按曲率选取基点的多分辨率表示重构算法

通过曲率引导选取一组基面来完成Eck等提出的任意拓扑三角网格多分辨率表示重构算法中的Voronoi划分．在提高效率的同时,可在相同网格规模下取得更好的重构质量;在重采样过程中以粗网格的Loop细分来指导参数域的细分,减轻了原算法因线性细分而产生的块状分界现象．最后提出一种自适应细分重采样技术,以减少数据冗余．     

一种基于可见边的平面细分遍历算法

文章描述了一种基于可见边的平面细分遍历算法。该算法不需要增加标志位,也不需要堆栈和队列,只使用O(1)的辅助内存空间,并且充分利用了边的可见性。对于面集为F、每个面f具有f条边的平面细分,该算法最多进行f∈F∑4·f·lnf2次边的比较。理论分析和实际运行结果都表明,该算法与同类遍历算法相比速度要快得多。     

二叉判定图最优化算法研究综述

对近年来二叉判定图(BDD)最优化算法的成果和发展趋势进行了综述和讨论，重点介绍精确排序算法和动态启发式排序算法．给出了BDD优化算法的改进建议：用不完全枚举法的优势和随机过程动态规划策略改进BDD优化算法．     

一种平面点集Voronoi 图的细分算法

Voronoi 图是计算几何中的重要概念之一,在计算机图形学、计算几何、计算机辅助几何设计、有限元网格划分、机器人轨迹控制、模式识别、气象学和地质学研究中得到广泛应用。借助于四叉树和区间算术,提出了一种新的构造平面点集Voronoi 图的细分算法, 并且和经典的增量算法、栅格扩张法进行了比较, 结果显示新细分算法更为有效。最重要的是细分算法原理简单,很容易编程实现。     

Region-expansion for the Voronoi diagram of 3D spheres

Given a set of spheres in 3D, constructing its Voronoi diagram in Euclidean distance metric is not easy at all even though many mathematical properties of its structure are known. This Voronoi diagram has been known for many important applications from science and engineering. In this paper, we characterize the Voronoi diagram of spheres in three-dimensional Euclidean space, which is also known as an additively weighted Voronoi diagram, and propose an algorithm to construct the diagram. Starting with the ordinary Voronoi diagram of the centers of the spheres, the proposed region-expansion algorithm constructs the desired diagram by expanding the Voronoi region of each sphere, one after another. We also show that the whole Voronoi diagram of n spheres can be constructed in O(n³) time in the worst case.     

Improved perspective visibility ordering for object-order volume rendering

Finding a correct a priori back-to-front (BTF) visibility ordering for the perspective projection of the voxels of a rectangular volume poses interesting problems. The BTF ordering presented by Frieder et al. [6] and the permuted BTF presented by Westover [14] are correct for parallel projection but not for perspective projection [12]. Swan presented a constructive proof for the correctness of the perspective BTF (PBTF) ordering [12]. This was a significant improvement on the existing orderings. However, his proof assumes that voxel projections are not larger than a pixel, i.e. voxel projections do not overlap in screen space. Very often the voxel projections do overlap, e.g. with splatting algorithms. In these cases, the PBTF ordering results in highly visible and characteristic rendering artefacts. In this paper we analyse the PBTF and show why it yields these rendering artefacts. We then present an improved visibility ordering that remedies the artefacts. Our new ordering is as good as the PBTF, but it is also valid for cases where voxel projections are larger than a single pixel, i.e. when voxel projections overlap in screen space. We demonstrate why and how our ordering works at fundamental and implementation levels.     

移动点Voronoi图拓扑维护策略的研究

移动环境下基于Voronoi图的最近邻查询必须要解决随时间不断改变的移动点Voronoi图的拓扑结构的维护问题。通过一组离散的,有限的事件序列对其对偶图Delaunay图拓扑改变过程的模拟来实现对移动点Voronoi图拓扑结构的维护。把带有事件驱动机制的移动数据结构（Kinetic Data Structure,KDS）模型作为移动点的运动模型,给出了KDS模型对其对偶图Delaunay图拓扑结构改变维护的具体策略,并对移动环境下动态插入或删除移动点时Voronoi图的拓扑维护问题进行了研究。最后给出了移动环境下基于Voronoi图的近邻查询的数据库实现模型。     

基于Voronoi图的组最近邻查询

组最近邻查询由于涉及多个查询点,因此比传统的最近邻查询更为复杂.充分考虑查询点的分布特征以及它们构成的几何图形的性质和特点,给出组最近邻所应满足的条件及判断组最近邻的理论方法.提出基于Voronoi图的组最近邻查询的VGNN算法,可以精确求解查询点集的最近邻.对于查询点不共线的情况,该算法的查询方式是以一点为中心、向外扩张式的;对于查询点共线的情况,该算法给出搜索范围,限定了参与计算的数据点的个数.给出基于Voronoi图的VTree索引.实验结果表明,基于VTree索引的VGNN算法具有较好的性能,并且当查询点不共线时,其性能具有较高的稳定性.     

Voronoi diagrams of moving points in the plane and of lines in space: tight bounds for simple configurations

The combinatorial complexities of (1) the Voronoi diagram of moving points in 2D and (2) the Voronoi diagram of lines in 3D, both under the Euclidean metric, continues to challenge geometers because of the open gap between the Ω(n²) lower bound and the O(n3+?) upper bound. Each of these two combinatorial problems has a closely related problem involving Minkowski sums: (1′) the complexity of a Minkowski sum of a planar disk with a set of lines in 3D and (2′) the complexity of a Minkowski sum of a sphere with a set of lines in 3D. These Minkowski sums can be considered “cross-sections” of the corresponding Voronoi diagrams. Of the four complexity problems mentioned, problems (1′) and (2′) have recently been shown to have a nearly tight bound: both complexities are O(n2+?) with lower bound Ω(n²).In this paper, we determine the combinatorial complexities of these four problems for some very simple input configurations. In particular, we study point configurations with just two degrees of freedom (DOFs), exploring both the Voronoi diagrams and the corresponding Minkowski sums. We consider the traditional versions of these problems to have 4 DOFs. We show that even for these simple configurations the combinatorial complexities have upper bounds of either O(n²) or O(n2+?) and lower bounds of Ω(n²).     

Conservative occlusion culling for urban visualization using a slice-wise data structure

In this paper, we propose a framework for urban visualization using a conservative from-region visibility algorithm based on occluder shrinking. The visible geometry in a typical urban walkthrough mainly consists of partially visible buildings. Occlusion-culling algorithms, in which the granularity is buildings, process these partially visible buildings as if they are completely visible. To address the problem of partial visibility, we propose a data structure, called slice-wise data structure, that represents buildings in terms of slices parallel to the coordinate axes. We observe that the visible parts of the objects usually have simple shapes. This observation establishes the base for occlusion-culling where the occlusion granularity is individual slices. The proposed slice-wise data structure has minimal storage requirements. We also propose to shrink general 3D occluders in a scene to find volumetric occlusion. Empirical results show that significant increase in frame rates and decrease in the number of processed polygons can be achieved using the proposed slice-wise occlusion-culling as compared to an occlusion-culling method where the granularity is individual buildings.     

基于Voronoi图的点群目标普适综合算法

点要素综合算法的目的是在点数减少的情况下尽量正确地传输包含在点群中的信息,但是目前提出的两种算法均不能达到此要求,如为居民地选取的增长算法不能很好处理拓扑信息,而基于Voronoi的算法又没有考虑点的重要性程度(即点包含的专题信息)。为克服这些缺点,提出了一个新的算法。该算法采用以下两种方法确保不同信息的正确传输：(1)根据基本选取法则确保点数的正确;(2)反复构造剩余点的Voronoi图,并根据一个点与其周围点重要性程度的比较来确定其删除与否,从而使拓扑、专题和几何信息能正确传输。该算法的缺点是没有考虑点的符号化,由此可能导致地图上符号的压盖和重叠。     

Voronoi Diagram for services neighboring a highway

We are given a transportation line where displacements happen at a bigger speed than in the rest of the plane. A shortest time path is a path between two points which takes less than or equal time to any other. We consider the time to follow a shortest time path to be the time distance between the two points. In this paper, we give a simple algorithm for computing the Time Voronoi Diagram, that is, the Voronoi Diagram of a set of points using the time distance.     

Analysis of an algorithm for fast ray tracing using uniform space subdivision

Ray tracing is becoming popular as the best method of rendering high quality images from three dimensional models. Unfortunately, the computational cost is high. Recently, a number of authors have reported on ways to speed up this process by means of space subdivision which is used to minimize the number of intersection calculations. We describe such an algorithm together with an analysis of the factors which affect its performance. The critical operation of skipping an empty space subdivision can be done very quickly, using only integer addition and comparison. A theoretical analysis of the algorithm is developed. It shows how the space and time requirements vary with the number of objects in the scene.     

Using geometry to solve the transportation problem in the plane

LetU andV be two sets of points in the plane, where ¦U¦=k,¦V¦=, andn=k+. These two sets of points induce a directed complete bipartite graph in which the points represent nodes and an edge is directed from each node inU to each node in K Each edge is given a cost equal to the distance between the corresponding nodes measured by some metricd on the plane. We consider thetransportation problem on such a graph. We present an 0(n^2,5 logn logN) algorithm, whereN is the magnitude of the largest supply or demand. The algorithm uses some fundamental results of computational geometry and scaling of supplies and demands. The algorithm is valid for the ₁ metric, the ₂ metric, and the metric. The running time for the ₁ and metrics can be improved to 0(n²(logn)³ logN).D. S. Atkinson was supported by the National Science Foundation under Grant CCR90-57481PYI. P. M. Vaidya was supported by the National Science Foundation under Grants CCR-9057481 and CCR-9007195.     

大规模场景的消隐技术

计算机图形学的快速发展使处理大规模场景中的数据变得日益重要,文章主要讨论了近几年最新发展的消隐算法。     

非平均化自适应Catmull-Clark细分算法

提出一种基于网格边的光滑度计算来进行Catmull-Clark自适应细分的新算法。该方法能够在满足显示需求的前提下较好地减小细分曲面过程中的网格生成数,同时解决了由于采用网格顶点曲率计算,来实现自适应细分方法中平均化生成顶点曲率带来的不足。通过对比试验,算法能更好地区别当前细分网格中光滑与非光滑区域,增加对非光滑区域网格加密密度,并且该算法能够普遍适用于较复杂的细分模式中,具有一定的推广价值。     

Sorting helps for voronoi diagrams

It is well known that, using standard models of computation, Ω(n logn) time is required to build a Voronoi diagram forn point sites. This follows from the fact that a Voronoi diagram algorithm can be used to sort. However, if the sites are sorted before we start, can the Voronoi diagram be built any faster? We show that for certain interesting, although nonstandard, types of Voronoi diagrams, sorting helps. These nonstandard types of Voronoi diagrams use a convex distance function instead of the standard Euclidean distance. A convex distance function exists for any convex shape, but the distance functions based on polygons (especially triangles) lead to particularly efficient Voronoi diagram algorithms. Specifically, a Voronoi diagram using a convex distance function based on a triangle can be built inO (n log logn) time after initially sorting then sites twice. Convex distance functions based on other polygons require more initial sorting.     

Hadoop下面元加权Voronoi图并行算法及应用

面元加权Voronoi图是生成元为面元的加权Voronoi图。针对大规模数据情况下面元加权Voronoi图存在的计算效率不高问题,结合面元边界点提取方法,提出一种基于Hadoop云平台的面元加权Voronoi图的并行生成算法,进行了单机和集群实验。实验结果表明,算法能有效处理大规模栅格数据,明显提高面元加权Voronoi图的生成速度。还可应用于城市绿地设计规划,为绿地设计提供决策依据。