要．求很高,时硬件平台的运算速度和能力都有很苛刻的要求。     

GPU编程模型下的实时辐射度着色方法的分析与探讨

Radiosity是模拟能量在场景中传递,最终达到平衡的一种阴影着色方法.Realtime Radiosity是这种算法在实时场景中的应用,本文总结了目前的两种实时辐射度算法的实现,并分析了各自的优缺点.     

The multi-projection method for weakly singular Fredholm integral equations of the second kind

In this paper, we propose a multi-projection method and its re-iterated algorithm for solving weakly singular Fredholm integral equations of the second kind. We apply our methods to Petrov–Galerkin versions to establish excellent superconvergence results, and we illustrate our theoretical results with a numerical example.     

A Multiprocessor Implementation of Radiosity

This paper describes a multi-processor implementation of form factor computation in the radiosity method. Form factors are computed using the ray casting method and the algorithm is enhanced with Binary Space Partition (BSP) Trees and bounding boxes. Experimental results are presented together with a discussion of load balance efficiency.     

A Monte Carlo approach for Galerkin radiosity

Galerkin radiosity solves the integral rendering equation by projecting the illumination functions into a set of higher-order basis functions. This paper presents a Monte Carlo approach for Galerkin radiosity to compute the coefficients of the basis functions. The new approach eliminates the problems with edge singularities between adjacent surfaces present in conventional Galerkin radiosity, the time complexity is reduced fromO(K ⁴) toO(K ²) for aK-order basis, and ideally specular energy transport can be simulated. As in conventional Galerkin radiosity, no meshing is required even for large or curved surfaces, thus reducing memory requirements, and no a posteriori Gouraud interpolation is necessary. The new algorithm is simple and can be parallelized on any parallel computer, including massively parallel systems.     

Optimal Source Selection in Shooting Random Walk Monte Carlo Radiosity

In this paper we study how to optimally select between different sources in shooting random walk Monte Carlo Radiosity. Until now the probability of selecting a source has been made proportional to the importance of that source for the region of interest. We will show here that, whenever the transition probabilities are the Form Factors, this is not optimal, and will consequently give the optimal case. This will correspond to probabilities proportional to the square root of importances, rather than to importances themselves.     

An Analysis of Quasi-Monte Carlo Integration Applied to the Transillumination Radiosity Method

This paper presents an enhanced transillumination radiosity method that can provide accurate solutions at relatively low computational cost. The proposed algorithm breaks down the double integral of the gathered power to an area integral that is computed analytically and to a directional integral that is evaluated by quasi-Monte Carlo techniques. Since the analytical integration results in a continuous function of finite variation, the quasi-Monte Carlo integration that follows the analytical integration will be efficient and its error can be bounded by the Koksma-Hlawka inequality. The paper also analyses the requirements of the convergence, presents theoretical error bounds and proposes error reduction techniques. The theoretical bounds are compared with simulation results.     

Bounded Radiosity – Illumination on General Surfaces and Clusters

Traditionally, Radiosity algorithms have been restricted to scenes made from planar patches. Most algorithms for computing form factors and the subdivision criterion for hierarchical methods implicitly assume planar patches. In this paper, we present a new radiosity algorithm that is solely based on simple geometric information about surface elements, namely their bounding boxes and cone of normals. Using this information allows to compute efficient error bounds that can be used for the subdivision oracle and for computing the energy transfer. Due to the simple interface to geometric objects, our algorithm not only allows for computing illumination on general curved surfaces, but it can also be directly applied to a hieararchy of clusters. Several examples demonstrate the advantages of the new approach.     

A New Radiosity Approach Using Area Sampling for Parametric Patches

A high precision illumination model is indispensable for lighting simulation and realistic image synthesis. For the purpose of improving realism, research on global illumination has been done, and several papers on radiosity methods have been presented. In the most recently proposed methods, the shapes of light sources and objects are restricted to polygons or simple curved surfaces. We present a more general method which can handle the kind of free-form surfaces widely used in industrial products and in architecture. The method proposed here solves the problem of the interreflection of light (i.e., radiosities) between patches, and form-factors, which play an important role in this process, are precisely calculated without aliasing through the use of an area sampling method (i.e., pyramid tracing). Furthermore the method can handle both non-uniform intensity curved sources and non-diffuse surfaces.