Improved techniques for ray tracing parametric surfaces

Several techniques for acceleration of ray tracing parametric surfaces are presented. Some of these are entirely new to ray tracing, while others are improvements of previously known techniques. First a uniform spatial subdivision scheme is adapted to parametric surfaces. A new space- and time-efficient algorithm for finding raysurface intersections is introduced. It combines numerical and subdivision techniques, thus allowing utilization of ray coherence and greatly reducing the average ray-surface intersection time. Non-scanline sampling orders of the image plane are proposed that facilitate utilization of coherence. Finally, a method to handle reflected, refracted, and shadow rays in a more efficient manner is described. Results of timing tests indicating the efficiency of these techniques for various environments are presented.     

Data structures and the time complexity of ray tracing

The time complexity of ray tracing is a function of the data structures used for space division. Octree and hierarchical extents have been suggested as effective choices. In this paper, complexity parameters are suggested to characterize images and show that both octrees and hierarchies are appropriate choices if given most favorable images. Also, a unified technique is proposed and shown to be better than previous methods for all images. Octrees and hierarchies are particular cases of the new proposed algorithm.     

Parallel ray tracing based upon a multilevel topological knowledge acquisition of the scene

Including the standard parallelization by grouping primary rays, this paper presents a new parallel ray-timing method based upon a topological knowledge acquisition of the scene. This topological knowledge focuses on relative positions between objects and processes and uses a new type of message. Indeed, instead of exchanging database pages or rays, processes exchange topological information. This information is used by each process to decrease its own list of objects to test against rays The acquisition of information about relative positions between objects and processes is obtained by a careful ordering of he pixel calculation. The processes are dispatched on a computer network including a parallel computer The organization of the processes on this network is a multilevel one leading to different levels of topological message exchanges This method is characterized by topological messages describing the scene, dynamic optimization of the database, easy parallelization on any network (no deadlock, fault tolerance, easily expandable and simple routing), and gives interesting results with true or simulated parallelism.     

Representing Quadric Surfaces Using NURBS Surfaces

A method for representing quadrc surfaces using NURBS is presented.By means of the necessary and sufficient conditons for NURBS curves to precisely represent circular arcs and other conics,quadric surfaces can be represented by NURBS surfaces with fewer control vertices.The method can be used not only for NURBS surface representation of quadric surfaces,but also for rounding polyhedrons.Many examples are given in the paper.     

基于Metropolis光线跟踪的组合滤波器

蒙特卡罗方法是计算全局光照的基础,目前已经有很多基于蒙特卡罗的全局光照算法,但大多数算法在渲染时间上都有一定局限性。在蒙特卡罗方法基础上,结合Metropolis光线跟踪算法和组合滤波器,提出一种新的全局光照算法。该算法分为两个部分,首先使用多组不同尺度的滤波器对图像进行处理,然后将多组滤波器处理后的结果组合成最终的结果。该算法使用相对均方根误差作为选择滤波尺度的依据,在采样和重建过程中自适应地为每个像素选择合适的滤波器,以最大化降低误差,得到更好的重建结果。实验结果表明,该算法相对于传统Metropolis算法在效率和图像质量上都有较大提高。     

Interactive rendering of NURBS surfaces

NURBS (Non-uniform rational B-splines) surfaces are one of the most useful primitives employed for high quality modeling in CAD/CAM tools and graphics software. Since direct evaluation of NURBS surfaces on the GPU is a highly complex task, the usual approach for rendering NURBS is to perform the conversion into Bézier surfaces on the CPU, and then evaluate and tessellate them on the GPU. In this paper we present a new proposal for rendering NURBS surfaces directly on the GPU in order to achieve interactive and real-time rendering. Our proposal, Rendering Pipeline for NURBS Surfaces (RPNS), is based on a new primitive KSQuad that uses a regular and flexible processing of NURBS surfaces, while maintaining their main geometric properties to achieve real-time rendering. RPNS performs an efficient adaptive discretization to fine tune the density of primitives needed to avoid cracks and holes in the final image, applying an efficient non-recursive evaluation of the basis function on the GPU. An implementation of RPNS using current GPUs is presented, achieving real-time rendering rates of complex parametric models. Our experimental tests show a performance several orders of magnitude higher than traditional approximations based on NURBS to Bézier conversion.     

基于历史缓存技术的射线跟踪加速算法研究*

通过分析影响射线跟踪效率的因素,提出一种基于历史缓存技术的射线跟踪加速算法,以提高射线跟踪的运算效率。通过建立一个缓存区存储历史信息,用来减少每条射线必须处理的建筑物面的数量和减少计算无效的交点。对提出的算法进行仿真计算,仿真结果证明了这种算法的正确性,有效降低了计算的复杂度。     

双二次NURBS曲面间的最短距离

利用双二次Bezier曲面为非负的充要条件,给出了分别位于两张双二次NURBS曲面上的点是否为这两张曲面间距离最近的点的判别方法．曲面非负是指在此显式曲面上没有位于XOY平面下方的点．在这一基础上,得到了计算双二次NURBS曲面间最短距离的一个算法．最后,给出了实验结果并将文中算法与采用分层数据结构的常用算法进行了比较。     

Shadows on bump-mapped surfaces in ray tracing

This paper presents a method of generating shadows on bump-mapped surfaces in ray tracing. The method yields images with realistic shadows influenced by bumpy surface geometry. In our method, intersections are calculated between eye/reflection/refraction rays and smooth original surfaces as usual, and the surfaces and shaded according to Blinn's bump mapping. For shadowing, however, we shift the intersection points based on the approximated bumpy surface shape, and the shadow rays are fired from the shifted intersection points. Since the method involves no explicit intersection calculation between rays and bumpy surfaces, it requires only a small amount of computation in addition to conventional ray tracting. It is easy to insert the method into existing ray tracers, and it can be applied to variants of ray tracing algorithms that use shadow rays.     

一种基于八叉树空间剖分技术的光线跟踪算法

光线跟踪算法是生成真实感图形的主要算法之一。为了提高光线追踪速度,在研究和比较各种光线跟踪算法的基础上,提出了一种基于八叉树数据结构的光线追踪算法。并结合基于重心坐标系的快速求交算法来提高光线跟踪的求交效率,使用重心坐标来表示包含三角形面片的参数平面,不用像三角形顶点一样需要长期存储,能够快速判定光线与三角形是否相交并计算出交点。实验结果表明,该算法能够在保证图像质量的同时提高绘制速度。     

Fast Evaluation Algorithm for NURBS Surfaces

Through a precise recursion of B-spline bases and the resursive expression of the derivatives of rational surfaces, this paper presents an efficient algorithm for the calculation of NURBS surfaces and all their directional derivatives. The algorithm requires less storage and proves to be stable.     

Parallel rendering of fractal surfaces

Fractal surfaces are a sueful modeling technique for terrain in computer graphics. Although an algorithm exists for ray tracing (Mandelbrot) fractal surfaces, the technique is computationally very expensive. The large degree of parallelism inherent in the problem suggests the use of parallel architectures for generating these images. We describe a parallel rendering algorithm for shared memory MIMD machines which takes advantage of image coherence to reduce computation. This algorithm has, on a Sequent Balance 2100 with 20 processors, demonstrated a near-linear speedup. We examine the possible synchronization bottlenecks by statically assigning different numbers of CPUs to sections of the screen.This work was supported in part by DARPA under contract MDA903-86-C-0182.     

一种NURBS曲面拟合精度的量化评测算法

曲面重构是逆向工程中的核心技术之一,由于NURBS曲面在光顺性和局部可编辑等方面所具有的优点,使其成为点云数据自由曲面重构的常见形式。目前对NURBS曲面重构技术的研究上取得了一些成果,但各方法在拟合精度和效果上各有参差,因此有必要对NURBS曲面拟合精度评价算法进行研究。在采用NURBS实现曲面拟合的基础上,对拟合精度的量化指标进行研究,设计了一种基于区域划分的搜索迭代算法,可快速地计算得到原始点云与NURBS曲面的偏差。     

Efficient parallel spatial subdivision algorithm for object-based parallel ray tracing

Parallel ray tracing of complex scenes on multicomputers requires the distribution of both computation and scene data to the processors. This is carried out during preprocessing and usually consumes too much time and memory. The paper presents an efficient parallel subdivision algorithm that decomposes a given scene into rectangular regions adaptively and maps the resultant regions to the node processors of a multicomputer. The proposed algorithm uses efficient data structures to identify the splitting planes quickly. Furthermore the mapping of the regions and the objects to the node processors is performed while parallel spatial subdivision proceeds. The proposed algorithm is implemented on an Intel iPSC/2 hypercube multicomputer and promising results have been obtained.     

An improved rendering technique for ray tracing Bézier and B‐spline surfaces

Both numerical and subdivision methods are widely used approaches for ray tracing parametric surfaces. However, the expense of finding the ray–surface intersection points is a major drawback. Thus, simpler and less memory‐intensive strategies are needed to improve these methods without further complicating them. This work presents an efficient algorithm for enhancing the performance of both numerical and subdivision methods. The proposed technique can be extended to most applications based on these two methods. The computational time of both approaches is improved by 16–40%. Copyright © 2000 John Wiley & Sons, Ltd.     

地磁场条件下短波三维射线追踪仿真研究

为了分析电离层不均匀特性和地磁场对电波传播路径的影响,从Haselgrove射线方程出发,采用国际参考电离层和国际地磁参考场模型计算等离子体参数和磁参数,运用龙格库塔法求解射线方程,实现了短波三维射线追踪.通过采用三维射线追踪对均匀和不均匀电离层模型下射线路径计算并描迹,对比分析得出:不考虑电离层不均匀性将对射线路径造成较大地面距离误差.采用三维射线追踪对有无地磁场影响下的射线路径进行计算,仿真结果表明,地磁场存在时射线路径发生偏离且偏离方向及大小均不同.     

Trimmed NURBS曲面参数域的快速三角化算法

本文介绍对裁剪后的ＮＵＲＢＳ曲面参数域的一个简单、快速的三角划分算法．该算法首先对参数域进行初始划分，然后对初始划分中的每个三角形进行取舍判断或裁剪，保留参数域内的部分，丢弃参数域外的部分．为了提高速度，本算法采用了近似参数域边界线、避免无效计算及避免重复计算等措施．测试所得的数据表明，三角划分的时间与划分数成线性关系．