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39
Dynamic Ray Shooting and Shortest Paths in Planar Subdivisions via Balanced Geodesic Triangulations
 J. Algorithms
, 1997
"... We give new methods for maintaining a data structure that supports ray shooting and shortest path queries in a dynamicallychanging connected planar subdivision S. Our approach is based on a new dynamic method for maintaining a balanced decomposition of a simple polygon via geodesic triangles. We ma ..."
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Cited by 39 (3 self)
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We give new methods for maintaining a data structure that supports ray shooting and shortest path queries in a dynamicallychanging connected planar subdivision S. Our approach is based on a new dynamic method for maintaining a balanced decomposition of a simple polygon via geodesic triangles. We maintain such triangulations by viewing their dual trees as balanced trees. We show that rotations in these trees can be implemented via a simple "diagonal swapping" operation performed on the corresponding geodesic triangles, and that edge insertion and deletion can be implemented on these trees using operations akin to the standard split and splice operations. We also maintain a dynamic point location structure on the geodesic triangulation, so that we may implement ray shooting queries by first locating the ray's endpoint and then walking along the ray from geodesic triangle to geodesic triangle until we hit the boundary of some region of S. The shortest path between two points in the same ...
Visibility with a moving point of view
 Algorithmica
, 1994
"... We investigate 3d visibility problems in which the viewing position moves along a straight flightpath. Specifically we focus on two problems: determining the points along the flightpath at which the topology of the viewed scene changes, and answering rayshooting queries for rays with origin on the ..."
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Cited by 30 (1 self)
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We investigate 3d visibility problems in which the viewing position moves along a straight flightpath. Specifically we focus on two problems: determining the points along the flightpath at which the topology of the viewed scene changes, and answering rayshooting queries for rays with origin on the flightpath. Three progressively more specialized problems are considered: general scenes, terrains, and terrains with vertical flightpaths. 1.
A Unified Approach to Dynamic Point Location, Ray Shooting, and Shortest Paths in Planar Maps
, 1992
"... We describe a new technique for dynamically maintaining the trapezoidal decomposition of a connected planar map M with 7 ~ vertices, and apply it to the development of a unified dynamic data structure that supports pointlocation, rayshooting, and shortestpath queries in M. The space requirement i ..."
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Cited by 20 (6 self)
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We describe a new technique for dynamically maintaining the trapezoidal decomposition of a connected planar map M with 7 ~ vertices, and apply it to the development of a unified dynamic data structure that supports pointlocation, rayshooting, and shortestpath queries in M. The space requirement is O(nlog n). Pointlocation queries take time O(log 7~). Rayshooting and shortestpath queries take time O(log3 TZ) (plus O(k) time if the k edges of the shortest path are reported in addition to its length). Updates consist of insertions and deletions of vertices and edges, and take O(log3 n) time (amortized for vertex updates).
Uniform Grids: A Technique for Intersection Detection on Serial and Parallel Machines
 Proceedings of AutoCarto 9
, 1989
"... Data structures which accurately determine spatial and topological relationships in large databases are crucial to future developments in automated cartography. The uniform grid technique presented here offers an efficient solution for intersection detection, which is the key issue in many problems ..."
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Cited by 12 (3 self)
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Data structures which accurately determine spatial and topological relationships in large databases are crucial to future developments in automated cartography. The uniform grid technique presented here offers an efficient solution for intersection detection, which is the key issue in many problems including map overlay. Databases from cartog raphy, VLSI, and graphics with up to 1 million edges are used. 1,819,064 edges were processed to find 6,941,110 intersections in 178 seconds on a Sun 4/280 workstation. This data structure is also ideally suited for implementation on a parallel machine. When executing on a 16 processor Sequent Balance 21000, total times averaged ten times faster than when using only one processor. Finding all 81,373 intersections in a 62,045 edge database took only 28 seconds elapsed time. These techniques also appear applicable to massively parallel SIMD (Single Instruction, Multiple Data Stream) com puters. We have also used these techniques to implement a prototype map overlay sys tem and performed preliminary tests on overlaying 2 copies of US state boundaries, with 3660 edges in total. Finding all the intersections, given the edges in memory, took only 1.73 seconds on a Sun 4/280. We estimate that the complete overlay would take under 20 seconds.
Approximating the visible region of a point on a terrain
 In Proc. Algorithm Engineering and Experiments (ALENEXâ€™04), accepted
, 2004
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A Simplified Technique for HiddenLine Elimination in Terrains
, 1992
"... In this paper we give a practical and efficient outputsensitive algorithm for constructing the display of a polyhedral terrain. It runs in O((d + n) log n) time and uses O(nff(n)) space, where d is the size of the final display, and ff(n) is a (very slowly growing) functional inverse of Ackermann&a ..."
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Cited by 11 (2 self)
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In this paper we give a practical and efficient outputsensitive algorithm for constructing the display of a polyhedral terrain. It runs in O((d + n) log n) time and uses O(nff(n)) space, where d is the size of the final display, and ff(n) is a (very slowly growing) functional inverse of Ackermann's function. Our implementation is especially simple and practical, because we try to take full advantage of the specific geometrical properties of the terrain. The asymptotic speed of our algorithm has been improved upon theoretically by other authors, but at the cost of higher space usage and/or high overhead and complicated code. Our main data structure maintains an implicit representation of the convex hull of a set of points that can be dynamically updated in O(log n) time. It is especially simple and fast in our application since there are no rebalancing operations required in the tree.
Parallel ObjectSpace Hidden Surface Removal
, 1990
"... A parallel objectspace hidden surface removal algorithm for polyhedral scenes is presented. The uniform grid technique is used to achieve parallelism for the hidden line removal. A conflictdetection and backoff strategy is then used to obtain parallelism for the visible region reconstruction from ..."
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Cited by 9 (3 self)
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A parallel objectspace hidden surface removal algorithm for polyhedral scenes is presented. The uniform grid technique is used to achieve parallelism for the hidden line removal. A conflictdetection and backoff strategy is then used to obtain parallelism for the visible region reconstruction from the visible segments. The algorithm has been implemented on a Sequent Balance 21000 sharedmemory parallel computer. An average speedup of 10 has been obtained using 15 processors.
Hidden Surface Removal for AxisParallel Polyhedra
 Proc. 31rst IEEE Symp. on Foundations of Computer Science
, 1990
"... Hidden surface removal for axisparallel polyhedra ..."
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Visualization of TINs
 Algorithmic Foundations of GIS, Lecture Notes in Comp. Science
, 1997
"... Geographic information systems often represent terrains, or other height fields, by triangulated irregular networks (TINs). The visualization of TINs is therefore a task any GIS has to be able to perform. This survey paper discusses two aspects of this task: the hiddensurface removal problem, which ..."
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Cited by 8 (0 self)
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Geographic information systems often represent terrains, or other height fields, by triangulated irregular networks (TINs). The visualization of TINs is therefore a task any GIS has to be able to perform. This survey paper discusses two aspects of this task: the hiddensurface removal problem, which is to determine which parts of the TIN are visible from a given view point, and the computation of data structures that allow the extraction of representations of the TIN at different levels of detail. 1 Introduction One of the fundamental tasks any GIS has to perform is the visualization of geographic data. Often the data will be elevation data describing a terrain. How to visualize such data depends on the representation used for the terrain, that is, on the digital elevation model used. Three of the most popular models are the regular square grid, the contourline model, and the triangulated irregular network. In this survey paper we shall concentrate on the visualization of triangulate...