scholarly journals A Geometric Orthogonal Projection Strategy for Computing the Minimum Distance Between a Point and a Spatial Parametric Curve

Algorithms ◽  
2016 ◽  
Vol 9 (1) ◽  
pp. 15 ◽  
Author(s):  
Xiaowu Li ◽  
Zhinan Wu ◽  
Linke Hou ◽  
Lin Wang ◽  
Chunguang Yue ◽  
...  
Keyword(s):  
Orthogonal Projection ◽  
Minimum Distance ◽  
Parametric Curve ◽  
Projection Strategy

scholarly journals Hybrid Second Order Method for Orthogonal Projection onto Parametric Curve in n-Dimensional Euclidean Space

Mathematics ◽  
2018 ◽  
Vol 6 (12) ◽  
pp. 306 ◽  
Author(s):  
Juan Liang ◽  
Linke Hou ◽  
Xiaowu Li ◽  
Feng Pan ◽  
Taixia Cheng ◽  
...  
Keyword(s):  
Euclidean Space ◽  
Orthogonal Projection ◽  
Second Order ◽  
Dimensional Euclidean Space ◽  
Order Method ◽  
Order Convergence ◽  
Initial Value ◽  
Parametric Curve ◽  
First Order ◽  
Special Cases

Orthogonal projection a point onto a parametric curve, three classic first order algorithms have been presented by Hartmann (1999), Hoschek, et al. (1993) and Hu, et al. (2000) (hereafter, H-H-H method). In this research, we give a proof of the approach’s first order convergence and its non-dependence on the initial value. For some special cases of divergence for the H-H-H method, we combine it with Newton’s second order method (hereafter, Newton’s method) to create the hybrid second order method for orthogonal projection onto parametric curve in an n-dimensional Euclidean space (hereafter, our method). Our method essentially utilizes hybrid iteration, so it converges faster than current methods with a second order convergence and remains independent from the initial value. We provide some numerical examples to confirm robustness and high efficiency of the method.

scholarly journals Modifications of the Charged Balls Method

2020 ◽  
Vol 10 (1) ◽  
pp. 30-32
Author(s):  
Majid Abbasov ◽  
Faramoz Aliev
Keyword(s):  
Computational Geometry ◽  
Orthogonal Projection ◽  
Numerical Experiments ◽  
Minimum Distance ◽  
Smooth Boundary ◽  
Optimization Methods ◽  
Closed Set ◽  
Convex Closed Set ◽  
Charged Ball

AbstractThe Charged Balls Method is based on physical ideas. It allows one to solve problem of finding the minimum distance from a point to a convex closed set with a smooth boundary, finding the minimum distance between two such sets and other problems of computational geometry. This paper proposes several new quick modifications of the method. These modifications are compared with the original Charged Ball Method as well as other optimization methods on a large number of randomly generated model problems.We consider the problem of orthogonal projection of the origin onto an ellipsoid. The main aim is to illustrate the results of numerical experiments of Charged Balls Method and its modifications in comparison with other classical and special methods for the studied problem.

Orthogonal Projection DOA Estimation with a Single Snapshot

2013 ◽  
Vol E96.B (5) ◽  
pp. 1215-1217 ◽  
Author(s):  
Ann-Chen CHANG ◽  
Chih-Chang SHEN
Keyword(s):  
Orthogonal Projection ◽  
Doa Estimation ◽  
Single Snapshot

Determining The Minimum Distance Between Centers of Two Parallel Tunnels to Apply The Law of Super Position in Order to Calculate Subsidence by Using The Software FLAC 3D

2015 ◽  
Vol 1 (1) ◽  
pp. 13-20
Author(s):  
Hamid Reza Samadi ◽  
Mohammad Reza Samadi
Keyword(s):  
Minimum Distance ◽  
Surface Subsidence ◽  
Urban Traffic ◽  
Underground Structures ◽  
Rapid Population Growth ◽  
The North ◽  
Flac 3D ◽  
The Law ◽  
3D Software ◽  
Twin Tunnels

Due to the development of cities as well as rapid population growth, urban traffic is increasing nowadays. Hence, to improve traffic flow, underground structures such as metro, especially in metropolises, are inevitable. This paper is a research on the twin tunnels Of Isfahan's metro between Shariaty station and Azadi station from the North towards the South. In this study, simultaneous drilling of subway's twin tunnels is simulated by means of Finite Difference Method (FDM) and FLAC 3D software. Moreover, the lowest distance between two tunnels is determined in a way that the Law of Super Position could be utilized to manually calculate the amount of surface subsidence, resulted by drilling two tunnels, by employing the results of the analysis of single tunnels without using simultaneous examination and simulation. In this paper, this distance is called "effective distance". For this purpose, first, the optimum dimensions of the model is chosen and then, five models with optimum dimensions will be analyzed separately, each of which in three steps. The results of analyses shows that the proportions (L/D) greater than or equal 2.80, the Law of Super Position can be applied for prediction of surface subsidence, caused by twin tunnels' construction

Detection of Small Target on the Sea Surface Using Orthogonal Projection

2014 ◽  
Vol 35 (1) ◽  
pp. 24-28
Author(s):  
Yong Yang ◽  
Shun-ping Xiao ◽  
De-jun Feng ◽  
Wen-ming Zhang
Keyword(s):  
Orthogonal Projection ◽  
Sea Surface ◽  
Small Target

Defining U.S. Atlantic Command's Role in the Power Projection Strategy

1998 ◽  
Author(s):  
Douglas C. Lovelace ◽  
Young Jr. ◽  
Thomas-Durell
Keyword(s):  
Power Projection ◽  
Projection Strategy

Determination of Pyridostigmine Bromide in Presence of its Related Impurities by Four Modified Classical Least Square Based Models: A Comparative Study

2020 ◽  
Vol 17 (1) ◽  
pp. 87-94
Author(s):  
Ibrahim A. Naguib ◽  
Fatma F. Abdallah ◽  
Aml A. Emam ◽  
Eglal A. Abdelaleem
Keyword(s):  
Comparative Study ◽  
Least Squares ◽  
Orthogonal Projection ◽  
Predictive Ability ◽  
Least Square ◽  
Projection To Latent Structures ◽  
Preprocessing Method ◽  
Spectral Residual ◽  
Latent Structures

: Quantitative determination of pyridostigmine bromide in the presence of its two related substances; impurity A and impurity B was considered as a case study to construct the comparison. Introduction: Novel manipulations of the well-known classical least squares multivariate calibration model were explained in detail as a comparative analytical study in this research work. In addition to the application of plain classical least squares model, two preprocessing steps were tried, where prior to modeling with classical least squares, first derivatization and orthogonal projection to latent structures were applied to produce two novel manipulations of the classical least square-based model. Moreover, spectral residual augmented classical least squares model is included in the present comparative study. Methods: 3 factor 4 level design was implemented constructing a training set of 16 mixtures with different concentrations of the studied components. To investigate the predictive ability of the studied models; a test set consisting of 9 mixtures was constructed. Results: The key performance indicator of this comparative study was the root mean square error of prediction for the independent test set mixtures, where it was found 1.367 when classical least squares applied with no preprocessing method, 1.352 when first derivative data was implemented, 0.2100 when orthogonal projection to latent structures preprocessing method was applied and 0.2747 when spectral residual augmented classical least squares was performed. Conclusion: Coupling of classical least squares model with orthogonal projection to latent structures preprocessing method produced significant improvement of the predictive ability of it.

ENSURING THE PEDESTRIAN’S SAFETY DESIGN OF URBAN STREET CROSSWALKS

2019 ◽  
pp. 103-110
Author(s):  
Dmitriy Nemchinov
Keyword(s):  
Traffic Flow ◽  
Minimum Distance ◽  
Travel Speed ◽  
Vehicle Speed ◽  
Urban Street ◽  
Safety Design ◽  
Positive Practices ◽  
Time Required ◽  
Pedestrian Crossing ◽  
The City

The article presents an analysis of positive practices for ensuring the safety of pedestrians at the inter-section of the city streets carriageway, as well as a description of some innovations of regulatory and tech-nical documents, including an increased number of cases when a safety island can be arranged at a pedestri-an crossing. requirements for providing visibility at a pedestrian crossing to determine the minimum distance of visibility at a pedestrian crossing based on the time required pedestrians for crossing the roadway, recommended options for using ground unregulated pedestrian crossings on trapezoidal artificial irregularities according to GOST R 52605; traffic flow) and Z-shaped (also in the direction of the traffic flow), the requirements for the size of the securi-ty island have been established to allow put bicycle inside of safety island, a recommended set of measures to reduce the vehicle speed and describes the types of activities and describes a method of their application, describes methods zones device with reduced travel speed - residential and school zones, set requirements for turboroundabouts and methods of their design.

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