Sifted Disks

Ebeida, Mohamed S.; Mahmoud, Ahmed H.; Awad, Muhammad A.; Mohammed, Mohammed A.; Mitchell, Scott A.; Rand, Alexander; Owens, John D.

doi:10.1111/cgf.12071

Cited by 6 publications

(8 citation statements)

References 39 publications

(54 reference statements)

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“…We have compared and contrasted these to the works of others. These variations [6,8], and their tradeoffs, led us to the conceptual framework for sampling illustrated in Fig. 13 A"Space"for"All"Sampling"Methods" Spa5al" Randomness" Geometric" Density"…”

Section: Discussionmentioning

confidence: 99%

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Exercises in High-Dimensional Sampling: Maximal Poisson-Disk Sampling and k-d Darts

Ebeida

Mitchell

Patney

et al. 2014

Mathematics and Visualization

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We review our recent progress on efficient algorithms for generating wellspaced samples of high dimensional data, and for exploring and characterizing these data, the underlying domain, and functions over the domain. To our knowledge, these techniques have not yet been applied to computational topology, but the possible connections are worth considering. In particular, computational topology problems often have difficulty in scaling efficiently, and these sampling techniques have the potential to drastically reduce the size of the data over which these computational topology algorithms must operate. We summarize the definition of these sample distributions; algorithms for generating them in low, moderate, and high dimensions; and applications in mesh generation, rendering, motion planning and simulation.

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Section: Discussionmentioning

confidence: 99%

“…However, it has the biggest restriction on the Lipschitz constant (< 1/2) and provides the weakest output quality guarantees. We have also explored sifted disks for reducing the discrete density of a maximal point set, by removing and relocating points, while still maintaining the MPS conditions [8].…”

Section: Variable Radii Mpsmentioning

confidence: 99%

Exercises in High-Dimensional Sampling: Maximal Poisson-Disk Sampling and k-d Darts

Ebeida

Mitchell

Patney

et al. 2014

Mathematics and Visualization

Self Cite

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“…Maximality guarantees for each point in the domain, there exists a sample no farther than r . Variants of MPS use different spatial constraints to provide different quality bounds [MREB12, YW12, EMA*13]. Observe that MPS only uses spheres as sampling constraints.…”

Section: The Strategymentioning

confidence: 99%

A Constrained Resampling Strategy for Mesh Improvement

Abdelkader

Mahmoud

Rushdi

et al. 2017

Computer Graphics Forum

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In many geometry processing applications, it is required to improve an initial mesh in terms of multiple quality objectives. Despite the availability of several mesh generation algorithms with provable guarantees, such generated meshes may only satisfy a subset of the objectives. The conflicting nature of such objectives makes it challenging to establish similar guarantees for each combination, e.g., angle bounds and vertex count. In this paper, we describe a versatile strategy for mesh improvement by interpreting quality objectives as spatial constraints on resampling and develop a toolbox of local operators to improve the mesh while preserving desirable properties. Our strategy judiciously combines smoothing and transformation techniques allowing increased flexibility to practically achieve multiple objectives simultaneously. We apply our strategy to both planar and surface meshes demonstrating how to simplify Delaunay meshes while preserving element quality, eliminate all obtuse angles in a complex mesh, and maximize the shortest edge length in a Voronoi tessellation far better than the state-of-the-art.

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“…We find the subregion of the void where a disk center covers all the corners, and randomly select the new center p from it. This is the same as the Sifted Disks [EMA*13] operation.…”

Section: Ejection Of Uniform Radii Disksmentioning

confidence: 99%

Disk Density Tuning of a Maximal Random Packing

Ebeida

Rushdi

Awad

et al. 2016

Computer Graphics Forum

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We introduce an algorithmic framework for tuning the spatial density of disks in a maximal random packing, without changing the sizing function or radii of disks. Starting from any maximal random packing such as a Maximal Poisson-disk Sampling (MPS), we iteratively relocate, inject (add), or eject (remove) disks, using a set of three successively more-aggressive local operations. We may achieve a user-defined density, either more dense or more sparse, almost up to the theoretical structured limits. The tuned samples are conflict-free, retain coverage maximality, and, except in the extremes, retain the blue noise randomness properties of the input. We change the density of the packing one disk at a time, maintaining the minimum disk separation distance and the maximum domain coverage distance required of any maximal packing. These properties are local, and we can handle spatially-varying sizing functions. Using fewer points to satisfy a sizing function improves the efficiency of some applications. We apply the framework to improve the quality of meshes, removing non-obtuse angles; and to more accurately model fiber reinforced polymers for elastic and failure simulations.

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Sifted Disks

Cited by 6 publications

References 39 publications

Exercises in High-Dimensional Sampling: Maximal Poisson-Disk Sampling and k-d Darts

Exercises in High-Dimensional Sampling: Maximal Poisson-Disk Sampling and k-d Darts

A Constrained Resampling Strategy for Mesh Improvement

Disk Density Tuning of a Maximal Random Packing

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