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 two viewpoints but is readable only from the viewpoint closer to the target. 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 of 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 of 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.
The notion of visibility is actively studied in different contexts: computer graphics and visualization @cite_5 @cite_22 and spatial databases @cite_15 @cite_12 @cite_13 . Most of these techniques consider visibility as a binary notion, i.e., a point is either visible or invisible from another point.
@cite_22 @cite_5 @cite_15 @cite_13 @cite_12
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This paper describes a robust, hardware-accelerated algorithm to compute an approximate visibility map, which describes the visible scene from a particular viewpoint. The user can control the degree of approximation, choosing more accuracy at the cost of increased execution time. The algorithm exploits item buffer hardware to coarsely determine visibility, which is later refined. The paper also describes a conceptually simple algorithm to compute a subset of the discontinuity mesh using the visibility map. Algorithms and Theory of Computation Handbook, Second Edition provides an up-to-date compendium of fundamental computer science topics and techniques. It also illustrates how the topics and techniques come together to deliver efficient solutions to important practical problems. New to the Second EditionAlong with updating and revising many of the existing chapters, this second edition contains more than 20 new chapters. 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In many applications involving spatial objects, we are only interested in objects that are directly visible from query points. In this paper, we formulate the visible k nearest neighbor (VkNN) query and present incremental algorithms as a solution, with two variants differing in how to prune objects during the search process. One variant applies visibility pruning to only objects, whereas the other variant applies visibility pruning to index nodes as well. Our experimental results show that the latter outperforms the former. We further propose the aggregate VkNN query that finds the visible k nearest objects to a set of query points based on an aggregate distance function. We also propose two approaches to processing the aggregate VkNN query. One accesses the database via multiple VkNN queries, whereas the other issues an aggregate k nearest neighbor query to retrieve objects from the database and then re-rank the results based on the aggregate visible distance metric. With extensive experiments, we show that the latter approach consistently outperforms the former one. In this paper, we identify and solve a new type of spatial queries, called continuous visible nearest neighbor (CVNN) search. Given a data set P, an obstacle set O, and a query line segment q, a CVNN query returns a set of (p, R) tuples such that p e P is the nearest neighbor (NN) to every point r along the interval R e q as well as p is visible to r. Note that p may be NULL, meaning that all points in P are invisible to all points in R, due to the obstruction of some obstacles in O. In this paper, we formulate the problem and propose efficient algorithms for CVNN query processing, assuming that both P and O are indexed by R-trees. In addition, we extend our techniques to several variations of the CVNN query. Extensive experiments verify the efficiency and effectiveness of our proposed algorithms using both real and synthetic datasets. In this paper, we study a novel form of continuous nearest neighbor queries in the presence of obstacles, namely continuous obstructed nearest neighbor (CONN) search. It considers the impact of obstacles on the distance between objects, which is ignored by most of spatial queries. Given a data set P, an obstacle set O, and a query line segment q in a two-dimensional space, a CONN query retrieves the nearest neighbor of each point on q according to the obstructed distance, i.e., the shortest path between them without crossing any obstacle. We formulate CONN search, analyze its unique properties, and develop algorithms for exact CONN query processing, assuming that both P and O are indexed by conventional data-partitioning indices (e.g., R-trees). Our methods tackle the CONN retrieval by performing a single query for the entire query segment, and only process the data points and obstacles relevant to the final result, via a novel concept of control points and an efficient quadratic-based split point computation algorithm. In addition, we extend our solution to handle the continuous obstructed k-nearest neighbor (COkNN) search, which finds the k (≥1)nearest neighbors to every point along q based on obstructed distances. A comprehensive experimental evaluation using both real and synthetic datasets has been conducted to demonstrate the efficiency and effectiveness of our proposed algorithms.