Results 1  10
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94
C.H.: Visibility Preprocessing For Interactive Walkthroughs
 In: Computer Graphics (SIGGRAPH 91 Proceedings
, 1991
"... The number of polygons comprising interesting architectural models is many more than can be rendered at interactive frame rates. However, due to occlusion by opaque surfaces (e.g., walls), only a small fraction of atypical model is visible from most viewpoints. We describe a method of visibility pre ..."
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Cited by 283 (15 self)
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The number of polygons comprising interesting architectural models is many more than can be rendered at interactive frame rates. However, due to occlusion by opaque surfaces (e.g., walls), only a small fraction of atypical model is visible from most viewpoints. We describe a method of visibility preprocessing that is efficient andeffective foraxisaligned oril.ria / architectural m[}dels, A model is subdivided into rectangular cc//.$whose boundaries coincide with major opaque surfaces, Nonopaque p(~rtc~/.rare identified rm cell boundaries. and used to form ana~ju{~’n~y,q)f~/>//con nectingthe cells nfthesubdivisicm. Next. theccl/r/~cc/ / visibility is computed for each cell of the subdivisirrn, by linking pairs of cells between which unobstructed.si,q/~t/inr. ~exist. During an interactive ww/krhrm/,q/~phase, an observer with a known ~~sition and\it)M~~~)~t>mov esthrc>ughthe model. At each frame, the cell containingthe observer is identified, and the contents {]fp{>tentially visible cells areretrieved from storage. The set of potentially visible cells is further reduced by culling it against theobserver’s view cone, producing the ~)yt>r~]t(>// \ i,$ibi/ify, The contents of the remaining visible cells arc then sent to a graphics pipeline for hiddensurface removal and rendering, Tests onmoderatelyc mnplex 2D and 3D axial models reveal substantially reduced rendering loads,
Surface Approximation and Geometric Partitions
 IN PROC. 5TH ACMSIAM SYMPOS. DISCRETE ALGORITHMS
, 1994
"... Motivated by applications in computer graphics, visualization, and scientific computation, we study the computational complexity of the following problem: Given a set S of n points sampled from a bivariate function f(x; y) and an input parameter " ? 0, compute a piecewise linear function \Si ..."
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Cited by 94 (15 self)
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Motivated by applications in computer graphics, visualization, and scientific computation, we study the computational complexity of the following problem: Given a set S of n points sampled from a bivariate function f(x; y) and an input parameter " ? 0, compute a piecewise linear function \Sigma(x; y) of minimum complexity (that is, a xymonotone polyhedral surface, with a minimum number of vertices, edges, or faces) such that j\Sigma(x p ; y p ) \Gamma z p j "; for all (x p ; y p ; z p ) 2 S: We prove that the decision version of this problem is NPHard . The main result of our paper is a polynomialtime approximation algorithm that computes a piecewise linear surface of size O(K o log K o ), where K o is the complexity of an optimal surface satisfying the constraints of the problem. The technique
Realistic Input Models for Geometric Algorithms
 IN PROC. 13TH ANNU. ACM SYMPOS. COMPUT. GEOM
, 1997
"... Many algorithms developed in computational geometry are needlessly complicated and slow because they have to be prepared for very complicated, hypothetical inputs. To avoid this, realistic models are needed that describe the properties that realistic inputs have, so that algorithms can de designed t ..."
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Cited by 91 (17 self)
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Many algorithms developed in computational geometry are needlessly complicated and slow because they have to be prepared for very complicated, hypothetical inputs. To avoid this, realistic models are needed that describe the properties that realistic inputs have, so that algorithms can de designed that take advantage of these properties. This can lead to algorithms that are provably efficient in realistic situations. We obtain some fundamental results in this research direction. In particular, we have the following results. ffl We show the relations between various models that have been proposed in the literature. ffl For several of these models, we give algorithms to compute the model parameter(s) for a given scene; these algorithms can be used to verify whether a model is appropriate for typical scenes in some application area. ffl As a case study, we give some experimental results on the appropriateness of some of the models for one particular type of scenes often encountered in ...
Approximation Algorithms for Geometric Tour and Network Design Problems (Extended Abstract)
"... ..."
Balanced Aspect Ratio Trees: Combining the Advantages of kd Trees and Octrees
"... Given a set S of n points in R^d, we show, for fixed d, how to construct in O(n log n) time a data structure we call the Balanced Aspect Ratio (BAR) tree. A BAR tree is a binary space partition tree on S that has O(logn) depth and in which every region is convex and “fat ” (that is, has a bounded as ..."
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Cited by 55 (7 self)
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Given a set S of n points in R^d, we show, for fixed d, how to construct in O(n log n) time a data structure we call the Balanced Aspect Ratio (BAR) tree. A BAR tree is a binary space partition tree on S that has O(logn) depth and in which every region is convex and “fat ” (that is, has a bounded aspect ratio). While previous hierarchical data structures, such as kd trees, quadtrees, octrees, fairsplit trees, and balanced box decompositions can guarantee some of these properties, we know of no previous data structure that combines alI of these properties simultaneously. The BAR tree data structure has numerous applications ranging from solving several geometric searching problems in fixed dimensional space to aiding in the visualization of graphs and threedimensional worlds.
Fast Rendering of Irregular Grids
, 2007
"... We propose a fast algorithm for rendering general irregular grids. Our method uses a sweepplane approach to accelerate ray casting, and can handle disconnected and nonconvex (even with holes) unstructured irregular grids with a rendering cost that decreases as the “disconnectedness” decreases. The ..."
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Cited by 43 (11 self)
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We propose a fast algorithm for rendering general irregular grids. Our method uses a sweepplane approach to accelerate ray casting, and can handle disconnected and nonconvex (even with holes) unstructured irregular grids with a rendering cost that decreases as the “disconnectedness” decreases. The algorithm is carefully tailored to exploit spatial coherence even if the image resolution differs substantially from the object space resolution. In this paper, we establish the practicality of our method through experimental results based on our implementation, and we also provide theoretical results, both lower and upper bounds, on the complexity of ray casting of irregular grids.
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 39 (13 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...
The lazy sweep ray casting algorithm for rendering irregular grids
 IEEE Transactions on Visualization and Computer Graphics
, 1997
"... ..."
Linear Size Binary Space Partitions for Uncluttered Scenes
 Algorithmica
, 1998
"... We describe a new and simple method for constructing binary space partitions in arbitrary dimensions. We also introduce the concept of uncluttered scenes, which are scenes with a certain property that we suspect many realistic scenes exhibit, and we show that our method constructs a BSP of size O ..."
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Cited by 32 (8 self)
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We describe a new and simple method for constructing binary space partitions in arbitrary dimensions. We also introduce the concept of uncluttered scenes, which are scenes with a certain property that we suspect many realistic scenes exhibit, and we show that our method constructs a BSP of size O(n) for an uncluttered scene consisting of n objects. The construction time is O(n log n). Because any set of disjoint fat objects is uncluttered, our result implies an efficient method to construct a linear size BSP for fat objects. We use our BSP to develop a data structure for point location in uncluttered scenes. The query time of our structure is O(log n), and the amount of storage is O(n). This result can in turn be used to perform range queries with nottoosmall ranges in scenes consisting of disjoint fat objects or, more generally, in socalled lowdensity scenes. 1 Introduction Many geometric problems can be solved more easily if a decomposition of the space of interest in...
RealTime Tracking of Complex Structures With onLine Camera Calibration
 In Proc. British Machine Vision Conference (BMVC’99
, 1999
"... This paper presents a novel threedimensional modelbased tracking system which has been incorporated into a visual servoing system. ..."
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Cited by 31 (4 self)
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This paper presents a novel threedimensional modelbased tracking system which has been incorporated into a visual servoing system.