scholarly journals Differential Privacy Trajectory Data Protection Algorithm Based on Polar Coordinate Transformation

2020 ◽  
Author(s):  
Zhenzhen Zhang ◽  
Jianping Cai ◽  
Lan Sun ◽  
Yongyi Guo ◽  
Yubing Qiu ◽  
...  
Keyword(s):  
Coordinate System ◽  
Data Protection ◽  
Differential Privacy ◽  
Polar Coordinates ◽  
Trajectory Data ◽  
Rectangular Coordinate System ◽  
Data Release ◽  
Information Research ◽  
Polar Coordinate ◽  
System Representation

Differential privacy technology has been widely used in the issue of trajectory data release. Improving the availability of data release under the premise of ensuring privacy and security is one of its basic research goals. At present, most trajectory data release methods use a rectangular coordinate system to represent location information. Research has shown that the availability of published data cannot be optimized through the rectangular coordinate system. In order to improve the effect of trajectory data release, this paper proposes a differential privacy trajectory data protection algorithm based on polar coordinates. First, the stay point detection method is used to find frequent stay points in the trajectory and the key location points related to personal privacy are detected by the type of location points. Then, this paper converts the rectangular coordinate system representation of the key position points to the polar coordinate system representation, and implement differential privacy trajectory data release by adding noise to the key position points represented by the polar coordinates. Experiments show that the algorithm proposed in this paper effectively improves the usability of trajectory data on real data sets.

scholarly journals Determination of Ship Approach Parameters in the Polar Coordinates System

2014 ◽  
Vol 96 (1) ◽  
pp. 1-8
Author(s):  
Andrzej Banachowicz ◽  
Adam Wolski
Keyword(s):  
Coordinate System ◽  
Target Position ◽  
Geometric Interpretation ◽  
Polar Coordinates ◽  
Polar Coordinate System ◽  
Polar Coordinate ◽  
Radar Measurements ◽  
Cartesian Coordinate ◽  
Radar Antenna

Abstract An essential aspect of the safety of navigation is avoiding collisions with other vessels and natural or man made navigational obstructions. To solve this kind of problem the navigator relies on automatic anti-collision ARPA systems, or uses a geometric method and makes radar plots. In both cases radar measurements are made: bearing (or relative bearing) on the target position and distance, both naturally expressed in the polar coordinates system originating at the radar antenna. We first convert original measurements to an ortho-Cartesian coordinate system. Then we solve collision avoiding problems in rectangular planar coordinates, and the results are transformed to the polar coordinate system. This article presents a method for an analysis of a collision situation at sea performed directly in the polar coordinate system. This approach enables a simpler geometric interpretation of a collision situation

Using a Polar Coordinate System in the Classroom

1990 ◽  
Vol 37 (8) ◽  
pp. 42-45
Author(s):  
William M. Carroll
Keyword(s):  
Elementary School ◽  
Coordinate System ◽  
School Level ◽  
Polar Coordinate System ◽  
School Students ◽  
Rectangular Coordinate System ◽  
Polar Coordinate ◽  
Supplementary Material ◽  
Cartesian Coordinate ◽  
Additional Exposure

Most elementary school students have experiences with a rectangular graphing system that helps to prepare them for ideas in algebra and analytic geometry. Mathematics books at the elementary school level contain a section on graphing, though it is often one of the later chapters, where it may be treated as supplementary material. In science and in social studies, students may find various data graphed or may have a project in which they have to graph daily temperatures, rainfall, or test scores. Biorhythms, record sales charts, or, for the more ambitious, the daily stock market give additional exposure. Designing graphics on the computer monitor often requires some placement by a rectangular coordinate system. By the time students meet the Cartesian coordinate system with its x- and y-axes and use it to graph equations, the idea and techniques should be somewhat familiar.

Research on Application of NC Polish-Grinding of Valve Stem and Instantaneous Compensation of Grinding Wheel

2011 ◽  
Vol 487 ◽  
pp. 515-520
Author(s):  
Ying Liang Yu ◽  
W.M. Li ◽  
Zhi Yi Miao ◽  
De Qing Yang
Keyword(s):  
Coordinate System ◽  
Open Loop ◽  
Grinding Wheel ◽  
Polar Coordinate System ◽  
Rectangular Coordinate System ◽  
Nc System ◽  
Polar Coordinate ◽  
In Series ◽  
Grinding Machine ◽  
Research On Application

According to the example of using a common grinding and composition of parts processing movement and achievement elements, the design of construction of special NC technologies in ordinary grinding machine was formulated. . The grinding and polish-grinding were performed by using two NC systems in series to achieve multi-axis movement. The function and application scope of NC technology were expanded because the instantaneous compensation of the grinding wheel and the polish-grinding wheel were performed under a rectangular coordinate system and a polar coordinate system by using an open loop NC system. The application of surface recovery of grinding wheel by NC reconstruction and extension applications of processing the track of involute curve were referred.

Research on Application of NC Polish-Grinding of Valve Stem and Instantaneous Compensation of Grinding Wheel

2012 ◽  
Vol 163 ◽  
pp. 191-195
Author(s):  
Ying Liang Yu ◽  
Zhan Li Huang ◽  
De Qing Yang ◽  
Zhi Yi Miao
Keyword(s):  
Coordinate System ◽  
Open Loop ◽  
Grinding Wheel ◽  
Polar Coordinate System ◽  
Rectangular Coordinate System ◽  
Nc System ◽  
Polar Coordinate ◽  
In Series ◽  
Grinding Machine ◽  
Research On Application

According to the example of using a common grinding and composition of parts processing movement and achievement elements, the design of construction of special NC technologies in ordinary grinding machine was formulated. . The grinding and polish-grinding were performed by using two NC systems in series to achieve multi-axis movement. The function and application scope of NC technology were expanded because the instantaneous compensation of the grinding wheel and the polish-grinding wheel were performed under a rectangular coordinate system and a polar coordinate system by using an open loop NC system. The application of surface recovery of grinding wheel by NC reconstruction and extension applications of processing the track of involute curve were referred.

Outlier detection by the EM algorithm for laser scanning in rectangular and polar coordinate systems

2015 ◽  
Vol 9 (3) ◽  
Author(s):  
Karl-Rudolf Koch ◽  
Boris Kargoll
Keyword(s):  
Em Algorithm ◽  
Coordinate System ◽  
Linear Model ◽  
Laser Scanning ◽  
Local Coordinate System ◽  
Polar Coordinates ◽  
Polar Coordinate System ◽  
Coordinate Systems ◽  
The Em Algorithm ◽  
Polar Coordinate

AbstractTo visualize the surface of an object, laser scanners determine the rectangular coordinates of points of a grid on the surface of the object in a local coordinate system. Vertical angles, horizontal angles and distances of a polar coordinate system are measured with the scanning. Outliers generally occur as gross errors in the distances. It is therefore investigated here whether rectangular or polar coordinates are better suited for the detection of outliers. The parameters of a surface represented by a polynomial are estimated in the nonlinear Gauss Helmert (GH) model and in a linear model. Rectangular and polar coordinates are used, and it is shown that the results for both coordinate systems are identical. It turns out that the linear model is sufficient to estimate the parameters of the polynomial surface. Outliers are therefore identified in the linear model by the expectation maximization (EM) algorithm for the variance-inflation model and are confirmed by the EM algorithm for the mean-shift model. Again, rectangular and polar coordinates are used. The same outliers are identified in both coordinate systems.

scholarly journals Polar Transforms for ITK

2006 ◽  
Author(s):  
Jakub Bican
Keyword(s):  
Image Processing ◽  
Coordinate System ◽  
Polar Coordinates ◽  
Polar Coordinate System ◽  
Cartesian Coordinates ◽  
Polar Coordinate ◽  
2D Space

Polar transform is a geometric transform, that transforms points form cartesian coordinates to so-called polar coordinates. In case of 2D space, a point in polar coordinate system is addressed by radius and angle. In image processing, polar transform is usually used to convert rotations around the origin of polar coordinate system to translations.This submission contains the implementation of forward and inverse polar transforms in two very simple classes for the Insight Toolkit.

scholarly journals Gauge invariance, polar coordinates and inflation

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Ali Akil ◽  
Xi Tong
Keyword(s):  
Coordinate System ◽  
Effective Potential ◽  
Gauge Invariance ◽  
Polar Coordinates ◽  
Quantum Corrections ◽  
Background Current ◽  
Gauge Invariant ◽  
Gauge Dependence ◽  
Current Term ◽  
Invariant Current

Abstract We point out the necessity of resolving the apparent gauge dependence in the quantum corrections of cosmological observables for Higgs-like inflation models. We highlight the fact that this gauge dependence is due to the use of an asymmetric background current which is specific to a choice of coordinate system in the scalar manifold. Favoring simplicity over complexity, we further propose a practical shortcut to gauge-independent inflationary observables by using effective potential obtained from a polar-like background current choice. We demonstrate this shortcut for several explicit examples and present a gauge-independent prediction of inflationary observables in the Abelian Higgs model. Furthermore, with Nielsen’s gauge dependence identities, we show that for any theory to all orders, a gauge-invariant current term gives a gauge-independent effective potential and thus gauge-invariant inflationary observables.

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