基于快速求交的自适应光线投射法

光线投射是一个重要的体绘制算法，但直线上采样点的确定是非常费时的，也是影响体绘制实时性的重要因素。该文利用直线和平面族的交点可以快速求得直线上的采样点及其特征值，该方法充分利用了直线的相关性，避免了大量的三线性插值计算。该文还基于快速求交提出了自适应采用方法，以提高绘制图像的质量。     

Interactive point-based isosurface exploration and high-quality rendering

We present an efficient point-based isosurface exploration system with high quality rendering. Our system incorporates two point-based isosurface extraction and visualization methods: edge splatting and the edge kernel method. In a volume, two neighboring voxels define an edge. The intersection points between the active edges and the isosurface are used for exact isosurface representation. The point generation is incorporated in the GPU-based hardware-accelerated rendering, thus avoiding any overhead when changing the isovalue in the exploration. We call this method edge splatting. In order to generate high quality isosurface rendering regardless of the volume resolution and the view, we introduce an edge kernel method. The edge kernel upsamples the isosurface by subdividing every active cell of the volume data. Enough sample points are generated to preserve the exact shape of the isosurface defined by the trilinear interpolation of the volume data. By employing these two methods, we can achieve interactive isosurface exploration with high quality rendering.     

应用于传递函数设定的交互式体绘制工具

传递函数是体绘制过程中用以定出体数据与光学特征的对应关系,因此,传递函数的设定对成像质量有着直接的影响,文章提出一应用于传递函数设定、简单且有效的交互式体绘制工具,由于二维纹理硬件在通用的个人计算机上被普遍使用,因而该工具采用基于二维纹理硬件的体绘制方法,利用本工具,用户能根据体数据的直方图来交互地分别设定R、G、B和A四种传递函数,以定出体数据与光学特征的对应关系,并获得实时的反馈视觉信息(绘制结果),该工具亦提供一虚拟轨迹球让用户交互地改变观察体数据的视点,用户不但可以交互地控制放大或缩小比率来绘制体数据,还可以选择采用光照或由多重纹理实现的三线性插值来获得不同的绘制效果,该文描述开发此工具的各种技术,并给出利用此工具得到的一些绘制结果。     

VDVR: verifiable visualization of projection-based data

Practical volume visualization pipelines are never without compromises and errors. A delicate and often-studied component is the interpolation of off-grid samples, where aliasing can lead to misleading artifacts and blurring, potentially hiding fine details of critical importance. The verifiable visualization framework we describe aims to account for these errors directly in the volume generation stage, and we specifically target volumetric data obtained via computed tomography (CT) reconstruction. In this case the raw data are the X-ray projections obtained from the scanner and the volume data generation process is the CT algorithm. Our framework informs the CT reconstruction process of the specific filter intended for interpolation in the subsequent visualization process, and this in turn ensures an accurate interpolation there at a set tolerance. Here, we focus on fast trilinear interpolation in conjunction with an octree-type mixed resolution volume representation without T-junctions. Efficient rendering is achieved by a space-efficient and locality-optimized representation, which can straightforwardly exploit fast fixed-function pipelines on GPUs.     

基于GPU的海量离散点高程并行插值算法

提出一种基于GPU的高程并行插值算法,实现了对三维地表上海量离散点的并行加速渲染。通过高程纹理组织三维地表网格高程数据作为离散点渲染的基础,并通过GLSL编写GPU着色器程序动态控制图形渲染管线,实现视点相关的高程并行插值算法。实验结果表明,提出的基于GPU的高程并行插值算法较传统的内存插值算法,将三维地表上海量离散点的渲染量级从百万级提高到了千万级。     

Interactive High-Quality Maximum Intensity Projection

Maximum Intensity Projection (MIP) is a volume rendering technique which is used to visualize high-intensity structures within volumetric data. At each pixel the highest data value, which is encountered along a corresponding viewing ray is depicted. MIP is, for example, commonly used to extract vascular structures from medical data sets (angiography). Due to lack of depth information in MIP images, animation or interactive variation of viewing parameters is frequently used for investigation. Up to now no MIP algorithms exist which are of both interactive speed and high quality. In this paper we present a high-quality MIP algorithm (trilinear interpolation within cells), which is up to 50 times faster than brute-force MIP and at least 20 times faster than comparable optimized techniques. This speed-up is accomplished by using an alternative storage scheme for volume cells (sorted by value) and by removing cells which do not contribute to any MIP projection (regardless of the viewing direction) in a preprocessing step. Also, a fast maximum estimation within cells is used to further speed up the algorithm.     

One Step Further Beyond Trilinear Interpolation and Central Differences: Triquadratic Reconstruction and its Analytic Derivatives at the Cost of One Additional Texture Fetch

Recently, it has been shown that the quality of GPU-based trilinear volume resampling can be significantly improved if the six additional trilinear samples evaluated for the gradient estimation also contribute to the reconstruction of the underlying function [Csé19]. Although this improvement increases the approximation order from two to three without any extra cost, the continuity order remains C⁰. In this paper, we go one step further showing that a C¹ continuous triquadratic B-spline reconstruction and its analytic partial derivatives can be evaluated by taking only one more trilinear sample into account. Thus, our method is the first volume-resampling technique that is nearly as fast as trilinear interpolation combined with on-the-fly central differencing, but provides a higher-quality reconstruction together with a consistent analytic gradient calculation. Furthermore, we show that our fast evaluation scheme can also be adapted to the Mitchell-Netravali [MN88] notch filter, for which a fast GPU implementation has not been known so far.     

Time and Space Optimal Data Parallel Volume Rendering Using Permutation Warping

In this paper we present a data parallel volume rendering algorithm that possesses numerous advantages over prior published solutions. Volume rendering is a three-dimensional graphics rendering algorithm that computes views of sampled medical and simulation data, but has been much slower than other graphics algorithms because of the data set sizes and the computational complexity. Our algorithm usespermutation warpingto achieve linear speedup (run time is O(S/P) forPprocessors whenP\= O(S/logS) forS\=n³samples), linear storage (O(S)) for large data sets, arbitrary view directions, and high-quality filters. We derived a new processor permutation assignment of five passes (our prior known solution was eight passes), and a new parallel compositing technique that is essential for scaling linearly on machines that have more processors than view rays to process (P>n²). We show a speedup of 15.7 for a 16k processor over a 1k processor MasPar MP-1 (16 is linear) and two frames/second with a 128³volume and trilinear view reconstruction. In addition, we demonstrate volume sizes of 256³, constant run time over angles 5 to 75°, filter quality comparisons, and communication congestion of just 19 to 29\%.     

快速3维坐标变换的绘制算法

目的 基于深度图的绘制(DIBR)是一种新型的虚拟视点生成技术,在诸多方面得到了广泛的应用。然而,该技术还不能满足实时性的绘制需求。为了在保证绘制质量不下降的前提下,尽可能地提高绘制速度,提出了一种高效的3D-Warping(3维坐标变换)算法。方法 主要在以下3个方面进行了改进:1)引入了深度—视差映射表技术,避免了重复地进行视差求取操作。2)对深度平坦的像素块进行基于块的3D-Warping,减少了映射的次数。对深度非平坦像素块中的像素点采取传统的基于像素点的3D-Warping,保证了映射的准确性。3)针对两种不同的3D-Warping方式,分别提出了相应的插值算法。在水平方向上,改进的像素插值算法对紧邻插值和Splatting(散射)插值算法进行了折中,只在映射像素点与待插值像素点很近的情况下才进行紧邻插值,否则进行Splatting插值;在深度方向上,它对Z-Buffer(深度缓存)技术进行了改进,舍弃了与前景物体太远的映射像素点,而对其他映射像素点按深度值进行加权操作。结果 实验结果表明,与标准绘制方案的整像素精度相比,绘制时间平均节省了72.05%;与标准绘制方案的半像素精度相比,PSNR平均提高了0.355dB,SSIM平均提高了0.00115。结论 改进算法非常适用于水平设置相机系统的DIBR技术中的整像素精度绘制,对包含大量深度平坦区域的视频序列效果明显,不但能够提高绘制的速度,而且可以有效地改善绘制的客观质量。     

Incremental Volume Rendering Using Hierarchical Compression

We present a new algorithm here for efficient incremental rendering of volumetric datasets. The primary goal of this algorithm is to give average workstations the ability to efficiently render volume data received over relatively low bandwidth network links in such a way that rapid user feedback is maintained. Common limitations of workstation rendering of volume data include: large memory overheads, the requirement of expensive rendering hardware, and high speed processing ability. The rendering algorithm presented here overcomes these problems by making use of the efficient Shear-Warp Factorisation method which does not require specialised graphics hardware. However the original Shear-Warp algorithm suffers from a high memory overhead and does not provide for incremental rendering which is required should rapid user feedback be maintained. Our algorithm represents the volumetric data using a hierarchical data structure which provides for the incremental classification and rendering of volume data. This exploits the multiscale nature of the octree data structure. The algorithm reduces the memory footprint of the original Shear-Warp Factorisation algorithm by a factor of more than two, while maintaining good rendering performance. These factors make our octree algorithm more suitable for implementation on average desktop workstations for the purposes of interactive exploration of volume models over a network. Results from tests using typical volume datasets will be presented which demonstrate the ability of the algorithm to achieve high rendering rates for both incremental rendering and standard rendering while reducing the runtime memory requirements.     

An Incremental Alignment Algorithm for Parallel Volume Rendering

This paper introduces a data distribution scheme and an alignment algorithm for parallel volume rendering. The algorithm performs a single wrap-around shear transformation which requires only a regular inter-processor communication pattern. The alignment can be implemented incrementally consisting of short distance shifts, thus significantly reducing the communication overhead. The alignment process is a non-destructive transformation, consisting of a single non-scaling shear operation. This is a unique feature which provides the basis for the incremental algorithm.     

基于K-Means++聚类的体绘制高维传递函数设计方法

如何将体数据中重要的信息高质量地绘制出来是医学可视化急需解决的问题。基于高维直方图的高维传递函数交互设计法是目前流行的方法,但是该方法设计复杂且效果不理想。针对高维特征的传递函数设计问题,提出一个基于改进的K均值(K-Means++)聚类的高维传递函数自动设计与交互式的体绘制方法：首先,对三维数据场进行特征提取;然后,采用基于K-Means++聚类的传递函数自动生成方法;最后,提供便捷的交互式界面给用户进行调整。还利用基于图形处理器(GPU)的体绘制方法,充分利用图形卡的强大并行计算能力,达到实时绘制的效果。实验结果表明,该方法能消除高维传递函数设计的复杂性,并且能有效地融合多种人体组织结构特征,提高渲染效果。     

Volume rendering of unstructured hexahedral meshes

Important engineering applications use unstructured hexahedral meshes for numerical simulations. Hexahedral cells, when compared to tetrahedral ones, tend to be more numerically stable and to require less mesh refinement. However, volume visualization of unstructured hexahedral meshes is challenging due to the trilinear variation of scalar fields inside the cells. The conventional solution consists in subdividing each hexahedral cell into five or six tetrahedra, approximating a trilinear variation by a nonadaptive piecewise linear function. This results in inaccurate images and increases the memory consumption. In this paper, we present an accurate ray-casting volume rendering algorithm for unstructured hexahedral meshes. In order to capture the trilinear variation along the ray, we propose the use of quadrature integration. A set of computational experiments demonstrates that our proposal produces accurate results, with reduced memory footprint. The entire algorithm is implemented on graphics cards, ensuring competitive performance. We also propose a faster approach that, as the tetrahedron subdivision scheme, also approximates the trilinear variation by a piecewise linear function, but in an adaptive and more accurate way, considering the points of minimum and maximum of the scalar function along the ray.     

High‐quality rendering of smooth isosurfaces

Animation and visualization of rectilinear data require interpolation schemes for smooth image generation. Piecewise trilinear interpolation, the de facto standard for interpolating rectilinear data, usually leads to significant visual artifacts in the resulting imagery. These artifacts reduce the confidence in the resulting visualization and may even lead to false interpretations of the data. This paper is concerned with the generation of smooth isosurface image sequences, obtained by casting rays through the image plane and computing their intersections with an isosurface. We describe a novel solution to this problem: we replace trilinear interpolation by tricubic interpolation, smoothing out the artifacts in the images; and we simplify the ray–isosurface intersection calculations by rotating and resampling the original rectilinear data in a second rectilinear grid—a grid with one family of grid planes parallel to the image plane. Our solution significantly reduces artifacts in individual images and leads to smooth animations. Copyright © 1999 John Wiley & Sons, Ltd.     

多层次并行体绘制算法的研究与应用

三维数据场的体绘制技术是科学可视化中一个重要的研究方向,本文在研究和总结体绘制的发展历程与关键技术的基础之上,着重研究了体绘制中的光线投射算法,结合多核处理器机群系统,提出并实现了一种基于多层次并行编程模型的并行光线投射体绘制算法,并成功地将该算法应用于三维城市浅层地质模型,取得了良好的可视化效果。分别对MPI环境和多层次并行编程MPI+OpenMP环境下的光线投射算法进行了不同计算规模的性能比较实验。实验和分析表明,多层次并行光线投射体绘制算法加快了体绘制的速度,MPI+OpenMP多层次并行模型性能高于纯MPI编程模型的性能。     

On marching cubes

A characterization and classification of the isosurfaces of trilinear functions is presented. Based upon these results, a new algorithm for computing a triangular mesh approximation to isosurfaces for data given on a 3D rectilinear grid is presented. The original marching cubes algorithm is based upon linear interpolation along edges of the voxels. The asymptotic decider method is based upon bilinear interpolation on faces of the voxels. The algorithm of this paper carries this theme forward to using trilinear interpolation on the interior of voxels. The algorithm described here will produce a triangular mesh surface approximation to an isosurface which preserves the same connectivity/separation of vertices as given by the isosurface of trilinear interpolation.     

三维地震数据场的并行体绘制算法

光线投射算法是一种应用广泛的体绘制基本算法,其存在的主要问题是绘制速度较慢.为了提高光线投射算法的绘制速度,利用光线间和光线内的并行性,结合三维地震数据场的特点和文件存储特性,提出了一种基于工作站机群的三维地震数据场的并行体绘制算法.地震油气解释实际应用表明本算法能满足地震解释的要求.     

FDGE: A forward-difference grid engine and its application in rendering algebraic surfaces in parallel

The display of an implicitly defined surface is obtained by its projection onto the viewing plane. Ray casting is a technique that accomplishes this projection byfiring a mapping ray through each pixel of the screen into the world space. The intersection points of this ray with the surface are found; these points are further tested to determine which one is visible and is within the viewing volume. Finally, if a point that satisfies the above conditions is found, then the point is further processed for the determination of its shading value.Much progress in rendering algebraic surfaces has been made recently. However, most of the proposed solutions are based on subdivision methods. This paper focuses on a method that performsdirect rendering of such a surface that will minimize the number of operations; this method will also replace almost all required multiplications with additions. Furthermore, the VLSI-oriented algorithm lends itself to parallelism. In addition, how this method can be used in the calculation of the shading values is described and a VLSI architecture is briefly discussed. Finally, a by-product of this method is that it can be used to efficiently calculate the values of a bivariate polynomial in a rectangular grid and in parallel.     

Incremental Polygonization of Implicit Surfaces

This paper describes an incremental polygonization technique for implicit surfaces built from skeletal elements. Our method is dedicated to fast previewing in an interactive modeling system environment. We rely on an octree decomposition of space combined with Lipschitz conditions to recursively subdivide cells until a given level of precision is reached and converge to the implicit surface. We use a trilinear interpolation approximation of the field function to create a topologically consistent tessellation characterized by an adjacency graph. Our algorithm aims at updating the mesh locally in regions of space where changes in the potential field occurred. Therefore, we propose an octree inflating and deflating strategy to preserve the octree structure as much as possible and to avoid useless or redundant computations. Timings show that our incremental algorithm dramatically speeds up the overall polygonization process for complex objects.     

非规则数据场并行体绘制算法

并行算法是实现体绘制加速的重要途径，然而现有的并行体制绘制算法大部分是针对规则数据场的。