A comparison of line integral algorithms

Mitchell, J. Ross; Dickof, Peter; Law, Alan

doi:10.1063/1.168381

Cited by 15 publications

(8 citation statements)

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“…Nevertheless, 18-connected and 26-connected lines are used in graphics for ray tracing. The reason is that the latter contain fewer voxels by a mean factor of 2, which implies a faster algorithm for computing lines [6][7][8][12][13][14]. Some algorithms can even switch between connectivities in order to achieve maximum precision with minimum computation time.…”

Section: Connectivity Of the Discrete Linementioning

confidence: 99%

“…However, the definition of this function is not unique and the choice of voxels representing the line is flexible, depending on the connectivity between them. A discrete line is said to have the containment property if it contains all voxels pierced by the continuous line [13]. A voxel of the 3-D discrete space shares 6 faces with the adjacent voxels, 12 edges, and 8 corners.…”

Section: Connectivity Of the Discrete Linementioning

confidence: 99%

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An Efficient CPU-GPU Implementation of the Multiple Absorption Coefficient Zonal Method (MACZM)

Ghannam

Nemer

Khoury

et al. 2012

Numerical Heat Transfer, Part B: Fundamentals

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International audienceThe multiple absorption coefficient zonal method (MACZM) is an efficient radiative heat transfer modeling method in nonisothermal inhomogeneous media. The method is of high interest for dynamic applications because of its ability to asses semitransparent radiative heat transfer in very short computation time. In this work, an efficient algorithm for MACZM is implemented. A connectivity control study is presented for taking into account the connectivity considerations required by the method. An identified ray traversal algorithm corresponding to part of the MACZM implementation is then selected among three different approaches presented in the article, based on well-known ray traver sal algorithms, the 6-tripod line algorithm and the 6-parametric line algorithm. On the other hand, the MACZM is highly parallel and is implemented in CUDA, a parallel computing architecture that enables easy use of a powerful graphics processing unit (GPU). An efficient implementation is discussed consisting of an optimal solution for exploiting the method parallelism (threading) and the use of the memory resources available on the GPU. Speed-ups going from 300 to 600 times are achieved, using a NVIDIA Tesla C 1060 GPU and an Intel Xeon CPU E5507 at 2.27 GHz. Radiative heat transfer is then simulated in a steel reheating furnace using the optimized GPU implementation. The computation time is further reduced by using a multigrid approach

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Section: Connectivity Of the Discrete Linementioning

confidence: 99%

Section: Connectivity Of the Discrete Linementioning

confidence: 99%

An Efficient CPU-GPU Implementation of the Multiple Absorption Coefficient Zonal Method (MACZM)

Ghannam

Nemer

Khoury

et al. 2012

Numerical Heat Transfer, Part B: Fundamentals

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show abstract

“…To remedy these issues, this paper advocates approximating the integral in (4) as a line integral of a piecewise constant approximation of l. The resulting approximation is continuous, can be used with large grid point spacing, and can be computed with complexity only O(Q 0 ) for a Q 0 × Q 0 × Q 0 grid. This technique, commonly used in other disciplines (see references in [43]), involves splitting the 3D space into voxels centered at the grid points X := {x X 1 , . .…”

Section: B Radio Tomographic Modelsmentioning

confidence: 99%

Aerial Base Station Placement via Propagation Radio Maps

Romero¹,

Viet²,

Shrestha³

2023

Preprint

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The technology of base stations on board unmanned aerial vehicles, also known as aerial base stations (ABSs), promises to deliver cellular connectivity in areas where the terrestrial infrastructure is overloaded, damaged, or inexistent. A central problem in this context is to determine the locations where these ABSs must be deployed to serve a set of users on the ground given the positions of the latter. However, existing schemes assume that the channel gain depends only on the length and (possibly) the elevation of the link. To alleviate this limitation, this paper proposes a scheme that accommodates arbitrary channel gains by means of a propagation radio map of the air-to-ground channel. The algorithm finds the locations of an approximately minimal number of ABSs to serve all ground terminals with a target rate while meeting the given constraints on the capacity of the backhaul links and respecting no-fly regions. A convex-relaxation formulation ensures convergence and the alternating-direction method of multipliers is utilized to derive an implementation whose complexity is linear in the number of ground terminals. Numerical results with tomographic as well as ray-tracing channel models corroborate the strengths of the proposed scheme.

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“…Instead, this work proposes adopting a different approximation to the integral in (4). The technique, commonly used in other disciplines (see references in [23]) and hinted in a different context in [21], involves splitting the 3D space in voxels centered at the grid points X := {x X 1 , . .…”

Section: An Algorithm For Air-to-ground Radio Tomographymentioning

confidence: 99%

Aerial Base Station Placement Leveraging Radio Tomographic Maps

Romero¹,

Viet²,

Leus³

2021

Preprint

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Mobile base stations on board unmanned aerial vehicles (UAVs) promise to deliver connectivity to those areas where the terrestrial infrastructure is overloaded, damaged, or absent. A fundamental problem in this context involves determining a minimal set of locations in 3D space where such aerial base stations (ABSs) must be deployed to provide coverage to a set of users. While nearly all existing approaches rely on average characterizations of the propagation medium, this work develops a scheme where the actual channel information is exploited by means of a radio tomographic map. A convex optimization approach is presented to minimize the number of required ABSs while ensuring that the UAVs do not enter nofly regions. A simulation study reveals that the proposed algorithm markedly outperforms its competitors.

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A comparison of line integral algorithms

Cited by 15 publications

References 0 publications

An Efficient CPU-GPU Implementation of the Multiple Absorption Coefficient Zonal Method (MACZM)

An Efficient CPU-GPU Implementation of the Multiple Absorption Coefficient Zonal Method (MACZM)

Aerial Base Station Placement via Propagation Radio Maps

Aerial Base Station Placement Leveraging Radio Tomographic Maps

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