Results 1  10
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An efficient outputsensitive hiddensurface removal algorithm for polyhedral terrains
, 1994
"... In this paper, we present an algorithm for hidden surface removal for a class of polyhedral surfaces which have a property that they can be ordered relatively quickly. For example, our results apply directly to terrain maps. A distinguishing feature of our algorithm is that its running time is sen ..."
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Cited by 36 (1 self)
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In this paper, we present an algorithm for hidden surface removal for a class of polyhedral surfaces which have a property that they can be ordered relatively quickly. For example, our results apply directly to terrain maps. A distinguishing feature of our algorithm is that its running time is sensitive to the actual size of the visible image, rather than the total number of intersections in the image plaue which can be much larger than the visible image. The time complexity of this algorithm is O((k + n) log ’ n) where n and /c are, respectively, the input and the output sizes. Thus, in a significant number of situations this will be faster than the worst case optimal algorithms which have running time of n(n²) irrespective of the output size.
Applications of Computational Geometry to Geographic Information Systems
"... Contents 1 Introduction 2 2 Map Data Modeling 4 2.1 TwoDimensional Spatial Entities and Relationships . . . . . . . . . . . . . . . . . . . . . 4 2.2 Raster and Vector Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.3 Subdivisions as Cell Complexes . . . . . . . ..."
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Cited by 22 (1 self)
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Contents 1 Introduction 2 2 Map Data Modeling 4 2.1 TwoDimensional Spatial Entities and Relationships . . . . . . . . . . . . . . . . . . . . . 4 2.2 Raster and Vector Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.3 Subdivisions as Cell Complexes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.4 Topological Data Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.5 Multiresolution Data Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 3 Map data processing 8 3.1 Spatial Queries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 3.2 Map Overlay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 3.3 Geometric Problems in Map Generalization . . . . . . . . . . . . . . . . . . . . . . . . . . 12 3.4 Map Labeling . . . . . . . . . . . . . . . . . . . . . . . . . . .
Contour Edge Analysis for Polyhedron Projections
 Geometric Modeling: Theory and Practice
, 1997
"... . Given a polyhedron (in 3space) and a view point, an edge of the polyhedron is called contour edge, if one of the two incident facets is directed towards the view point, and the other incident facet is directed away from the view point. Algorithms on polyhedra can exploit the fact that the number ..."
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Cited by 20 (3 self)
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. Given a polyhedron (in 3space) and a view point, an edge of the polyhedron is called contour edge, if one of the two incident facets is directed towards the view point, and the other incident facet is directed away from the view point. Algorithms on polyhedra can exploit the fact that the number of contour edges is usually much smaller than the overall number of edges. The main goal of this paper is to provide evidence for (and quantify) the claim, that the number of contour edges is small in many situations. An asymptotic analysis of polyhedral approximations of a sphere with Hausdorff distance " shows that while the required number of edges for such an approximation grows like \Theta(1="), the number of contour edges in a random orthogonal projection is \Theta(1= p " ). In an experimental study we investigate a number of polyhedral objects from several application areas. We analyze the expected number of contour edges and the expected number of intersections of contour edges in ...
Persistent data structures
 IN HANDBOOK ON DATA STRUCTURES AND APPLICATIONS, CRC PRESS 2001, DINESH MEHTA AND SARTAJ SAHNI (EDITORS) BOROUJERDI, A., AND MORET, B.M.E., "PERSISTENCY IN COMPUTATIONAL GEOMETRY," PROC. 7TH CANADIAN CONF. COMP. GEOMETRY, QUEBEC
, 1995
"... ..."
A Polygonal Approach to HiddenLine and HiddenSurface Elimination
, 1999
"... this paper we give an algorithm for the hiddenline elimination problem that is optimal in the worst case, and also takes advantage of problem instances that are "simpler" than in the worst case. Intuitively, our approach is to exploit the polygonal 2 ..."
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Cited by 7 (1 self)
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this paper we give an algorithm for the hiddenline elimination problem that is optimal in the worst case, and also takes advantage of problem instances that are "simpler" than in the worst case. Intuitively, our approach is to exploit the polygonal 2
OutputSensitive Methods for Rectilinear Hidden Surface Removal
, 1993
"... We present an algorithm for the hiddensurface elimination problem for rectangles, which is also known as window rendering. The time complexity of our algorithm is dependent on both the number of input rectangles, n, and on the size of the output, k. Our algorithm obtains a tradeoff between these t ..."
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Cited by 4 (0 self)
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We present an algorithm for the hiddensurface elimination problem for rectangles, which is also known as window rendering. The time complexity of our algorithm is dependent on both the number of input rectangles, n, and on the size of the output, k. Our algorithm obtains a tradeoff between these two components, in that its running time is O(r(n 1 1=r k)), where 1 r log n is a tunable parameter. By using this method while adjusting the parameter r "on the fly" one can achieve a running time that is O(n log n k(log n= log(1 k=n))). Note that when k is \Theta(n), this achieves an O(n log n) running time, and when k is \Theta(n 1 ffl ) for any positive constant ffl, then this achieves an O(k) running time, both of which are optimal. A preliminary announcement of this research is to appear at the 17th International Colloquium on Automata, Languages, and Programming. Part of this research was carried out while the authors were visiting Princeton University for the DIMACS ...
The Object Complexity Model For HiddenSurface Removal
, 1998
"... We define a new model of complexity, called object complexity, for measuring the performance of hiddensurface removal algorithms. This model is more appropriate for predicting the performance of these algorithms on current graphics rendering systems than the standard measure of scene complexity ..."
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Cited by 2 (1 self)
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We define a new model of complexity, called object complexity, for measuring the performance of hiddensurface removal algorithms. This model is more appropriate for predicting the performance of these algorithms on current graphics rendering systems than the standard measure of scene complexity used in computational geometry. We also
An Improved Outputsize Sensitive Parallel Algorithm for HiddenSurface Removal for Terrains
, 1998
"... We describe an efficient parallel algorithm for hiddensurface removal for terrain maps. The algorithm runs in O#log 4 n# steps on the CREW PRAM model with a work bound of O##n + k#polylog#n## where n and k are the input and output sizes respectively. In order to achieve the work bound we use a num ..."
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We describe an efficient parallel algorithm for hiddensurface removal for terrain maps. The algorithm runs in O#log 4 n# steps on the CREW PRAM model with a work bound of O##n + k#polylog#n## where n and k are the input and output sizes respectively. In order to achieve the work bound we use a number of techniques, among which our use of persistent datastructures is somewhat novel in the context of parallel algorithms. To the best of our knowledge this is the most efficient parallel algorithm for hiddensurface removal for an important class of 3D scenes. 1. Introduction 1.1. The Problem The hiddensurface elimination problem (see [24] for early history) has been a fundamental problem in computer graphics and can be stated as  given n polyhedral faces in R 3 and a projection plane, we wish to determine which portions of the faces are visible when viewed in a given direction. We are interested in an objectspace solution (independent of the display device) for this problem. Tha...
Computation of the Axial View of a Set of lsothetic Palrallelepipeds
"... We present a new technique to display a scene of threedimensional isothetic parallelepipeds (3Drectangles), viewed from infinity along one of the coordinate axes (axial view). In this situation, there always exists a topological sorting of the 3Drectangles based on the relation of occlusion (a do ..."
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We present a new technique to display a scene of threedimensional isothetic parallelepipeds (3Drectangles), viewed from infinity along one of the coordinate axes (axial view). In this situation, there always exists a topological sorting of the 3Drectangles based on the relation of occlusion (a dominance relation). The arising total order is used to generate the axial view, where the twodimensional view of each 3Drectangle is incrementally added, starting from the closest 3Drectangle. The proposed scenesensitiue algorithm runs in time O(N logzN + d log N), where N is the number of 3Drectangles and d is the number of edges of the display. This improves over the previously best known technique based on the same approach.
A Simple OutputSensitive Hidden Surface Removal Algorithm for
"... We derive a simple outputsensitive algorithm for hidden surface removal in a collection of n triangles in space for which a (partial) depth order is known, If k is the combinatorial complexity of the output risibility map, the method runs in time 0 ( n V & log n), The method is extended to work for ..."
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We derive a simple outputsensitive algorithm for hidden surface removal in a collection of n triangles in space for which a (partial) depth order is known, If k is the combinatorial complexity of the output risibility map, the method runs in time 0 ( n V & log n), The method is extended to work for other classes of objects as well, sometimes with even improved time bounds. For example, we obtain an algorithm that performs hidden surface removal for n (nonintersecting) balls in time 0(n3J210g n + k).