Quadratic bounds for hidden line elimination

Dévai, Frank

doi:10.1145/10515.10544

Cited by 36 publications

(17 citation statements)

References 16 publications

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“…Worst-case optimal algorithms are presented by Devai and McKenna. 9 ' 13 The running time of more recent algorithms depends on the input size and the scene complexity. 3 ' 7,8 ' 12 ' 17 ' 18 ' 19 The fastest known algorithm for hidden-surface removal takes time 0(n 2 / 3+e fc 2 / 3 + n 1+c ), where n is the size of the input and k is the scene complexity.…”

Section: The Object Complexity Modelmentioning

confidence: 99%

The Object Complexity Model for Hidden-Surface Removal

Grove¹,

Murali

Vitter

1999

Int. J. Comput. Geom. Appl.

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We define a new model of complexity, called object complexity, for measuring the performance of hidden-surface removal algorithms. This model is more appropriate for predicting the performance of these algorithms on current graphics rendering systems than the standard measure of scene complexity used in computational geometry. We also consider the problem of determining the set of visible windows in scenes consisting of n axis-parallel windows in E 3 . We present an algorithm that runs in optimal O(nlogn) time. The algorithm solves in the object complexity model the same problem that Bern 3 addressed in the scene complexity model.

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Section: The Object Complexity Modelmentioning

confidence: 99%

The Object Complexity Model for Hidden-Surface Removal

Grove¹,

Murali

Vitter

1999

Int. J. Comput. Geom. Appl.

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“…The worst-case size of the visible image of a scene with O(n) edges is equal to O(n2) (Devai 1986, Schmitt 1981. This bound holds also for the size v of the visible image of a PTM, as shown by Cole and Sharir (Cole and Sharir 1989).…”

Section: State-of-the-artmentioning

confidence: 99%

“…The problem of computing the visible image of a scene is generally referred as the Hidden Surface Removal (HSR) problem. The general quadratic upper bound to the space complexity of the visible image (Devai 1986, Schmitt 1981) applies also to a polyhedral terrain, thus giving a worst-case space requirement of O(n2) for a PTM with n vertices.…”

Section: Introductionmentioning

confidence: 99%

Representing the visibility structure of a polyhedral terrain through a horizon map

Floriani¹,

Magillo²

1996

International journal of geographical information systems

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We present a model for describing the visibility of a polyhedral terrain from a fixed viewpoint, based on a collection of nested horizons. We briefly introduce the concepts of mathematical and digital terrain models, and some background notions for visibility problems on terrains. Then, we define horizons on a polyhedral terrain, and introduce a visibility model, that we call the horizon map. We present a construction algorithm and a data structure for encoding the horizon map, and show how it can be used for solving point visibility queries with respect to a fixed viewpoint. IntroductionDescribing a terrain through visibility information has a variety of applications, such as geomorphology, navigation and terrain exploration. Problems which can be solved based on visibility are, for instance, the computation of the minimum number of observation points needed to view a region, or the computation of optimal locations for television transmitters (Cole and Sharir 1989, Goodchild and Lee 1989, Lee 1991.A terrain can be mathematically modelled as a surface described by a continuous function z =+(x, y), defined over a connected, not necessarily convex, domain D. Two points on a terrain are considered mutually visible when they can be joined by a straight-line segment lying above the terrain. In practice, a mathematical terrain model is approximated through a digital model, built on the basis of a finite set of points belonging to the terrain. Visibility algorithms developed in the computational geometry literature usually operate on polyhedral digital models, i.e., planar-faced approximations of a terrain (Agarwal and Sharir 1986, Mulmuley 1989, De Berg et al. 1991, Katz et al. 1991, Overmars and Sharir 1992, Reif and Sen 1988. Visibility algorithms operating on gridded DTMs are also available in commercial GIs. Such algorithms, though simple in structure and implementation, are not necessarily efficient and accurate-the visibility information they produce is not generally accurate because it is computed by using the grid cells as visibility units and by assuming arbitrary simplifications for the surface defined over each cell (Lee 1991); see also (Fisher 1993) for a discussion of uncertainty in information obtained by existing grid visibility algorithms.In this paper, we address the problem of representing the visibility of a polyhedral terrain from a fixed viewpoint and efficiently solving point visibility queries, i.e.,

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“…These requirements have encouraged the development of numerous properly structured visible line determination algorithms [1] such as Robert's Algorithm, Apple's Algorithm, Haloed Lines, The z-Buffer Algorithm, List-priority Algorithms, The DepthSort Algorithm, The Binary Space Partition(BSP) Tree Algorithm, Scan-line Algorithms etc. Recently Devai [3] proposed algorithm that runs in the O(n 2 ) time which is worstcase optimal but limited within fixed viewpoint.…”

Section: Introductionmentioning

confidence: 99%

An easier approach to visible edge determination from moving viewpoint

Rabban

Abdullah

Ahmed

et al. 2014

2014 International Conference on Electrical Engineering and Information &Amp; Communication Technology

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In this paper, we present an algorithm for visible edge determination from moving viewpoint in 2D-space by an easier approach. We show implementation details and performance analysis of the algorithm to justify the efficiency and correctness of the proposed algorithm. The time complexity of the algorithm is O(n 2 ) in the worst case but we hope time complexity can be reduced practically because of the effective optimization in case of sorting angularly and finding intersection of points in a fixed range. Further modification of this algorithm is expected to determine the visible surface from moving perspective yielding the near optimal solution in 3D-space.

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Quadratic bounds for hidden line elimination

Cited by 36 publications

References 16 publications

The Object Complexity Model for Hidden-Surface Removal

The Object Complexity Model for Hidden-Surface Removal

Representing the visibility structure of a polyhedral terrain through a horizon map

An easier approach to visible edge determination from moving viewpoint

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