Improving spatial coverage while preserving the blue noise of point sets

Ebeida, Mohamed S.; Awad, Muhammad A.; Ge, Xinna; Mahmoud, Ahmed H.; Mitchell, Scott A.; Knupp, Patrick; Wei, Li-Yi

doi:10.1016/j.cad.2013.08.015

Cited by 13 publications

(12 citation statements)

References 28 publications

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“…The methods of generating points cloud disturbing can be improved. Several studies show the numerical methods to improve spatial distraining with postprocessing algorithms [9]. Using Voronoi diagram to create open and connected cell gives satisfactory results.…”

Section: Resultsmentioning

confidence: 99%

Simulation and Optimization of Porous Bone-Like Microstructures With Specific Mechanical Properties

Wit

Wronski

Tarasiuk

2019

APP

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Bone trabecular structure can be characterized as a connected network of mineral bars and plates with unique mechanical properties. Standard methods of producing bone-like structures based on periodic structures or foams have same limitations. The organization of the trabecular bone (meso scale) is adapted to the values of stresses and strains aﬀecting the skeletal system. To simulate bone-like structure, the methodology of generating stochastic structure based on hyperuniform spatial points distribution is proposed. Statistical analysis of generated structure shows the possibility to generate clouds of points in wide range of random close packing density, up to 59.52%. Points connected by Voronoi tessellation produce to unique porous topology with no closed-cells and with wide range of connectivity. Manufacturing of a generated structure is only limited by used technique. The proposed algorithm was developed regardless of the manufacturing technique, however, same examples of the structure were printed using 3D addictive technology. The mechanical properties of developed structure are strongly dependent on the material from which they are made, but the modiﬁcation of the structure allows to change the strength in speciﬁc and controlled way.

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Section: Resultsmentioning

confidence: 99%

Simulation and Optimization of Porous Bone-Like Microstructures With Specific Mechanical Properties

Wit

Wronski

Tarasiuk

2019

APP

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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%

“…5. We have also explored adapting a point set to obtain a smaller coverage radius, which improves interpolation error and mesh quality, by a method we call opt-beta, locally optimizing the position of nodes [6].…”

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

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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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“…Ebeida et al [30] proposed the notion of a well-spaced blue noise distribution. This is a distribution that both has the blue noise property and at the same time an improved spatial coverage ratio.…”

Section: Poisson Disk Samplingmentioning

confidence: 99%

Poisson disk sampling through disk packing

et al. 2015

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Poisson disk sampling is an important problem in computer graphics and has a wide variety of applications in imaging, geometry, rendering, etc. In this paper, we propose a novel Poisson disk sampling algorithm based on disk packing. The key idea uses the observation that a relatively dense disk packing layout naturally satisfies the Poisson disk distribution property that each point is no closer to the others than a specified minimum distance, i.e., the Poisson disk radius. We use this property to propose a relaxation algorithm that achieves a good balance between the random and uniform properties needed for Poisson disk distributions. Our algorithm is easily adapted to image stippling by extending identical disk packing to unequal disks. Experimental results demonstrate the efficacy of our approaches.

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Improving spatial coverage while preserving the blue noise of point sets

Cited by 13 publications

References 28 publications

Simulation and Optimization of Porous Bone-Like Microstructures With Specific Mechanical Properties

Simulation and Optimization of Porous Bone-Like Microstructures With Specific Mechanical Properties

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

Poisson disk sampling through disk packing

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