• Journal of applied mathematics & informatics
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• v.32 no.5_6
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• pp.783-790
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• 2014

Most distance functions, including taxicab distance, are defined on Cartesian plane, and recent studies on distance functions have been mainly focused on Cartesian plane. However, most streets in cities include not only straight lines but also curves. Therefore, there is a significant need for a distance function to be defined on a curvilinear coordinate system. In this paper, we define a new function named polar taxicab distance, using polar coordinates. We prove that this function satisfies the conditions of distance function. We also investigate the geometric properties and classifications of circles in the plane with polar taxicab distance.

• Aerospace Engineering and Technology
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• v.10 no.1
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• pp.116-121
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• 2011

The tracking radar systems in NARO space center are used in order to acquire the TSPI (Time, Space, and Position Information) data of the launch vehicle. The tracking radar produce the measurements of tracked targets in the radar-centered coordinate system. When the tracking radar is in the Cartesian/Polar tracking mode, the state vector data is sent in radar-centered Cartesian/Polar coordinate system to RCC. RCC also send the slaving data in Test Range coordinate system to the tracking radar. So, the tracking radars have to transform the slaving data in Test Range coordinate system into in radar-centered coordinate system. In this study, we described the coordinate transformation between radar-centered coordinate system and Test Range coordinated system.

• Bulletin of the Society of Naval Architects of Korea
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• v.2 no.1
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• pp.15-19
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• 1965

The stability curves are very important data to decide the seaworthiness of all kinds of ships among waves. Both statical and dynamical stability curves on a rectangular coordinate system have broadly been handled at ship yards or at the government concerned, up to data. As concerns a method of obtaining a statical stability curve on polar coordinate system, the papers were presented once. Also, it is of use to research the dynamical stability curve on polar coordinate system. Author treated of the dynamical stability curve by four different methods, and tried to set the stability indicator inboard, adopted those proposals, in order to give some aids for good navigation on the sea. Fig. 1. shows a drawing method in case of the position of centre of buoyancy can be previously pointed out on the line corresponding to its inclination. Fig. 2. shows a method used a statical stability curve on polar coordinate. Fig. 3. shows a method obtained by the most simplified means. Fig. 4. shows dynamical stability curve made by geometrical expression method, instead of dynamical lever. A simple stability indicator which was mechanized above characteristics is attempted by author as shown Fig. 5 and Fig.6. It is demanded at hand, for more advanced improvement of such indicator.

• Journal of the Institute of Electronics Engineers of Korea SC
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• v.45 no.4
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• pp.20-28
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• 2008

We propose a radial image processing method in a discrete polar coordinate system based on L1-norm. For this purpose, we first verified that the polar coordinate based on L2-norm can not exist in discrete system and then develop a method converting the Cartesian coordinate to the discrete polar coordinate. We apply the proposed method to smooth mass images of breast tissue and to detect the boundaries of extremely deformable objects. Compared to the Gaussian smoothing method performed in the Cartesian coordinate system, the proposed method stabilized the image signal while maintaining the overall radial shape of mass images. The proposed boundary detection method can detect shapes with high precision while conventional edge detectors can not accurately detect the shape of deformable objects. We also exploit the method to perform pupil detection and have had good experimental results.

• Korean Journal of Mathematics
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• v.22 no.3
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• pp.567-581
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• 2014

Over the years, there has been much research conducted on quadratic curves and the set of points with the generalized notion of eccentricity in a plane with metrics such as taxicab distance or Chinese-checker distance. On the other hand, polar taxicab distance has been newly proposed on the polar coordinate system, a type of curvilinear coordinate system, to overcome the limitation of pre-existing metrics in terms of describing curved routes. Previous study has looked into the fundamental properties of this metric. From this point of view, we study the quadratic curves and the set of points with the generalized notion of eccentricity in a plane with polar taxicab distance.

• Journal of the Institute of Electronics and Information Engineers
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• v.52 no.11
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• pp.147-155
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• 2015

For the image processing system to be classified the selected object in the nature, the rotation, scale and transition invariant features is to be necessary. There are many investigations to get the information for the object processing system and the log-polar transform which is to be get the invariant feature for the scale and rotation is used. In this paper, we suggested the 2 points polar coordinate transform methods to measure the selected object position out of the center in input image including the centroid method. In this proposed system, the position results of objects are very good, and we obtained the similarity ratio 99~104% for the object coordinate values.

• Journal of the Korean Institute of Telematics and Electronics A
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• v.33A no.6
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• pp.178-188
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• 1996

In this paper, we propose a new opto-digital object recognition system which has rotation, scale, and shift invariant characteristics. The fourier power spectrum of the object image is modified to get shift invariance. The log-polar transform is used for rotation and scale invariance. And the decision of similarities is performed by nonlinear joint transform correlator (NJTC) that can control the ratio of phase and amplitude signals. Experimental verification of th eproposed optical object recognition system is presented.

• Journal of the Ergonomics Society of Korea
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• v.21 no.2
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• pp.47-58
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• 2002

This research suggested the mathematical model (forward kinematics method) to provide the reference points of driver space more easily and accurately in designing the package layout of vehicle interiors. For this purpose, the lengths of body segments of drivers and various joint angles occurred while were used. The length data between joints for the mathematical model were extracted from $SAFEWORK^{\circed{R}}$ as well as 95th percentile male and 5th percentile female body dimensions were utilized. In addition, the angles of body segments were applied on its diverse values within proper ranges in order to compare them each other. the mathematical model in this study was based on the concept of converting polar coordinate system to Cartesian coordinate system so that reference points of driver space were acquired in Cartesian coordinate system after using the segment lengths of drivers and the joint angles of driving postures as an input of polar coordinate system. It is expected that reference points of driver space obtained from this research are helpful to the study on package layout that is appropriate for physical characteristics of drivers.

• Journal of the Institute of Electronics Engineers of Korea TC
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• v.47 no.9
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• pp.1-8
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• 2010

A digital phase wrapping modulation (DPM) open-loop polar transmitter can be efficiently applied to a wideband orthogonal frequency division multiplexing (OFDM) communication system by converting in-phase and quadrature signals to envelope and phase signals and then employing the signal mapping process. This mapping process is very similar to quantization in a general communication system, and when taking into account the error that appears during mapping process, one can replace the coordinates rotation digital computer (CORDIC) algorithm in the coordinate conversion part with the Taylor series approximation method. In this paper, we investigate the application of the Taylor series approximation to the cartesian to polar coordinate conversion part of a DPM polar transmitter for wideband OFDM systems. The conventional approach relies on the CORDIC algorithm. To achieve efficient application, we perform computer simulation to measure mean square error (MSE) of the both approaches and find the minimum approximation order for the Taylor series approximation compatible to allowable error of the CORDIC algorithm in terms of hardware design. Furthermore, comparing the processing speeds of the both approaches in the implementation with FPGA reveals that the Taylor series approximation with lower order improves the processing speed in the coordinate conversion part.

• The Transactions of the Korean Institute of Electrical Engineers D
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• v.52 no.1
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• pp.22-30
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• 2003

A Coordinate-Transformation Extended Robust Kalman Filter (CERKF) designed in the Krein space is proposed, and then applied to a nonlinear incoming ballistic missile tracking system with parameter uncertainties. First, the Extended Robust Kalman filter (ERKF) is proposed to handle the nonlinearity of measurement equation which occurs whenever the polar coordinate system is transformed into the Cartesian coordinate system. Moreover, linearization error inevitably occurs and deteriorates the tracking performance, which is considerably reduced by the proposed CERKF. Through the simulation results, we show that the proposed CERKF, which uses the measurement coordinate system, has less RMS error than the previous ERKF which is designed in the Krein space using the Cartesian system. We also verify that the robustness and the stability of the proposed filter are guaranteed in two radars: the phased way radar and the scanning radar