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76
Polyhedral Visual Hulls for RealTime Rendering
 In Proceedings of Twelfth Eurographics Workshop on Rendering
, 2001
"... . We present new algorithms for creating and rendering visual hulls in realtime. Unlike voxel or sampled approaches, we compute an exact polyhedral representation for the visual hull directly from the silhouettes. This representation has a number of advantages: 1) it is a viewindependent represent ..."
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Cited by 157 (4 self)
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. We present new algorithms for creating and rendering visual hulls in realtime. Unlike voxel or sampled approaches, we compute an exact polyhedral representation for the visual hull directly from the silhouettes. This representation has a number of advantages: 1) it is a viewindependent representation, 2) it is wellsuited to rendering with graphics hardware, and 3) it can be computed very quickly. We render these visual hulls with a viewdependent texturing strategy, which takes into account visibility information that is computed during the creation of the visual hull. We demonstrate these algorithms in a system that asynchronously renders dynamically created visual hulls in realtime. Our system outperforms similar systems of comparable computational power. 1
Arrangements and Their Applications
 Handbook of Computational Geometry
, 1998
"... The arrangement of a finite collection of geometric objects is the decomposition of the space into connected cells induced by them. We survey combinatorial and algorithmic properties of arrangements of arcs in the plane and of surface patches in higher dimensions. We present many applications of arr ..."
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Cited by 89 (20 self)
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The arrangement of a finite collection of geometric objects is the decomposition of the space into connected cells induced by them. We survey combinatorial and algorithmic properties of arrangements of arcs in the plane and of surface patches in higher dimensions. We present many applications of arrangements to problems in motion planning, visualization, range searching, molecular modeling, and geometric optimization. Some results involving planar arrangements of arcs have been presented in a companion chapter in this book, and are extended in this chapter to higher dimensions. Work by P.A. was supported by Army Research Office MURI grant DAAH049610013, by a Sloan fellowship, by an NYI award, and by a grant from the U.S.Israeli Binational Science Foundation. Work by M.S. was supported by NSF Grants CCR9122103 and CCR9311127, by a MaxPlanck Research Award, and by grants from the U.S.Israeli Binational Science Foundation, the Israel Science Fund administered by the Israeli Ac...
An Exact Interactive Time Visibility Ordering Algorithm for Polyhedral Cell Complexes
, 1998
"... A visibility ordering of a set of objects, from a given viewpoint, is a total order on the objects such that if object a obstructs object b,thenb precedes a in the ordering. Such orderings are extremely useful for rendering volumetric data. We present an algorithm that generates a visibility orderin ..."
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Cited by 45 (14 self)
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A visibility ordering of a set of objects, from a given viewpoint, is a total order on the objects such that if object a obstructs object b,thenb precedes a in the ordering. Such orderings are extremely useful for rendering volumetric data. We present an algorithm that generates a visibility ordering of the cells of an unstructured mesh, provided that the cells are convex polyhedra and nonintersecting, and that the visibility ordering graph does not contain cycles. The overall mesh may be nonconvex and it may have disconnected components. Our technique employs the sweep paradigm to determine an ordering between pairs of exterior (mesh boundary) cells which can obstruct one another. It then builds on Williams' MPVO algorithm [33] which exploits the ordering implied by adjacencies within the mesh. The partial ordering of the exterior cells found by sweeping is used to augment the DAG created in Phase II of the MPVO algorithm. Our method thus removes the assumption of the MPVO algorithm t...
Spatial Join Techniques
"... A variety of techniques for performing a spatial join are reviewed. Instead of just summarizing the literature and presenting each technique in its entirety, distinct components of the different techniques are described and each is decomposed into an overall framework for performing a spatial join. ..."
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Cited by 45 (5 self)
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A variety of techniques for performing a spatial join are reviewed. Instead of just summarizing the literature and presenting each technique in its entirety, distinct components of the different techniques are described and each is decomposed into an overall framework for performing a spatial join. A typical spatial join technique consists of the following components: partitioning the data, performing internalmemory spatial joins on subsets of the data, and checking if the full polygons intersect. Each technique is decomposed into these components and each component addressed in a separate section so as to compare and contrast similar aspects of each technique. The goal of this survey is to describe the algorithms within each component in detail, comparing and contrasting competing methods, thereby enabling further analysis and experimentation with each component and allowing the best algorithms for a particular situation to be built piecemeal, or, even better, enabling an optimizer to choose which algorithms to use. Categories and Subject Descriptors: H.2.4 [Database Management]: Systems—Query processing; H.2.8 [Database Management]: Database Applications—Spatial databases and GIS
Robust Plane Sweep for Intersecting Segments
, 1997
"... In this paper, we reexamine in the framework of robust computation the BentleyOttmann algorithm for reporting intersecting pairs of segments in the plane. This algorithm has been reported as being very sensitive to numerical errors. Indeed, a simple analysis reveals that it involves predicates of d ..."
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Cited by 29 (3 self)
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In this paper, we reexamine in the framework of robust computation the BentleyOttmann algorithm for reporting intersecting pairs of segments in the plane. This algorithm has been reported as being very sensitive to numerical errors. Indeed, a simple analysis reveals that it involves predicates of degree 5, presumably never evaluated exactly in most implementation. Within the exactcomputation paradigm we introduce two models of computation aimed at replacing the conventional model of realnumber arithmetic. The first model (predicate arithmetic) assumes the exact evaluation of the signs of algebraic expressions of some degree, and the second model (exact arithmetic) assumes the exact computation of the value of...
Route Planning and Map Inference with Global Positioning Traces
 In Computer Science in Perspective
"... Abstract. Navigation systems assist almost any kind of motion in the physical world including sailing, flying, hiking, driving and cycling. On the other hand, traces supplied by global positioning systems (GPS) can track actual time and absolute coordinates of the moving objects. Consequently, this ..."
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Cited by 20 (2 self)
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Abstract. Navigation systems assist almost any kind of motion in the physical world including sailing, flying, hiking, driving and cycling. On the other hand, traces supplied by global positioning systems (GPS) can track actual time and absolute coordinates of the moving objects. Consequently, this paper addresses efficient algorithms and data structures for the route planning problem based on GPS data; given a set of traces and a current location, infer a short(est) path to the destination. The algorithm of Bentley and Ottmann is shown to transform geometric GPS information directly into a combinatorial weighted and directed graph structure, which in turn can be queried by applying classical and refined graph traversal algorithms like Dijkstras ’ singlesource shortest path algorithm or A*. For highprecision map inference especially in car navigation, algorithms for road segmentation, map matching and lane clustering are presented. 1
Derandomization in Computational Geometry
, 1996
"... We survey techniques for replacing randomized algorithms in computational geometry by deterministic ones with a similar asymptotic running time. 1 Randomized algorithms and derandomization A rapid growth of knowledge about randomized algorithms stimulates research in derandomization, that is, repla ..."
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Cited by 19 (1 self)
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We survey techniques for replacing randomized algorithms in computational geometry by deterministic ones with a similar asymptotic running time. 1 Randomized algorithms and derandomization A rapid growth of knowledge about randomized algorithms stimulates research in derandomization, that is, replacing randomized algorithms by deterministic ones with as small decrease of efficiency as possible. Related to the problem of derandomization is the question of reducing the amount of random bits needed by a randomized algorithm while retaining its efficiency; the derandomization can be viewed as an ultimate case. Randomized algorithms are also related to probabilistic proofs and constructions in combinatorics (which came first historically), whose development has similarly been accompanied by the effort to replace them by explicit, nonrandom constructions whenever possible. Derandomization of algorithms can be seen as a part of an effort to map the power of randomness and explain its role. ...
Drawing Nice Projections of Objects in Space
, 1995
"... Given a polygonal object (simple polygon, geometric graph, wireframe, skeleton or more generally a set of line segments) in three dimensional Euclidean space, we consider the problem of computing a variety of "nice" parallel (orthographic) projections of the object. We show that given a g ..."
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Cited by 18 (8 self)
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Given a polygonal object (simple polygon, geometric graph, wireframe, skeleton or more generally a set of line segments) in three dimensional Euclidean space, we consider the problem of computing a variety of "nice" parallel (orthographic) projections of the object. We show that given a general polygonal object consisting of n line segments in space, deciding whether it admits a crossingfree projection can be done in O(n 2 log n+k) time and O(n 2 +k) space, where k is the number of edge intersections of forbidden quadrilaterals (i.e. set of directions that admits a crossing) and varies from zero to O(n 4 ). This implies for example that given a simple polygon in 3space we can determine if there exists a plane on which the projection is a simple polygon, within the same complexity. Furthermore, if such a projection does not exist, a minimumcrossing projection can be found in O(n 4 ) time and space. We show that an object always admits a regular projection (of interest to k...
Efficient gpubased construction of occupancy grids using several laser rangefinders
 In IEEE International Conference on Intelligent Systems and Robots
, 2006
"... Abstract — Building occupancy grids (OGs) in order to model the surrounding environment of a vehicle implies to fusion occupancy information provided by the different embedded sensors in the same grid. The principal difficulty comes from the fact that each can have a different resolution, but also t ..."
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Cited by 18 (5 self)
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Abstract — Building occupancy grids (OGs) in order to model the surrounding environment of a vehicle implies to fusion occupancy information provided by the different embedded sensors in the same grid. The principal difficulty comes from the fact that each can have a different resolution, but also that the resolution of some sensors varies with the location in the field of view. In this article we present a new efficient approach to this issue based upon a graphical processor unit (GPU). In that perspective, we explain why the problem of switching coordinate systems is an instance of the texture mapping problem in computer graphics. We also present an exact algorithm in order to evaluate the accuracy of such a device, which is not precisely known due to the several approximations made by the hardware. To validate our method, the results with GPU are also compared to results obtained through the exact approach and the GPU precision is shown to be good enough for robotic applications. Therefore we describe a whole and general calculus architecture to build occupancy grids for any kind of rangefinder with a graphical processor unit (GPU). And we present computational time results that can allow to compute occupancy grids for 50 sensors at frame rate even for a very fine grid. I.
Computing faces in segment and simplex arrangements
 In Proc. 27th Annu. ACM Sympos. Theory Comput
, 1995
"... For a set S of n line segments in the plane, we give the first workoptimal deterministic parallel algorithm for constructing their arrangement. It runs in O(log 2 n) time using O(n log n + k) work in the EREW PRAM model, where k is the number of intersecting line segment pairs, and provides a fairl ..."
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Cited by 16 (10 self)
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For a set S of n line segments in the plane, we give the first workoptimal deterministic parallel algorithm for constructing their arrangement. It runs in O(log 2 n) time using O(n log n + k) work in the EREW PRAM model, where k is the number of intersecting line segment pairs, and provides a fairly simple divideandconquer alternative to the optimal sequential “planesweep ” algorithm of Chazelle and Edelsbrunner. Moreover, our method can be used to output all k intersecting pairs while using only O(n) working space, which solves an open problem posed by Chazelle and Edelsbrunner. We also describe a sequential algorithm for computing a single face in an arrangement of n line segments that runs in O(n 2 (n) log n) time, which improves on a previous O(n log 2 n) time algorithm. For collections of simplices in IR d, we give methods for constructing a set of m = O(n d,1 log c n+k) cells of constant descriptive complexity that covers their arrangement, where c> 1 is a constant and k is the number of faces in the arrangement. The construction is performed sequentially in O(m) time, or in O(log n) time using O(m) work in the EREW PRAM model. The covering can be augmented to answer point location queries in O(log n) time. In addition to supplying the first parallel methods for these problems, we improve on the previous best sequential methods by reducing the query times (from O(log 2 n) in IR 3 and O(log 3 n) in IR d, d>3), and also the size and construction cost of the covering (from O(n d,1+ + k)). 1