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A survey of visibility for walkthrough applications
 IEEE TRANSACTIONS ON VISUALIZATION AND COMPUTER
, 2003
"... Visibility algorithms for walkthrough and related applications have grown into a significant area, spurred by the growth in the complexity of models and the need for highly interactive ways of navigating them. In this survey, we review the fundamental issues in visibility and conduct an overview of ..."
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Cited by 145 (8 self)
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Visibility algorithms for walkthrough and related applications have grown into a significant area, spurred by the growth in the complexity of models and the need for highly interactive ways of navigating them. In this survey, we review the fundamental issues in visibility and conduct an overview of the visibility culling techniques developed in the last decade. The taxonomy we use distinguishes between pointbased and fromregion methods. Pointbased methods are further subdivided into object and imageprecision techniques, while fromregion approaches can take advantage of the cellandportal structure of architectural environments or handle generic scenes.
Multilevel ray tracing algorithm
 ACM Trans. on Graphics
, 2005
"... We propose new approaches to ray tracing that greatly reduce the required number of operations while strictly preserving the geometrical correctness of the solution. A hierarchical “beam” structure serves as a proxy for a collection of rays. It is tested against a kdtree representing the overall sc ..."
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Cited by 124 (2 self)
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We propose new approaches to ray tracing that greatly reduce the required number of operations while strictly preserving the geometrical correctness of the solution. A hierarchical “beam” structure serves as a proxy for a collection of rays. It is tested against a kdtree representing the overall scene in order to discard from consideration the subset of the kdtree (and hence the scene) that is guaranteed not to intersect with any possible ray inside the beam. This allows for all the rays inside the beam to start traversing the tree from some node deep inside thus eliminating unnecessary operations. The original beam can be further subdivided, and we can either continue looking for new optimal entry points for the subbeams, or we can decompose the beam into individual rays. This is a hierarchical process that can be adapted to the geometrical complexity of a particular view direction allowing for efficient geometric antialiasing. By amortizing the cost of partially traversing the tree for all the rays in a beam, up to an order of magnitude performance improvement can be achieved enabling interactivity for complex scenes on ordinary desktop machines.
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 26 (16 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
Visibility Preprocessing for Urban Scenes using Line Space Subdivision
 In Proceedings of Pacific Graphics (PG’01
, 2001
"... We present an algorithm for visibility preprocessing of urban environments. The algorithm uses a subdivision of line space to analytically calculate a conservative potentially visible set for a given region in the scene. We present a detailed evaluation of our method including a comparison to anothe ..."
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Cited by 20 (6 self)
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We present an algorithm for visibility preprocessing of urban environments. The algorithm uses a subdivision of line space to analytically calculate a conservative potentially visible set for a given region in the scene. We present a detailed evaluation of our method including a comparison to another recently published visibility preprocessing algorithm. To the best of our knowledge the proposed method is the first algorithm that scales to large scenes and efficiently handles large view cells.
HardwareAccelerated FromRegion Visibility Using a Dual Ray Space
 In Rendering Techniques 2001: 12th Eurographics Workshop on Rendering
, 2001
"... In this paper a novel fromregion visibility algorithm is described. Its unique properties allow conducting remote walkthroughs in very large virtual environments, without preprocessing and storing prohibitive amounts of visibility information. The algorithm retains its speed and accuracy even wh ..."
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Cited by 20 (2 self)
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In this paper a novel fromregion visibility algorithm is described. Its unique properties allow conducting remote walkthroughs in very large virtual environments, without preprocessing and storing prohibitive amounts of visibility information. The algorithm retains its speed and accuracy even when applied to large viewcells. This allows computing fromregion visibility online, thus eliminating the need for visibility preprocessing. The algorithm utilizes a geometric transform, representing visibility in a twodimensional space, the dual ray space. Standard rendering hardware is then used for rapidly performing visibility computation. The algorithm is robust and easy to implement, and can trade off between accuracy and speed. We report results from extensive experiments that were conducted on a virtual environment that accurately depicts 160 square kilometers of the city of London.
A Sum of Squares Theorem for Visibility Complexes and Applications
, 2001
"... We present a new method to implement in constant amortized time the ip operation of the socalled Greedy Flip Algorithm, an optimal algorithm to compute the visibility graph or the visibility complex of a collection of pairwise disjoint bounded convex sets of constant complexity. The method uses sim ..."
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Cited by 11 (1 self)
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We present a new method to implement in constant amortized time the ip operation of the socalled Greedy Flip Algorithm, an optimal algorithm to compute the visibility graph or the visibility complex of a collection of pairwise disjoint bounded convex sets of constant complexity. The method uses simple data structures and only the leftturn or counterclockwise predicate; it relies, among other things, on a sum of squares like theorem for visibility complexes stated and proved in this paper. (The sum of squares theorem for a simple arrangement of lines states that the average value of the square of the number of vertices of a face of the arrangement is a O(1).)
A 'Sum of Squares' Theorem for Visibility Complexes (Extended Abstract)
, 2000
"... We present a new and simpler method to implement in constant amortized time the flip operation of the socalled 'Greedy Flip Algorithm', an optimal algorithm to compute the visibility graph/complex of a collection of pairwise disjoint bounded convex sets of constant complexity. The method uses only ..."
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We present a new and simpler method to implement in constant amortized time the flip operation of the socalled 'Greedy Flip Algorithm', an optimal algorithm to compute the visibility graph/complex of a collection of pairwise disjoint bounded convex sets of constant complexity. The method uses only the incidence structure of the visibility complex and only the primitive predicate which states that the angle of a first bitangent is less than the angle of a second bitangent, both bitangents being tangent to the same convex. The method relies on a 'sum of squares' like theorem for visibility complexes stated and proved in this paper. (The "sum of squares" theorem for an arrangement of lines states that the average value of the square of the number of vertices of a face of the arrangement is a O(1).)
LORIA, Technopôle de NancyBrabois, Campus scientifique, On the Expected Size of the 2D Visibility Complex
"... Abstract: We study the expected size of the 2D visibility complex of randomly distributed objects in the plane. We prove that the expected asymptotic number of free bitangents (which correspond to the 0faces of the visibility complex) among unit discs or polygons of bounded aspect ratio is linear a ..."
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Abstract: We study the expected size of the 2D visibility complex of randomly distributed objects in the plane. We prove that the expected asymptotic number of free bitangents (which correspond to the 0faces of the visibility complex) among unit discs or polygons of bounded aspect ratio is linear and exhibit bounds in terms of the density of the objects. We also make an experimental assessment of the size of the visibility complex for disjoint random unit discs. We provide experimental estimates of the onset of the linear behavior and of the asymptotic slope and yintercept of the number of free bitangents in terms of the density of discs. Finally, we analyze the quality of our estimates in terms of the density of discs. Keywords: computational geometry, visibility complex.