• Journal of the Korean Society for Precision Engineering
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• v.19 no.11
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• pp.160-166
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• 2002

In this paper, data acquisition and analysis of a measuring machine for marine engine's cams is discussed. A rotary encoder and linear scale of the machine to measure angular and linear displacement respectively are interfaced to the PC via encoder board with 2 channels. The design and measuring data are interpolated by cubic spline curves to compute the precision error which is defined by the maximum and minimum distances between two curves. The minimum zone fit of ISO is employed to evaluate the geometric deviation. The developed system takes only 5 minutes to measure and analyze while the CMM takes over 1 hours even with a skilled operator.

• International Journal of Precision Engineering and Manufacturing
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• v.5 no.4
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• pp.21-27
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• 2004

In this paper, data acquisition and analysis of a measuring machine for marine engine's cams are discussed. A rotary encoder and linear scale of the machine to measure angular and linear displacement, respectively, are interfaced to the PC via an encoder board with 2 channels. The design and measuring data are interpolated by cubic spline curves to compute the precision error which is defined by the maximum and minimum distances between two curves. The minimum zone fit of ISO is employed to evaluate the geometric deviation. The developed system takes only 5 minutes to measure and analyze the precision error while the CMM takes over I hours even with a skilled operator.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 1997.10a
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• pp.150-153
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• 1997

In this paper, a control and data analysis S/W of a dedicated measuring machine for cams is developed. A rotary encoder is employed to measure the angular displacement of the motor, and a linear scale does the linear displacement of the prove. The design and measuring data are interpolated by cubic spline curves respectively to compute the error which is defined by the maximum distance between two curves. Further, optimization module to find the exact error is also developed to remove the error occurred due initial measuring position. The developed system takes only 6 minutes to measure the cam and to analyze the measuring data while the CMM takes about 1 hours even with a skilled operator.

• Journal of Computational Design and Engineering
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• v.2 no.4
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• pp.218-232
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• 2015

Piecewise linear (G01-based) tool paths generated by CAM systems lack $G_1$ and $G_2$ continuity. The discontinuity causes vibration and unnecessary hesitation during machining. To ensure efficient high-speed machining, a method to improve the continuity of the tool paths is required, such as B-spline fitting that approximates G01 paths with B-spline curves. Conventional B-spline fitting approaches cannot be directly used for tool path B-spline fitting, because they have shortages such as numerical instability, lack of chord error constraint, and lack of assurance of a usable result. Progressive and Iterative Approximation for Least Squares (LSPIA) is an efficient method for data fitting that solves the numerical instability problem. However, it does not consider chord errors and needs more work to ensure ironclad results for commercial applications. In this paper, we use LSPIA method incorporating Energy term (ELSPIA) to avoid the numerical instability, and lower chord errors by using stretching energy term. We implement several algorithm improvements, including (1) an improved technique for initial control point determination over Dominant Point Method, (2) an algorithm that updates foot point parameters as needed, (3) analysis of the degrees of freedom of control points to insert new control points only when needed, (4) chord error refinement using a similar ELSPIA method with the above enhancements. The proposed approach can generate a shape-preserving B-spline curve. Experiments with data analysis and machining tests are presented for verification of quality and efficiency. Comparisons with other known solutions are included to evaluate the worthiness of the proposed solution.

• Journal of Korean Academy of Oral and Maxillofacial Radiology
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• v.29 no.1
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• pp.65-85
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• 1999

Objectives: To determine the effect of interpolation functions when processing the digital periapical images. Material and Methods: The digital images were obtained by Digora and CDR system on the dry skull and human subject. 3 oral radiologists evaluated the 3 portions of each processed image using 7 interpolation methods, and ROC curves were obtained by trapezoidal methods. Results: The heighest Az value(0.96) was obtained with cubic spline method and the lowest Az value(0.03) was obtained with facet model method in Digora system. The heighest Az value (0.79) was obtained with gray segment expansion method and the lowest Az value(0.07) was obtained with facet model method in CDR system. There was significant difference of Az value in original image between Digora and CDR system at a=0.05 level. There were significant differences of Az values between Digora and CDR images with cubic spline method, facet model method, linear interpolation method and non-linear interpolation method at α=0.1 level.

• Journal of the Korean Society for Precision Engineering
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• v.17 no.1
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• pp.192-197
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• 2000

In CNC machining, a free curve is cut into small linear segments using the linear interpolation(G01) method. Therefore, the interpolation error along the curve is not constant due to the changing curvature. This paper presents a NURBS (Non-Uniform Rational B-Spline) interpolation algorithm for machining free curves with high precision and high speed. The proposed NURBS interpolation defines the tool path with NURBS parameters and limits the interpolation error to any desired level by adjusting the feed rate considering the curvature of the shape and sampling time. Both linear and NURBS interpolations are compared to show the validity of the proposed algorithm.

• Journal of the Korean Society of Manufacturing Technology Engineers
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• v.5 no.4
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• pp.47-52
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• 1996

The interpolator is very important in CNC machines. This study proposed a parametric curve interpolator(PCI) which can be used for machining any sculptured surface represented in a parametric form and generates commands for tool motion between CAD data points according to given accuracy demands. The proposed interpolator is superior to the existing linear interpolator in accuracy, feed rate and acceleration continuity. Moreover in comparison to the recently developed cubic spline interpolator, the PCI has the capability of handling higher order parametric curves and also ensures precise tracking in the velocity domain. Results from real time simulations and experiments on open architecture CNC machines equipped with the proposed interpolator are presented to show its practical capagility. It is believed that the combination of the proposed interpolator and the open architecture machine controller further advances the area of command generation which is an important aspect of CAD/CAM.

• KIPS Transactions on Software and Data Engineering
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• v.3 no.7
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• pp.277-284
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• 2014

The detection method of curves for the lanes which is powerful for the variation by utilizing the lane variation vector and cardinal spline on the inverse perspective transformation screen images which do not required the camera parameters are suggested in this paper. This method detects the lane area by setting the expected lane area in the s frame and next s+1 frame where the inverse perspective transformation and entire process of the lane filter are adapted, and expects the points of lane location in the next frames with the lane variation vector calculation from the detected lane areas. The scan area is set from the nextly expected lane position and new lane positions are detected within these areas, and the lane variation vectors are renewed with the detected lane position and the lanes are detected with application of cardinal spline for the control points inside the lane areas. The suggested method is a powerful method for curved lane detection, but it was adopted to the linear lanes too. It showed an excellent lane detection speed of about 20ms in processing a frame.

• Communications for Statistical Applications and Methods
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• v.29 no.3
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• pp.287-299
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• 2022

In radiation epidemiology, the excess relative risk (ERR) model is used to determine the dose-response relationship. In general, the dose-response relationship for the ERR model is assumed to be linear, linear-quadratic, linear-threshold, quadratic, and so on. However, since none of these functions dominate other functions for expressing the dose-response relationship, a Bayesian semiparametric method using splines has recently been proposed. Thus, we improve the Bayesian semiparametric method for the selection of the tuning parameters for splines as the number and location of knots using a Bayesian knot selection method. Equally spaced knots cannot capture the characteristic of radiation exposed dose distribution which is highly skewed in general. Therefore, we propose a nonparametric Bayesian knot selection method based on a Dirichlet process mixture model. Inference of the spline coefficients after obtaining the number and location of knots is performed in the Bayesian framework. We apply this approach to the life span study cohort data from the radiation effects research foundation in Japan, and the results illustrate that the proposed method provides competitive curve estimates for the dose-response curve and relatively stable credible intervals for the curve.

• Proceedings of the KSME Conference
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• 2002.08a
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• pp.683-686
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• 2002

The hydrodynamic instability of the three-dimensional boundary-layer over a rotating disk has been numerically investigated for three cases flows using linear stability theory (i.e. Rossby number, Ro = -1, 0, and 1). Detailed numerical values of the disturbance wave number, wave frequency, azimuth angle, radius (Reynolds number, Re) and other characteristics have been calculated for $K{\acute{a}}rm{\acute{a}}n$, Ekman and $B{\"{o}}ewadt$ boundary-layer flows. Neutral curves for these flows are presented. Presented are the neutral stability results concerning the two instability modes (Type I and Type II) by using a two-point boundary value problem code COLUEW that was based upon the adaptive orthogonal collocation method using B-spline. The prediction from the present results on both instability modes among the three cases agrees with the previously known numerical and experimental data well.