scholarly journals A Boundary Construction Algorithm for a Complex Planar Point Set

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Zhenxiu Liao ◽  
Guodong Shi

It is difficult to extract the boundary of complex planar points with nonuniform distribution of point density, concave envelopes, and holes. To solve this problem, an algorithm is proposed in this paper. Based on Delaunay triangulation, the maximum boundary angle threshold is introduced as the parameter in the extraction of the rough boundary. Then, the point looseness threshold is introduced, and the fine boundary extraction is conducted for the local areas such as concave envelopes and holes. Finally, the complete boundary result of the whole point set is obtained. The effectiveness of the proposed algorithm is verified by experiments on the simulated point set and practical measured point set. The experimental results indicate that it has wider applicability and more effectiveness in engineering applications than the state-of-the-art boundary construction algorithms based on Delaunay triangulation.

2011 ◽  
Vol 130-134 ◽  
pp. 2915-2919
Author(s):  
Ping Duan ◽  
Jia Tian Li ◽  
Jia Li

Spherical Delaunay triangulation (SDT) which is a powerful tool to represent, organize and analyze spherical space data has become a focus of spherical GIS research. Projection stitching algorithm is one of the main construction algorithms of SDT. The basic idea of stitching algorithm is that the sphere is divided into two hemispheres to avoid projected image point coincidence. So, the practicality of projection stitching algorithm is lower because of merging two hemispheres. Aimed at the disadvantage of projection stitching algorithm, this paper puts forward a new algorithm to construct SDT used perspective projection principle. The projection center is placed on sphere to establish one-to-one mapping between spherical space points and plane image points. Experiment shows that the time complexity of our algorithm depends on Delaunay triangulation construction algorithm of the plane.


2020 ◽  
Vol 67 ◽  
pp. 607-651
Author(s):  
Margarita Paz Castro ◽  
Chiara Piacentini ◽  
Andre Augusto Cire ◽  
J. Christopher Beck

We investigate the use of relaxed decision diagrams (DDs) for computing admissible heuristics for the cost-optimal delete-free planning (DFP) problem. Our main contributions are the introduction of two novel DD encodings for a DFP task: a multivalued decision diagram that includes the sequencing aspect of the problem and a binary decision diagram representation of its sequential relaxation. We present construction algorithms for each DD that leverage these different perspectives of the DFP task and provide theoretical and empirical analyses of the associated heuristics. We further show that relaxed DDs can be used beyond heuristic computation to extract delete-free plans, find action landmarks, and identify redundant actions. Our empirical analysis shows that while DD-based heuristics trail the state of the art, even small relaxed DDs are competitive with the linear programming heuristic for the DFP task, thus, revealing novel ways of designing admissible heuristics.


2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Zhenxiu Liao ◽  
Jun Liu ◽  
Guodong Shi ◽  
Junxia Meng

On the basis of Alpha Shapes boundary extraction algorithm for discrete point set, a grid partition variable step Alpha Shapes algorithm is proposed to deal with the shortcomings of the original Alpha Shapes algorithm in the processing of nonuniform distributed point set and multiconcave point set. Firstly, the grid partition and row-column index table are established for the point set, and the point set of boundary grid partition is quickly extracted. Then, the average distance of the k -nearest neighbors of the point is calculated as the value of α . For the point set of boundary grid partition extracted in the previous step, Alpha Shapes algorithm is used to quickly construct the point set boundary. The proposed algorithm is verified by experiments of simulated point set and measured point set, and it has high execution efficiency. Compared with similar algorithms, the larger the number of point sets is, the more obvious the execution efficiency is.


Author(s):  
Tülin İnkaya ◽  
Sinan Kayalıgil ◽  
Nur Evin Özdemirel

Boundary extraction is a fundamental post-clustering problem. It facilitates interpretability and usability of clustering results. Also, it provides visualization and dataset reduction. However, it has not attracted much attention compared to the clustering problem itself. In this work, we address the boundary extraction of clusters in 2- and 3-dimensional spatial datasets. We propose two algorithms based on Delaunay Triangulation (DT). Numerical experiments show that the proposed algorithms generate the cluster boundaries effectively. Also, they yield significant amounts of dataset reduction.


2020 ◽  
Vol 36 (11) ◽  
pp. 3516-3521 ◽  
Author(s):  
Lixiang Zhang ◽  
Lin Lin ◽  
Jia Li

Abstract Motivation Cluster analysis is widely used to identify interesting subgroups in biomedical data. Since true class labels are unknown in the unsupervised setting, it is challenging to validate any cluster obtained computationally, an important problem barely addressed by the research community. Results We have developed a toolkit called covering point set (CPS) analysis to quantify uncertainty at the levels of individual clusters and overall partitions. Functions have been developed to effectively visualize the inherent variation in any cluster for data of high dimension, and provide more comprehensive view on potentially interesting subgroups in the data. Applying to three usage scenarios for biomedical data, we demonstrate that CPS analysis is more effective for evaluating uncertainty of clusters comparing to state-of-the-art measurements. We also showcase how to use CPS analysis to select data generation technologies or visualization methods. Availability and implementation The method is implemented in an R package called OTclust, available on CRAN. Contact [email protected] or [email protected] Supplementary information Supplementary data are available at Bioinformatics online.


Acta Numerica ◽  
2000 ◽  
Vol 9 ◽  
pp. 133-213 ◽  
Author(s):  
Herbert Edelsbrunner

The Delaunay triangulation of a finite point set is a central theme in computational geometry. It finds its major application in the generation of meshes used in the simulation of physical processes. This paper connects the predominantly combinatorial work in classical computational geometry with the numerical interest in mesh generation. It focuses on the two- and three-dimensional case and covers results obtained during the twentieth century.


2015 ◽  
Vol 19 (5) ◽  
pp. 881-899 ◽  
Author(s):  
Claude Paraponaris ◽  
Martine Sigal

Purpose – Knowledge management is shot through with complex questions. This is certainly the case with regard to boundaries, as they constitute both a bounding line that has to be crossed if the knowledge required for innovation is to be diffused and a form of protection for scientific and technological organisations and institutions. This examination of boundaries leads to a state-of-the-art review that begins with the question of knowledge transfer. The authors start with foundations of the knowledge dynamic within organisations. Nevertheless, certain gaps were identified in the theory, as it did not seem so easy to carry out transfers. This led in turn to attempts to identify the boundaries that were causing difficulties and that had to be crossed. This led to an examination of the role of boundaries. What status could boundaries have when knowledge was expanding enormously within communities? Finally, the authors come face-to-face with knowledge management systems that have tended to redefine the forms that boundaries take. Design/methodology/approach – The paper uses a conceptual approach and is a meta analysis of the state-of-the-art review conducted to introduce the Special Issue “Knowledge Across Boundaries” JKM Volume 19, No. 5, 2015 (October). Findings – The notions of transfer and boundary demonstrated their usefulness in the development of a new theory, namely the knowledge-based view. These concepts were then critiqued, with reference, first, to the contexts in which communication takes place and, second, to the cognitive dimensions of the activity. Finally, studies showed that the cognitive and organisational approaches can be linked and that they shed light on many knowledge-sharing situations. Boundaries are no longer the object of attention, the focus having switched to the collective process of creating new concepts. Research limitations/implications – This state-of-the-art review is limited to the papers about Management Science. Practical implications – Knowledge hybridization is possible but must be referred to resources made available by the division of labour between disciplines (Shinn, 1997). Expansive learning (Engeström, 2010) is close to boundary construction (Holford, 2015) to indicate the dialectical view between instituting and instituted society (Castoriadis, 1975, 1987). We are now perhaps at the point of transition between the interest in “boundary spanners” and a new concern with “boundary construction”. Social implications – This paper introduces a methodology of knowledge transfer knowledge transfer in firms strategies of learning. Originality/value – The paper provides the concept (with examples) of ‘boundary construction’.


2014 ◽  
Vol 24 (02) ◽  
pp. 125-152 ◽  
Author(s):  
JEAN-DANIEL BOISSONNAT ◽  
RAMSAY DYER ◽  
ARIJIT GHOSH

We present an algorithm that takes as input a finite point set in ℝm, and performs a perturbation that guarantees that the Delaunay triangulation of the resulting perturbed point set has quantifiable stability with respect to the metric and the point positions. There is also a guarantee on the quality of the simplices: they cannot be too at. The algorithm provides an alternative tool to the weighting or refinement methods to re-move poorly shaped simplices in Delaunay triangulations of arbitrary dimension, but in addition it provides a guarantee of stability for the resulting triangulation.


2020 ◽  
Vol 34 (07) ◽  
pp. 12717-12724
Author(s):  
Yang You ◽  
Yujing Lou ◽  
Qi Liu ◽  
Yu-Wing Tai ◽  
Lizhuang Ma ◽  
...  

Point cloud analysis without pose priors is very challenging in real applications, as the orientations of point clouds are often unknown. In this paper, we propose a brand new point-set learning framework PRIN, namely, Pointwise Rotation-Invariant Network, focusing on rotation-invariant feature extraction in point clouds analysis. We construct spherical signals by Density Aware Adaptive Sampling to deal with distorted point distributions in spherical space. In addition, we propose Spherical Voxel Convolution and Point Re-sampling to extract rotation-invariant features for each point. Our network can be applied to tasks ranging from object classification, part segmentation, to 3D feature matching and label alignment. We show that, on the dataset with randomly rotated point clouds, PRIN demonstrates better performance than state-of-the-art methods without any data augmentation. We also provide theoretical analysis for the rotation-invariance achieved by our methods.


1995 ◽  
Vol 06 (05) ◽  
pp. 639-649
Author(s):  
A. KARTASHOV ◽  
R. FOLK

We present a straightforward iterative algorithm constructing the planar Delaunay triangulation in [Formula: see text] time. The algorithm proceeds iteratively by adding new points one by one to a partial point set pre-ordered by one coordinate and adjusting the partial diagram correspondingly. We introduce the techniques of safe fragments, showing that the larger part of a partial digram cannot be changed by adding further points; in the average case of a random point set the amount of information which need be stored in memory at any moment does not exceed [Formula: see text]. The computational overhead for the memory management is linear in N. In particular, this makes very large Delaunay triangulations (and Voronoi tessellations) accessible for simulations on personal computers.


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