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.     

多视点成像的多边形模板法

该文提出一种对场景进行多视点成像的方法。该方法首先为场景中的多边形生成多边形模板，一个多边形模板，包括一条轮廓路径和一组纹条，而一个纹条是平行成像画的一个平面与多边形相交的直线段。由于纹条相对于不同视点的透视投影的变化是线性的，因此，绘制多边形时可以基于模板逐个纹条地处理，而不必按照传统的扫描转换方法逐个点地处理，绘制速度可以提高很多。同时，与视点无关的光照和纹理可以预先计算并保存在模板中，以便在成像时利用基于图像绘制的技术来生成高质量的图像。该方法中，视点可以放置在三维空间的任意位置，并且在场景漫游时可以根据视点位置自动地实现多分辨率绘制。     

一种基于视觉约束的当前视点画面生成方法

由于视点变化中画面可见性的变化以及在当前视点物体表面的扩张,仅由一幅带深度的源参考图像的三维重投影所得到的目标视点画面存在空洞问题.为此,人们采取多源参考图像的合成方法来解决此问题.如何从具有大量冗余信息的多幅源参考图像中快速提取当前目标视点所需信息,成为基于图像的虚拟环境建模和绘制的关键技术.该文给出一种从多幅源参考图像(目前仅两幅)合成当前视点画面的算法.算法结合正向映射及逆向映射技术完成对当前视点画面的合成,并且利用视觉约束-极线约束这一性质从其他源参考图像中寻找填补空洞的像素,从而避免了整幅参考图像的重投影过程及深度比较.同时,算法利用极线对上像素的排序特性和已有目标图像的信息加速填补空洞像素的搜索.算法在不增加原有图像映射算法复杂度的基础上,大大降低了原有多幅图像合成算法的计算量.     

Accelerated Walkthroughs of Virtual Environments Based on Visibility Preprocessing and Simplification

This paper proposes a new preprocessing method for interactive rendering of complex polygonal virtual environments. The approach divides the space that observer can reach into many rectangular viewpoint regions. For each region, an outer rectangular volume (ORV) is established to surround it. By adaptively partitioning the boundary of the ORV together with the viewpoint region, all the rays that originate from the viewpoint region are divided into the beams whose potentially visible polygon number is less than a preset threshold. If a resultant beam is the smallest and intersects many potentially visible polygons, the beam is simplified as a fixed number of rays and the averaged color of the hit polygons is recorded. For other beams, their potentially visible sets (PVS) of polygons are stored respectively. During an interactive walkthrough, the visual information related to the current viewpoint is retrieved from the storage. The view volume clipping, visibility culling and detail simplification are efficiently supported by these stored data. The rendering time is independent of the scene complexity.     

结构化骨架求取和内窥可见性计算

提出了包含距离和拓扑信息的结构化骨架提取方法和骨架指导的内窥可见性计算方法,并将其有机地应用于虚拟漫游系统中.结构化骨架提取算法结合了并行细化算法和距离变换算法,使得骨架能够有效地控制虚拟内窥镜的视点移动和漫游位置的跟踪,有利于准确地观察病变位置.内窥可见性算法利用人体器官的封闭管状特征,将其分割成许多网格单元,并在预处理中使用深度缓存计算单元间的可见性,同时对每个单元建立可见性树.虚拟漫游时,通过当前视点信息可进一步动态地删减所在单元的可见性树,从而得到实时可见性,最终实现实时漫游并保持漫游图像的质量.     

Image-space visibility ordering for cell projection volume rendering of unstructured data

Projection methods for volume rendering unstructured data work by projecting, in visibility order, the polyhedral cells of the mesh onto the image plane, and incrementally compositing each cell's color and opacity into the final image. Normally, such methods require an algorithm to determine a visibility order of the cells. The meshed polyhedra visibility order (MPVO) algorithm can provide such an order for convex meshes by considering the implications of local ordering relations between cells sharing a common face. However, in nonconvex meshes, one must also consider ordering relations along viewing rays which cross empty space between cells. In order to include these relations, the algorithm described in this paper, the scanning exact meshed polyhedra visibility ordering (SXMPVO) algorithm, scan-converts the exterior faces of the mesh and saves the ray-face intersections in an A-buffer data structure which is then used for retrieving the extra ordering relations. The image which SXMPVO produces is the same as would be produced by ordering the cells exactly, even though SXMPVO does not compute an exact visibility ordering. This is because the image resolution used for computing the visibility ordering relations is the same as that which is used for the actual volume rendering and we choose our A-buffer rays at the same sample points that are used to establish a polygon's pixel coverage during hardware scan conversion. Thus, the algorithm is image-space correct. The SXMPVO algorithm has several desirable features; among them are speed, simplicity of implementation, and no extra (i.e., with respect to MPVO) preprocessing.     

VC-dimension of exterior visibility

In this paper, we study the Vapnik-Chervonenkis (VC)-dimension of set systems arising in 2D polygonal and 3D polyhedral configurations where a subset consists of all points visible from one camera. In the past, it has been shown that the VC-dimension of planar visibility systems is bounded by 23 if the cameras are allowed to be anywhere inside a polygon without holes. Here, we consider the case of exterior visibility, where the cameras lie on a constrained area outside the polygon and have to observe the entire boundary. We present results for the cases of cameras lying on a circle containing a polygon (VC-dimension=2) or lying outside the convex hull of a polygon (VC-dimension=5). The main result of this paper concerns the 3D case: We prove that the VC-dimension is unbounded if the cameras lie on a sphere containing the polyhedron, hence the term exterior visibility.     

Mapping Simple Polygons: How Robots Benefit from Looking Back

We consider the problem of mapping an initially unknown polygon of size n with a simple robot that moves inside the polygon along straight lines between the vertices. The robot sees distant vertices in counter-clockwise order and is able to recognize the vertex among them which it came from in its last move, i.e. the robot can look back. Other than that the robot has no means of distinguishing distant vertices. We assume that an upper bound on n is known to the robot beforehand and show that it can always uniquely reconstruct the visibility graph of the polygon. Additionally, we show that multiple identical and deterministic robots can always solve the weak rendezvous problem in which the robots need to position themselves such that all of them are mutually visible to each other. Our results are tight in the sense that the strong rendezvous problem, where robots need to gather at a vertex, cannot be solved in general, and, without knowing a bound beforehand, not even n can be determined. In terms of mobile agents exploring a graph, our result implies that they can reconstruct any graph that is the visibility graph of a simple polygon. This is in contrast to the known result that the reconstruction of arbitrary graphs is impossible in general, even if n is known.     

A cell-based point-in-polygon algorithm suitable for large sets of points

The paper describes a new algorithm for solving the point-in-polygon problem. It is especially suitable when it is necessary to check whether many points are placed inside or outside a polygon. The algorithm works in two steps. First, a grid of cells equal in size is generated, and the polygon is laid on that grid. A heuristic approach is proposed for cell dimensioning. The cells of the grid are marked as being inside, outside, or on the polygon border. A modified flood-fill algorithm is applied for cell classification. In the second step, points are tested individually. If the tested point falls into an inner or an outer cell, the result is returned without any additional calculations. If the cell contains the polygon border, it is possible to determine the local point position. The analysis of time complexity shows that the initialization is finished in time, while the expected time complexity for checking an individual point is , where n represents the number of polygon edges. The algorithm works with O(n) space complexity. The paper also gives practical results using artificial and real polygons from a GIS environment.     

A Unified Approach to Conic Visibility

{In this paper we present linear time algorithms for computing the shortest path tree from a point and the weak visibility polygon of an arc inside a triangulated curved polygon. We also present a linear time algorithm for computing the planar subdivision (in the parametric space) of the set of rays emanating from a fixed arc, such that each face of the subdivision corresponds to rays hitting the same arc of the polygon. Although these results, which involve nontrivial generalizations of known results for rectilinear polygons, may have some interest in its own right, the main result of this paper is a linear time algorithm for computing the conic (circular, elliptic, parabolic, and hyperbolic) visibility polygon of a point inside a simple polygon. The main advantage of our technique over previous results on circular visibility is that it provides a simple, unified approach to conic visibility. Finally, we present a linear time algorithm for computing the planar subdivision, in the parametric space, of two-parametric families of conic rays emanating from a fixed point, such that each face of the subdivision corresponds to conic rays hitting the same edge of the polygon. All these algorithms are asymptotically optimal.} Received August 21, 1997; revised December 27, 1998.     

Partitioning Trimmed Spline Surfaces into NonSelf-Occluding Regions for Visibility Computation

Computing the visible portions of curved surfaces from a given viewpoint is of great interest in many applications. It is closely related to the hidden surface removal problem in computer graphics, and machining applications in manufacturing. Most of the early work has focused on discrete methods based on polygonization or ray-tracing and hidden curve removal. In this paper we present an algorithm for decomposing a given surface into regions so that each region is either completely visible or hidden from a given viewpoint. Initially, it decomposes the domain of each surface based on silhouettes and boundary curves. To compute the exact visibility, we introduce a notion of visibility curves obtained by projection of silhouette and boundary curves and decomposition of the surface into nonoverlapping regions. These curves are computed using marching methods and we present techniques to compute all the components. The nonoverlapping and visible portions of the surface are represented as trimmed surfaces and we present a representation based on polygon trapezoidation algorithms. The algorithms presented use some recently developed algorithms from computational geometry like triangulation of simple polygons and point location. Given the nonoverlapping regions, we use an existing randomized algorithm for visibility computation. We also present results from a preliminary implementation of our algorithm.     

Lazy Visibility Evaluation for Exact Soft Shadows

This paper presents a novel approach to compute high quality and noise‐free soft shadows using exact visibility computations. This work relies on a theoretical framework allowing to group lines according to the geometry they intersect. From this study, we derive a new algorithm encoding lazily the visibility from a polygon. Contrary to previous works on from‐polygon visibility, our approach is very robust and straightforward to implement. We apply this algorithm to solve exactly and efficiently the visibility of an area light source from any point in a scene. As a consequence, results are not sensitive to noise, contrary to soft shadows methods based on area light source sampling. We demonstrate the reliability of our approach on different scenes and configurations.     

Conservative Visibility and Strong Occlusion for Viewspace Partitioning of Densely Occluded Scenes

Computing the visibility of out-door scenes is often much harder than of in-door scenes. A typical urban scene, for example, is densely occluded, and it is effective to precompute its visibility space, since from a given point only a small fraction of the scene is visible. The difficulty is that although the majority of objects are hidden, some parts might be visible at a distance in an arbitrary location, and it is not clear how to detect them quickly. In this paper we present a method to partition the viewspace into cells containing a conservative superset of the visible objects. For a given cell the method tests the visibility of all the objects in the scene. For each object it searches for a strong occluder which guarantees that the object is not visible from any point within the cell. We show analytically that in a densely occluded scene, the vast majority of objects are strongly occluded, and the overhead of using conservative visibility (rather than visibility) is small. These results are further supported by our experimental results. We also analyze the cost of the method and discuss its effectiveness.     

Road junction convex mirrors

Lateral visibility at road junctions can be improved by a convex mirror. Mainly in built-up areas, where visibility on one or both sides of an intersection may be hampered by space limitations, such a device is attractive because of its low cost and its actuated operating mode. However, little information is yet available concerning its efficiency and optimisation. The usefulness of a convex mirror from a safety viewpoint is experimentally assessed in a road junction where drivers who have to give way can observe lateral traffic through a convex mirror. Comparison is made between mirror users and non-users, in relation to their give way behaviour. The main finding is that the mirror appears as a device that enhances safety behaviour and can be recommended as a traffic aid.     

On sorting triangles in a delaunay tessellation

In a two-dimensional Delaunay-triangulated domain, there exists a partial ordering of the triangles (with respect to a vertex) that is consistent with the two-dimensional visibility of the triangles from that vertex. An equivalent statement is that a polygon that is star-shaped with respect to a given vertex can be extended, one triangle at a time, until it includes the entire domain. Arbitrary planar triangulations do not possess this useful property which allows incremental processing of the triangles.     

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.     

Conflict Neutralization on Binary Space Partitioning

The Binary Space Partitioning (BSP) tree achieves fast hidden surface removal for most practical applications where an observer can move through a scene of static objects. However, the BSP algorithm generally increases the number of polygons in a scene due to its splitting stage resulting in a detrimental effect on the priority ordering and more significantly, the display calculations (shading, lighting, shadows, etc.) of the rendering pipeline.
We present the Conflict Neutralization algorithm which attempts to reduce the number of splits more effectively than existing techniques whilst maintaining the 'standard' model of a BSP tree. Our idea is similar to Conflict Minimization proposed by Fuchs; the significant difference is that our algorithm recognizes that a polygon suitable for selection in the Minimization criterion may subsequently stop the remainder of polygons achieving some reductions in cuts—with Conflict Neutralization, such a polygon is demoted.
We compare the results of Conflict Neutralization against Conflict Minimization, the Least-crossed with Most-crossed tie-breaking criterion and our own, enhanced implementation of Conflict Minimization. We show how these techniques fall into different 'depths of analysis'.     

Computer chess move-ordering schemes using move influence

The chessmaps heuristic is a pattern-oriented approach to ordering moves for the game of chess. It uses a neural network to learn a relation between the control of the squares and the influence of a move. Depending on what squares a player controls, the chessmaps heuristic tries to determine where the important areas of the chessboard are. Moves that influence these important areas are then ordered first. The heuristic has been incorporated into a move-ordering algorithm that also takes account of immediate tactical threats. Human players also rely strongly on patterns when selecting moves, but would also consider immediate tactical threats, so this move-ordering algorithm is an attempt to mimic something of the human thought process when selecting a move. This paper presents a new definition for the influence of a move, which improves the performance of the heuristic. It also presents a new experience-based approach to determining what areas of the chessboard are important, which may actually be preferred to the chessmaps heuristic. The results from game-tree searches suggest that the move-ordering algorithm could compete with the current best alternative of using the history heuristic with capture moves in a brute-force search.     

判定凸多边形可碰撞的最优算法

设P与Q是平面内任意二互不相交的凸多边形,d为任一给定方向,本文研究P沿d以平移方式运动可否与Q碰撞的判定问题.文中定义了凸多边形顶点集上的偏序关系,给出了判定可碰撞性的新的充分必要条件,据此采用四分搜索方法构造了判定可碰撞的算法.在最坏情况下算法的复杂度为O(logn),在不计常数因子的情况下,这是最优的.     

Scalable visibility color map construction in spatial databases

Recent advances in 3D modeling provide us with real 3D datasets to answer queries, such as “What is the best position for a new billboard?” and “Which hotel room has the best view?” in the presence of obstacles. These applications require measuring and differentiating the visibility of an object (target) from different viewpoints in a dataspace, e.g., a billboard may be seen from many points but is readable only from a few points closer to it. In this paper, we formulate the above problem of quantifying the visibility of (from) a target object from (of) the surrounding area with a visibility color map (VCM). A VCM is essentially defined as a surface color map of the space, where each viewpoint of the space is assigned a color value that denotes the visibility measure of the target from that viewpoint. Measuring the visibility of a target even from a single viewpoint is an expensive operation, as we need to consider factors such as distance, angle, and obstacles between the viewpoint and the target. Hence, a straightforward approach to construct the VCM that requires visibility computation for every viewpoint of the surrounding space of the target is prohibitively expensive in terms of both I/Os and computation, especially for a real dataset comprising thousands of obstacles. We propose an efficient approach to compute the VCM based on a key property of the human vision that eliminates the necessity for computing the visibility for a large number of viewpoints of the space. To further reduce the computational overhead, we propose two approximations; namely, minimum bounding rectangle and tangential approaches with guaranteed error bounds. Our extensive experiments demonstrate the effectiveness and efficiency of our solutions to construct the VCM for real 2D and 3D datasets.