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17
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 ..."
Abstract

Cited by 37 (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 in Geographic Information Systems
 Handbook of Computational Geometry
, 1997
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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 of ..."
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Cited by 21 (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., &QUOT;PERSISTENCY IN COMPUTATIONAL GEOMETRY,&QUOT; PROC. 7TH CANADIAN CONF. COMP. GEOMETRY, QUEBEC
, 1995
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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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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 ...
Reconstructing Visible Regions From Visible Segments
, 1986
"... An algorithm is presented for reconstructing visible regions from visible edge segments in object space. This has applications in hidden surface algerithms operating on polyhedral scenes (e.g.W.R. Franklin, "A linear time exact hidden surface algorithm," ACM Computer Graphics 14(3), 117 ..."
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Cited by 4 (3 self)
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An algorithm is presented for reconstructing visible regions from visible edge segments in object space. This has applications in hidden surface algerithms operating on polyhedral scenes (e.g.W.R. Franklin, "A linear time exact hidden surface algorithm," ACM Computer Graphics 14(3), 117123, 1980). A special case of reconstruction can be formulated as a graph problem: "Determine the faces of a straightedge planar graph given in terms of its edges." This is accomplished in O (n log n) time using linear space for a graph with n edges, and is worstcase optimal. (The graph may have separate components but the components must not contain each other.) The general problem of reconstruction is then solved by applying our algorithm to each component in the containment relation.
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
OutputSensitive Hidden Surface Elimination for Rectangles
, 1988
"... We present an algorithm for the wellknown hiddensurface elimination problem for rectangles, which is also known as the window rendering problem. The time complexity of our algorithm is sensitive to the size of the output. Specifically, it runs in time that is O(n1mS + k), where k is the size of th ..."
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Cited by 1 (0 self)
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We present an algorithm for the wellknown hiddensurface elimination problem for rectangles, which is also known as the window rendering problem. The time complexity of our algorithm is sensitive to the size of the output. Specifically, it runs in time that is O(n1mS + k), where k is the size of the output (which can be as large as 0(n’)). For values of k in the range between n’s6 / log n and n², our algorithm is asymptotically faster than previous ones.