The Priority Face Determination Tree for Hidden Surface Removal

Many virtual environments are built from a set of polygons that form the basis of objects in the scene. Using priority-list algorithms, the sequence in which these polygons are drawn is dependent upon the location of an observer; the polygons must be ordered correctly before a realistic image can be displayed. It is necessary for a scene to be drawn correctly in real time from all locations before the observer can move interactively around the scene with complete freedom.
The binary-space partitioning (BSP) tree developed by Fuchs, Kedem and Naylor in 1980 stores the view independent priority of a set of polygons which can be used to obtain the correct order for any given view-point. However, the number of polygons grows significantly due to the BSP splitting stage, increasing the number of nodes in the tree. This affects linearly the number of tests necessary to traverse the tree to obtain the priority of the set of polygons.
The algorithm presented here is built using its associated BSP tree, but attempts to reduce the number of tests to, log_4/3 n , at the cost of a tree of size of O ( N 1.5^{log4/3 n −1}), where n is the initial number of polygons in the scene, and N the resulting number after BSP splitting. To achieve the increase in run-time efficiency, a height plane is used to restrict the view point of the observer to a fixed height, but the key to the efficiency of the algorithm is in the use of polygonal dependencies . In the scene; if we know our location relative to the front or back of a polygon, then our position relative to one-quarter of the remaining polygons, in the expected worst-case, can be determined.     

A comparison of three shadow volume algorithms

This paper describes and compares three different approaches to computing shadows. Each is based on the idea of shadow volumes: basic algorithm, Shadow Volume BSP Tree algorithm, and Shadow Tiling, based on 2D space subdivision. Binary Space Partition trees are used to organise the polygons in the scene in a front-toback order from the point of view of the light source, and then shadows on a polygon are computed by clipping the polygon to the shadow volumes of polygons closer to the light source. The three algorithms differ in their approach to minimising the number of comparisons of a polygon with the shadow volumes of its predecessors, and one of the algorithms represents the total shadow volume itelf by a BSP tree. The algorithms are compared analytically and statistically.     

基于深度缓存和BSP树技术的表面消隐技术研究

主要介绍了两种消隐技术,深度缓存算法是通过两个缓存来实现的,其中的一个是用来存放颜色的颜色缓存器,而另一个是用来存放深度的深度缓存器。BSP就是二叉空间分区树,将视景中要显示的多边形或者实物,使用二叉树的原理组织成一种数据结构,通过这种数据结构存储多边形(实物)。     

基于BSP树的启发式阴影生成算法

阴影的生成在虚拟现实领域一直是个难题,特别是针对动态光源的大规模场景,目前还没有较成熟的阴影算法。通过对现有阴影生成算法和场景组织算法的研究,该文提出了基于二维空间分割树(BSP树)的启发式阴影生成算法:首先创建场景BSP树,随着观察者视点的改变,选取视剪裁体内的节点创建以光源为视点的遮挡体BSP树,然后通过对该BSP树的遍历拣选出阴影启发区内的物体,经过处理后BSP树只留下一些生成阴影必要的多边形大大减少了计算量,最后能够快速生成阴影。     

基于凸剖分的多边形窗口线裁剪算法

以不增加新点的方式将多边形剖分为一些凸多边形,并基于这些多边形的边建立二叉树进行管理.裁剪计算时,根据二叉树快速地找到与被裁剪线有相交的凸多边形,然后运用高效的凸多边形裁剪算法进行线裁剪.该方法能自适应地降低裁剪计算的复杂度,使其在O(logn)和O(n)之间变化,并在大多数情况下小于O(n),其中n是多边形边数.虽然该方法需要进行预处理,但在许多应用(如多边形窗口对多边形的裁剪)中,其总执行时间(包括预处理时间和裁剪时间)比已有的不需要预处理的裁剪算法少很多.     

一种改进的点在多边形内外判断算法

为解决多边形内外算法中BSP树退化为链表的问题,提出一种改进的点在多边形内外的判断算法。在构建水平扫描线的BSP树之前,对水平扫描线按照Y值进行排序,将排好序的水平扫描线按照二分法的顺序插入到BSP树中,其查找时间复杂度为O(lbn)。实验结果表明,该算法在不增加BSP构建时间复杂度的前提下,能够保证BSP树的查找效果总是最优的,且简单易行,具有较好的通用性。     

Improved Binary Space Partition merging

This paper presents a new method for evaluating boolean set operations between Binary Space Partition (BSP) trees. Our algorithm has many desirable features, including both numerical robustness and O(n) output sensitive time complexity, while simultaneously admitting a straightforward implementation. To achieve these properties, we present two key algorithmic improvements. The first is a method for eliminating null regions within a BSP tree using linear programming. This replaces previous techniques based on polygon cutting and tree splitting. The second is an improved method for compressing BSP trees based on a similar approach within binary decision diagrams. The performance of the new method is analyzed both theoretically and experimentally. Given the importance of boolean set operations, our algorithms can be directly applied to many problems in graphics, CAD and computational geometry.     

An Efficient Adaptive Algorithm for Constructing the Convex Differences Tree of a Simple Polygon

The convex differences tree (CDT) representation of a simple polygon is useful in computer graphics, computer vision, computer aided design and robotics. The root of the tree contains the convex hull of the polygon and there is a child node recursively representing every connectivity component of the set difference between the convex hull and the polygon. We give an O(n log K + K log² n) time algorithm for constructing the CDT, where n is the number of polygon vertices and K is the number of nodes in the CDT. The algorithm is adaptive to a complexity measure defined on its output while still being worst case efficient. For simply shaped polygons, where K is a constant, the algorithm is linear. In the worst case K = O(n) and the complexity is O(n log² n). We also give an O(n log n) algorithm which is an application of the recently introduced compact interval tree data structure.     

用于索引视域的凸多边形树

智能手机等设备在拍摄照片和录制视频时会将拍摄位置和光学参数记录到影像文件中,可以提取并利用这些信息,在二维平面空间中还原出图片所对应的扇形视域(field-of-view,FOV).将影像文件及其对应的FOV存储在计算机中,用来支持用户对影像文件的空间查询.一种典型的空间查询是用户在地图上指定查询区域,计算机找出拍摄到...     

Polygon visibility ordering via Voronoi diagrams

Visibility determination is one of the oldest problems in computer graphics. The visibility, in terms of back-to-front polygon visibility ordering, is determined by updating a priority list as the viewpoint moves. A new list-priority algorithm, utilizing a property of Voronoi diagrams, is proposed in this paper. The operation is in two phases. First, in a pre-processing phase the scene is divided into Voronoi cells. A sub-list associated with each cell contains references to those polygons that intersect with it. The polygons are assigned a fixed set of view-independent priority orders within the cluster. Last, an interactive phase sorts the clusters according to the depth value of each Voronoi site. The most time-consuming work is performed during the pre-processing phase that only has to be executed once for the scene. Since all the polygons in a cell are pre-computed to obtain the fixed priority order within the cluster, a relatively simple task is left in the interactive phase, which is only to sort the clusters repeatedly when the viewpoint is changed. This method contains performance benefits that make it better shaped than previous BSP based methods.     

An exact algorithm for minimizing vertex guards on art galleries

We consider the problem [art gallery problem (AGP)] of minimizing the number of vertex guards required to monitor an art gallery whose boundary is an n‐vertex simple polygon. In this paper, we compile and extend our research on exact approaches for solving the AGP. In prior works, we proposed and tested an exact algorithm for the case of orthogonal polygons. In that algorithm, a discretization that approximates the polygon is used to formulate an instance of the set cover problem, which is subsequently solved to optimality. Either the set of guards that characterizes this solution solves the original instance of the AGP, and the algorithm halts, or the discretization is refined and a new iteration begins. This procedure always converges to an optimal solution of the AGP and, moreover, the number of iterations executed highly depends on the way we discretize the polygon. Notwithstanding that the best known theoretical bound for convergence is Θ(n³) iterations, our experiments show that an optimal solution is always found within a small number of them, even for random polygons of many hundreds of vertices. Herein, we broaden the family of polygon classes to which the algorithm is applied by including non‐orthogonal polygons. Furthermore, we propose new discretization strategies leading to additional trade‐off analysis of preprocessing vs. processing times and achieving, in the case of the novel Convex Vertices strategy, the most efficient overall performance so far. We report on experiments with both simple and orthogonal polygons of up to 2500 vertices showing that, in all cases, no more than 15 minutes are needed to reach an exact solution, on a standard desktop computer. Ultimately, we more than doubled the size of the largest instances solved to optimality compared with our previous experiments, which were already five times larger than those previously reported in the literature.     

基于中介面加快光线跟踪计算

提出一种新的光线跟踪方法,以提高光线找到相交面片的效率.它在场景中生成一些面积较大的规整中介面片,然后为中介面上的每个点建立一个场,以记录到达该点的不同方向的光线将相交的面片.由此,光线跟踪时,一条光线可方便地找到相交的中介面,并通过查找中介面上所记录的内容,就能得到它所相交的面片.与已有方法相比,新方法不仅能很好加速主光线与阴影光线的计算,而且能很好地加速反射、折射等二次光线的计算.它能在GPU上方便地实现,并能有效地处理动态场景.     

Approximate Guarding of Monotone and Rectilinear Polygons

We show that vertex guarding a monotone polygon is NP-hard and construct a constant factor approximation algorithm for interior guarding monotone polygons. Using this algorithm we obtain an approximation algorithm for interior guarding rectilinear polygons that has an approximation factor independent of the number of vertices of the polygon. If the size of the smallest interior guard cover is OPT for a rectilinear polygon, our algorithm produces a guard set of size O(OPT ²).     

基于凸片段分解的多边形窗口线裁剪算法

将多边形窗口的边顺序地分割成一些片段,使得每个片段都能局部地形成一个凸多边形,称为凸片段,并建立一个二叉树来管理这些凸片段．在裁剪计算时,先根据二叉树快速地找到与被裁剪线段相交的凸片段,再利用高效的凸多边形线裁剪算法对这些凸片段进行裁剪操作．文中算法能有效地降低裁剪计算的时间复杂度,使其在O（logN）～O（N）之间自适应地变化,且大部分情况下时间复杂度小于O（N）．     

Computing Dynamic Changes to BSP Trees

This paper investigates a new method for dynamically changing Binary Space Partition (BSP) trees. A BSP tree representation of a 3D polygonal scene provides an ideal data structure for rapidly performing the hidden surface computations involved in changing the viewpoint. However, BSP trees have generally been thought to be unsuitable for applications where the geometry of objects in the scene changes dynamically. The purpose of this paper is to introduce a dynamic BSP tree algorithm which does allow for such changes, and which maintains the simplicity and integrity of the BSP tree representation. The algorithm is extended to include dynamic changes to shadows. We calibrate the algorithms by transforming a range of objects in a scene, and reporting on the observed timing results.     

多连通多边形三角化找桥算法的研究及实现

已有的多边形三角化剖分算法,对多连通任意多边形的处理方法不一,算法大多复杂,可靠性低,而且往往只适合于特定的多边形剖分。本文结合现有的多边形三角剖分算法,提出了一个简洁高效、高可靠性的多连通任意多边形三角化剖分的找桥算法,该算法可用于各种多连通任意多边形的三角化剖分处理,并且成功运用于本单位研制开发的城市三维数码景观系统中,收到了较好的效果。     

Industrial strength polygon clipping: A novel algorithm with applications in VLSI CAD

We present an algorithm to compute the topology and geometry of an arbitrary number of polygon sets in the plane, also known as the map overlay. This algorithm can perform polygon clipping and related operations of interest in VLSI CAD. The algorithm requires no preconditions from input polygons and satisfies a strict set of post conditions suitable for immediate processing of output polygons by downstream tools. The algorithm uses sweepline to compute a Riemann–Stieltjes integral over polygon overlaps in O((n+s)log(n)) time given n polygon edges with s intersections. The algorithm is efficient and general, handling degenerate inputs implicitly. Particular care was taken in implementing the algorithm to ensure numerical robustness without sacrificing efficiency. We present performance comparisons with other polygon clipping algorithms and give examples of real world applications of our algorithm in an industrial software setting.     

Front-to-back display of BSP trees

A technique for displaying binary space partitioning (BSP) trees that is faster than the usual back-to-front display method is presented. By combining polygon scan-conversion with a dynamic screen data structure, the technique, a front-to-back approach, provides significant speedup in the display time of polygonal scenes that depend on BSP trees, especially in cases where the number of polygons is large. This speedup is confirmed by applying the technique to randomly generated triangles     

基于点索引的网格模型的层次结构

针对稠密采样的网格模型．提出一种基于面片中心点索引的新的场景BSP树结构．与常规RSP树构造方式不同,文中RSP树以面片中心点位置作为场景中各面片二叉分类的依据,避免了常规BSP树构造方法中因分割与削分平面相交的面片引起的场景复杂度的增加,大大简化了BSP树的构造过程．实验结果表明：对稠密网格场景,文中的BSP树比常规方式构造的BSP树任加速光线跟踪算法中的求交测试具有明显的优势．     

Optimal BSR Solutions to Several Convex Polygon Problems

This paper focuses on BSR (Broadcasting with Selective Reduction) implementation of algorithms solving basic convex polygon problems. More precisely, constant time solutions on a linear number, max(N, M) (where N and M are the number of edges of the two considered polygons), of processors for computing the maximum distance between two convex polygons, finding critical support lines of two convex polygons, computing the diameter, the width of a convex polygon and the vector sum of two convex polygons are described. These solutions are based on the merging slopes technique using one criterion BSR operations.