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DavenportSchinzel Sequences and Their Geometric Applications
, 1998
"... An (n; s) DavenportSchinzel sequence, for positive integers n and s, is a sequence composed of n distinct symbols with the properties that no two adjacent elements are equal, and that it does not contain, as a (possibly noncontiguous) subsequence, any alternation a \Delta \Delta \Delta b \Delta \ ..."
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Cited by 418 (116 self)
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An (n; s) DavenportSchinzel sequence, for positive integers n and s, is a sequence composed of n distinct symbols with the properties that no two adjacent elements are equal, and that it does not contain, as a (possibly noncontiguous) subsequence, any alternation a \Delta \Delta \Delta b \Delta \Delta \Delta a \Delta \Delta \Delta b \Delta \Delta \Delta of length s + 2 between two distinct symbols a and b. The close relationship between DavenportSchinzel sequences and the combinatorial structure of lower envelopes of collections of functions make the sequences very attractive because a variety of geometric problems can be formulated in terms of lower envelopes. A nearlinear bound on the maximum length of DavenportSchinzel sequences enable us to derive sharp bounds on the combinatorial structure underlying various geometric problems, which in turn yields efficient algorithms for these problems.
Accelerated occlusion culling using shadow frusta
 In Proc. of ACM Symposium on Computational Geometry
, 1997
"... Many applications in computer graphics and virtual environments need to render datasets with large numbers of primitives and high depth complexity at interactive rates. However, standard techniques like view frustum culling and a hardware zbuffer are unable to display datasets composed of hundred o ..."
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Cited by 73 (9 self)
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Many applications in computer graphics and virtual environments need to render datasets with large numbers of primitives and high depth complexity at interactive rates. However, standard techniques like view frustum culling and a hardware zbuffer are unable to display datasets composed of hundred of thousands of polygons at interactive frame rates on current highend graphics systems. We add a "conservative' ' visibility culling stage to the rendering pipeline, attempting to identify and avoid processing of occluded polygons. Given a moving viewpoint, the algorithm dynamically chooses a set of occluder3. Each occluder is used to compute a 3h.adow frustum, and all primitives contained within this frustum are culled. The algorithm hierarchically traverses the model, culling out parts not visible from the current viewpoint using efficient, robust, and in some cases specialized interference detection algorithms. The algorithm's performance varies with the location of the viewpoint and the depth complexity of the model. In the worst case it is linear in the input size with a small constant. In this paper, we demonstrate its performance on a city model composed of 500,000 polygons and possessing varying depth complexity. We are able to cull an average of 55 % of the polygons that would not be culled by viewfrustum culling and obtain a commensurate improvement in frame rate. The overall approach is ejJecti11e and •calable, is applicable to all polygonal models, and can be easily implemented on top of viewfrustum culling. 1
Interactive Sensor Planning
 In Computer Vision and Pattern Recognition Conference
, 1998
"... This paper describes an interactive sensor planning system that can be used to select viewpoints subject to camera visibility, field of view and task constraints. Application areas for this method include surveillance planning, safety monitoring, architectural site design planning, and automated sit ..."
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Cited by 44 (8 self)
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This paper describes an interactive sensor planning system that can be used to select viewpoints subject to camera visibility, field of view and task constraints. Application areas for this method include surveillance planning, safety monitoring, architectural site design planning, and automated site modeling. Given a description of the sensor's characteristics, the objects in the 3D scene, and the targets to be viewed, our algorithms compute the set of admissible view points that satisfy the constraints. The system first builds topologically correct solid models of the scene from a variety of data sources. Viewing targets are then selected, and visibility volumes and field of view cones are computed and intersected to create viewing volumes where cameras can be placed. The user can interactively manipulate the scene and select multiple target features to be viewed by a camera. The user can also select candidate viewpoints within this volume to synthesize views and verify the correctn...
Hierarchical BackFace Computation
 Eurographics Rendering Workshop
, 1996
"... We presentasublinear algorithm for computing and culling backfacing polygons that yields a signi#cant performance improvement in the interactive rendering of large polygonal models. The algorithm partitions a polygonal model it into hierarchical clusters based on the normals and positions of the p ..."
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Cited by 24 (0 self)
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We presentasublinear algorithm for computing and culling backfacing polygons that yields a signi#cant performance improvement in the interactive rendering of large polygonal models. The algorithm partitions a polygonal model it into hierarchical clusters based on the normals and positions of the polygons. It does not explicitly compute all the backfacing polygons but rather decides, in expectedconstant time, whether an entire cluster is backfacing. As a preprocessing step, the algorithm partitions the space into regions with respect to each cluster. During rendering, it exploits frametoframe coherence to track the viewpoint. The algorithm has been applied to a number of models and its performance is a function of number of clusters, the depth of the hierarchies, and the characteristics of the graphics system. In practice, we are able to cull 30 , 55# of the polygons in about 5 , 10# of the total CPU time per frame on an SGI Indigo2 Extreme for models composed of tens of tho...
Lines and free line segments tangent to arbitrary threedimensional convex polyhedra
 SIAM Journal on Computing
, 2006
"... SUE WHITESIDES∗ ∗ Abstract. Motivated by visibility problems in three dimensions, we investigate the complexity and construction of the set of tangent lines in a scene of threedimensional polyhedra. We prove that the set of lines tangent to four possibly intersecting convex polyhedra in R 3 with a ..."
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Cited by 24 (14 self)
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SUE WHITESIDES∗ ∗ Abstract. Motivated by visibility problems in three dimensions, we investigate the complexity and construction of the set of tangent lines in a scene of threedimensional polyhedra. We prove that the set of lines tangent to four possibly intersecting convex polyhedra in R 3 with a total of n edges consists of Θ(n 2) connected components in the worst case. In the generic case, each connected component is a single line, but our result still holds for arbitrarily degenerate scenes. More generally, we show that a set of k possibly intersecting convex polyhedra with a total of n edges admits, in the worst case, Θ(n 2 k 2) connected components of maximal free line segments tangent to at least four polytopes. Furthermore, these bounds also hold for possibly occluded lines rather than maximal free line segments. Finally, we present an O(n 2 k 2 log n) time and O(nk 2) space algorithm that, given a scene of k possibly intersecting convex polyhedra, computes all the minimal free line segments that are tangent to any four of the polytopes and are isolated transversals to the set of edges they intersect; in particular, we compute at least one line segment per connected component of tangent lines. Key words. computational geometry, 3D visibility, visibility complex, visual events
Fast Horizon Computation at All Points of a Terrain With Visibility and Shading Applications
 IEEE Transactions on Visualization and Computer Graphics
, 1998
"... ..."
Towards Accurate Recovery of Shape from Shading under Diffuse Lighting
 IEEE Transactions on Pattern Analysis and Machine Intelligence
, 1997
"... A new surface radiance model for diffuse lighting is presented which incorporates shadows, interreflections, and surface orientation. An algorithm is presented that uses this model to compute shapefromshading under diffuse lighting. The algorithm is tested on both synthetic and real images, and ..."
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Cited by 17 (2 self)
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A new surface radiance model for diffuse lighting is presented which incorporates shadows, interreflections, and surface orientation. An algorithm is presented that uses this model to compute shapefromshading under diffuse lighting. The algorithm is tested on both synthetic and real images, and is found to perform more accurately than the only previous algorithm for this problem. Index Terms: shapefromshading, diffuse lighting, interreflections, shadows, visual events, horizon, skyline I. Introduction The classical formulation of the shapefromshading problem has been to assume that surface radiance is determined entirely by the surface orientation relative to a point light source at infinity [5], [7]. Shadows and interreflections are usually ignored. When the light source is diffuse, however, this model is not applicable [9], [10]. To see this, consider the following two examples: The first is a scene consisting of a convex Lambertian object resting on a ground plane, il...
Hierarchical BackFace Culling
 In 7th Eurographics Workshop on Rendering
, 1996
"... We present a sublinear algorithm for computing and culling backfacing polygons that yields a significant performance improvement in the interactive rendering of large polygonal models. The algorithm partitions a polygonal model it into hierarchical clusters based on the normals and positions of th ..."
Abstract

Cited by 13 (3 self)
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We present a sublinear algorithm for computing and culling backfacing polygons that yields a significant performance improvement in the interactive rendering of large polygonal models. The algorithm partitions a polygonal model it into hierarchical clusters based on the normals and positions of the polygons. It does not explicitly compute all the backfacing polygons but rather decides, in expected constant time, whether an entire cluster is backfacing. As a preprocessing step, the algorithm partitions the space into regions with respect to each cluster. During rendering, it exploits frametoframe coherence to track the viewpoint. The algorithm has been applied to a number of models and its performance is a function of number of clusters, the depth of the hierarchies, and the characteristics of the graphics system. In practice, we are able to cull 30 \Gamma 55% of the polygons in about 5 \Gamma 10% of the total CPU time per frame on an SGI Indigo2 Extreme for models composed of t...
Incremental Update of the Visibility Map as Seen by a Moving Viewpoint in Two Dimensions
 In Seventh International Eurographics Workshop on Computer Animation and Simulation
, 1996
"... . Consider the following problem: A viewpoint moves amongst a set of line segments in the plane and it is desired to maintain the sequence of lines visible from the viewpoint at every increment in its position. The sequence of visible lines is identical for most increments in the position of the vie ..."
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Cited by 11 (2 self)
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. Consider the following problem: A viewpoint moves amongst a set of line segments in the plane and it is desired to maintain the sequence of lines visible from the viewpoint at every increment in its position. The sequence of visible lines is identical for most increments in the position of the viewpoint. It is different only when the viewpoint crosses a visual discontinuity line. Our objective is to be able to quickly report whether the sequence of visible lines needs to be updated and perform the update quickly in that case. We propose an algorithm that satisfies both criteria while using space linear in the number of visual discontinuity lines. This last condition is important because constructing the arrangement of these lines would take space quadratic in their number. Keywords: animation, visibility maps, online algorithms, incremental update, discontinuity lines. 1 Introduction As a viewpoint moves along a trajectory in a static scene represented by a set of line segments, ...
Maintenance of the Set of Segments Visible from a Moving Viewpoint in Two Dimensions
 In Proc. 12th ACM Sympos. Comput. Geom
, 1996
"... Introduction Consider a viewpoint moving amongst a set of non intersecting line segments in the plane. We would like to compute efficiently the set of segments visible at successive positions along the viewpoint trajectory. This problem can be solved in either the offline or the online settin ..."
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Cited by 10 (2 self)
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Introduction Consider a viewpoint moving amongst a set of non intersecting line segments in the plane. We would like to compute efficiently the set of segments visible at successive positions along the viewpoint trajectory. This problem can be solved in either the offline or the online setting. The latter case, in which the updates of the viewpoint are known only as they occur, is more interesting for interactive systems. This video illustrates a simple algorithm to solve this problem. For a scene containing m visual discontinuities, each discontinuity crossing is performed in time O(log 2 m) using space O(m). The space bound is an important consideration, as m can become very large in real applications. Pocchiola [Poc90] maintains each update in the view in logarithmic time for a viewpoint moving amidst a set of objects in the plane (offline version). For<