• Journal of Information Processing Systems
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• v.4 no.4
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• pp.153-158
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• 2008

This paper deals with the geometric fitting algorithms for parametric curves and surfaces in 2-D/3-D space, which estimate the curve/surface parameters by minimizing the square sum of the shortest distances between the curve/surface and the given points. We identify three algorithmic approaches for solving the nonlinear problem of geometric fitting. As their general implementation we describe a new algorithm for geometric fitting of parametric curves and surfaces. The curve/surface parameters are estimated in terms of form, position, and rotation parameters. We test and evaluate the performances of the algorithms with fitting examples.

• Journal of applied mathematics & informatics
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• v.7 no.3
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• pp.983-994
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• 2000

We consider the problem of determining the circle of best fit to a set of data points in the plane. In [1] and [2] several algorithms already have been given for fitting a circle in least squares sense of minimizing the geometric distances to the given data points. In this paper we present another new descent algorithm which computes a parametric represented circle in order to minimize the sum of the squares of the distances to the given points. For any choice of starting values our algorithm has the advantage of ensuring convergence to a local minimum. Numerical examples are given.

• Communications of the Korean Mathematical Society
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• v.37 no.3
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• pp.915-938
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• 2022

We are interested in the problem of fitting a parabola to a set of data points in ℝ³. It can be usually solved by minimizing the geometric distances from the fitted parabola to the given data points. In this paper, a parabola fitting algorithm will be proposed in such a way that the sum of the squares of the geometric distances is minimized in ℝ³. Our algorithm is mainly based on the steepest descent technique which determines an adequate number λ such that h(λ) = Q(u - λ𝛁Q(u)) < Q(u). Some numerical examples are given to test our algorithm.

• Communications of the Korean Mathematical Society
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• v.34 no.3
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• pp.1029-1047
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• 2019

We are interested in the problem of determining the best fitted circle to a set of data points in space. This can be usually obtained by minimizing the geometric distances or various approximate algebraic distances from the fitted circle to the given data points. In this paper, we propose an algorithm in such a way that the sum of the squares of the geometric distances is minimized in ${\mathbb{R}}^3$. Our algorithm is mainly based on the steepest descent method with a view of ensuring the convergence of the corresponding objective function Q(u) to a local minimum. Numerical examples are given.

• IE interfaces
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• v.13 no.4
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• pp.703-708
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• 2000

In manufacturing processes, manufacturing features always deviate somewhat from their nominal design specifications due to several types of errors. This study suggests a fitting algorithm of the geometric profile parameters of leading and trailing edges for turbine compressor airfoils. In reality, industry personnels inspect the airfoil profile by trial-and-error method to determine the geometric feature parameters. In this study we propose an exploration approach based on factorial design with center point to minimize the effect of measurement errors caused by probe slip. By adopting the fitting method developed in this paper, one can enhance the precision and efficiency of fitting the airfoil edge profile.

• International Journal of Precision Engineering and Manufacturing
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• v.6 no.2
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• pp.12-18
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• 2005

A geometric compensation of thin-walled molded parts in reverse engineering is presented. Researches in reverse engineering have focused on the fitting of points to curves and surfaces. However, the reconstructed model is not the geometric model because the molded parts have some dimensional errors in measurements and deformation during molding. Geometric information can give an improved accuracy in reverse engineering. Thus, measurement data must be compensated with geometric information to reconstruct the mathematical model. The functional and geometric concepts of the part can be derived from geometric information. LSM (Least square method) is adopted to determine the geometric information. Also, an example of geometric compensation is given to improve the accuracy of geometric model and to inspect the reconstructed model.

• Korean Journal of Remote Sensing
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• v.32 no.1
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• pp.49-60
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• 2016

This paper presents a set of methods to evaluate the image quality of smartphone cameras as compared with that of a DSLR camera. In recent years, smartphone cameras have been used broadly for many purposes. As the performance of smartphone cameras has been enhanced considerably, they can be considered to be used for precise mapping instead of metric cameras. To evaluate the possibility, we tested the quality of one DSLR camera and 3 smartphone cameras. In the first step, we compare the amount of lens distortions inherent in each camera using camera calibration sheet images. Then, we acquired target sheet images, extracted reference lines from them and evaluated the geometric quality of smartphone cameras based on the amount of errors occurring in fitting a straight line to observed points. In addition, we present a method to evaluate the radiometric quality of the images taken by each camera based on planar fitting errors. Also, we propose a method to quantify the geometric quality of the selected camera using edge displacements observed in target sheet images. The experimental results show that the geometric and radiometric qualities of smartphone cameras are comparable to those of a DSLR camera except lens distortion parameters.

• Korean Journal of Applied Biomechanics
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• v.23 no.1
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• pp.53-62
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• 2013

The methods of fitting a circle to measured data, geometric fit and algebraic fit, have been studied profoundly in various areas of science. However, they have not been applied exactly to a biomechanics discipline for locating the center of rotation of a human joint. The purpose of this study was to generalize the methods to fitting spheres to the points in 3-dimension, and to estimate the center of rotation of a hip joint by three of geometric fit methods(Levenberg-Marquardt, Landau, and Sp$\ddot{a}$th) and four of algebraic fit methods(Delogne-K${\aa}$sa, Pratt, Taubin, and Hyper). 1000 times of simulation experiments for flexion/extension and ad/abduction at an artificial hip joint with four levels of range of motion(10, 15, 30, and $60^{\circ}$) and three levels of angular velocity(30, 60, and $90^{\circ}$/s) were executed to analyze the responses of the estimated center of rotation. The results showed that the Sp$\ddot{a}$th estimate was very sensitive to the marker near the center of rotation. The bias of Delogne-K${\aa}$sa estimate existed in an even larger range of motion. The Levenberg-Marquardt algorithm of geometric fit and the Pratt of algebraic fit showed the best results. The combination of two methods, using the Pratt's estimate as initial values of the Levenberg-Marquardt algorithm, could be a candidate of more valid estimator.

• 제어로봇시스템학회:학술대회논문집
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• 2005.06a
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• pp.2010-2014
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• 2005

Object detection and parameter estimation in point cloud data is a relevant subject to robotics, reverse engineering, computer vision, and sport mechanics. In this paper a software is presented for fully-automatic object detection and parameter estimation in unordered, incomplete and error-contaminated point cloud with a large number of data points. The software consists of three algorithmic modules each for object identification, point segmentation, and model fitting. The newly developed algorithms for orthogonal distance fitting (ODF) play a fundamental role in each of the three modules. The ODF algorithms estimate the model parameters by minimizing the square sum of the shortest distances between the model feature and the measurement points. Curvature analysis of the local quadric surfaces fitted to small patches of point cloud provides the necessary seed information for automatic model selection, point segmentation, and model fitting. The performance of the software on a variety of point cloud data will be demonstrated live.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2002.10a
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• pp.139-145
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• 2002

In this study, the geometric modeling has been conducted for 2 models of lower end fitting of advanced LWR fuel using three-dimensional solid modeler, Solidworks. Then, the optimization and the three-dimensional stress analysis using the finite element method has been peformed. The evaluation for the mechanical integrity of 2 models has been peformed based on the stress distribution obtained from the finite element analysis.