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49
Fast Computation of Shadow Boundaries Using Spatial Coherence and Backprojections
, 1994
"... This paper describes a fast, practical algorithm to compute the shadow boundariesin a polyhedral scene illuminated by a polygonal light source. The shadow boundaries divide the faces of the scene into regions such that the structure or "aspect" of the visible area of the light source is co ..."
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Cited by 70 (5 self)
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This paper describes a fast, practical algorithm to compute the shadow boundariesin a polyhedral scene illuminated by a polygonal light source. The shadow boundaries divide the faces of the scene into regions such that the structure or "aspect" of the visible area of the light source is constant within each region. The paper also describes a fast, practical algorithm to compute the structure of the visible light source in each region. Both algorithms exploit spatial coherence and are the most efficient yet developed. Given the structure of the visible light source in a region, queries of the form "What specific areas of the light source are visible?" can be answered almost instantly from any point in the region. This speeds up by several orders of magnitude the accurate computation of first level diffuse reflections due to an area light source. Furthermore, the shadow boundaries form a good initial decomposition of the scene for global illumination computations. CR category: I.3.7 [Co...
Efficient Hidden Surface Removal for Objects with Small Union Size
, 1991
"... Let S be a set of n nonintersecting objects in space for which we want to determine the portions visible from some viewing point. We assume that the objects are ordered by depth from the viewing point (e.g., they are all horizontal and are viewed from infinity from above). In this paper we give ..."
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Cited by 47 (16 self)
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Let S be a set of n nonintersecting objects in space for which we want to determine the portions visible from some viewing point. We assume that the objects are ordered by depth from the viewing point (e.g., they are all horizontal and are viewed from infinity from above). In this paper we give an algorithm that computes the visible portions in time O((U(n)+ k)log 2 n), where U(n ) is a superadditive bound on the maximal complexity of the union of (the projections on a viewing plane of) any n objects from the family under consideration, and k is the complexity of the resulting visibility map. The algorithm uses O(U(n)logn) working storage. The algorithm is useful when the objects are "fat" in the sense that the union of the projection of any subset of them has small (i.e., subquadratic) complexity. We present three applications of this general technique: (i) For disks (or balls in space) we have U(n) = O(n), thus the visibility map can be computed in time O((n + k) log 2 n). (ii) For 'fat' triangles (where each internal angle is at least some fixed 0 degrees) we have U(n) = O(nloglogn) and the algorithm runs in time O((n log log n + k)log 2 n). (iii) The method also applies to computing the visibility map for a polyhedral terrain viewed from a fixed point, and yields an O((na(n)+ k)logn) algorithm.
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 35 (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.
Visibility Sorting and Compositing without Splitting for Image Layer Decomposition
 In Proceedings of the 25th Annual Conference on Computer Graphics & Interactive Techniques
, 1998
"... We present an efficient algorithm for visibility sorting a set of moving geometric objects into a sequence of image layers which are composited to produce the final image. Instead of splitting the geometry as in previous visibility approaches, we detect mutual occluders and resolve them using an app ..."
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Cited by 33 (3 self)
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We present an efficient algorithm for visibility sorting a set of moving geometric objects into a sequence of image layers which are composited to produce the final image. Instead of splitting the geometry as in previous visibility approaches, we detect mutual occluders and resolve them using an appropriate image compositing expression or merge them into a single layer. Such an algorithm has many applications in computer graphics; we demonstrate two: rendering acceleration using image interpolation and visibilitycorrect depth of field using image blurring. We propose a new, incremental method for identifying mutually occluding sets of objects and computing a visibility sort among these sets. Occlusion queries are accelerated by testing on convex bounding hulls; less conservative tests are also discussed. Kdtrees formed by combinations of directions in object or image space provide an initial cull on potential occluders, and incremental collision detection algorithms are adapted to resolve pairwise occlusions, when necessary. Mutual occluders are further analyzed to generate an image compositing expression; in the case of nonbinary occlusion cycles, an expression can always be generated without merging the objects into a single layer. Results demonstrate that the algorithm is practical for realtime animation of scenes involving hundreds of objects each comprising hundreds or thousands of polygons.
Efficient Ray Shooting and Hidden Surface Removal
 ALGORITHMICA
, 1991
"... In this paper we study the ray shooting problem for three special classes of polyhedral objects in space: axisparallel polyhedra, curtains (unbounded polygons with three edges, two of which are parallel to the zaxis and extend downward to minus infinity) and fat horizontal triangles (triangles ..."
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Cited by 31 (5 self)
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In this paper we study the ray shooting problem for three special classes of polyhedral objects in space: axisparallel polyhedra, curtains (unbounded polygons with three edges, two of which are parallel to the zaxis and extend downward to minus infinity) and fat horizontal triangles (triangles parallel to the yplane whose angles are greater than some fixed constant). For all three problems structures are presented using O(n 2+) preprocessing, for any fixed e > 0, with O(log n) query time. We also study the general ray shooting problem in an arbitrary set of (possibly intersecting) triangles. Here we present a structure that uses O(n 4+e) preprocessing and has a query time of O(log n). As an
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 28 (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.
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...