• Journal of KIISE:Software and Applications
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• v.32 no.5
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• pp.357-365
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• 2005

We present a B-spline fitting method based on genetic algorithm for the extraction of object contours from the complex image sequence, where objects with similar shape and intensity are adjacent each other. The proposed algorithm solves common malfitting problem of the existing B-spline fitting methods including snakes. Classical snake algorithms have not been successful in such an image sequence due to the difficulty in initialization and existence of multiple extrema. We propose a B-spline fitting method using a genetic algorithm with a new initial population generation and fitting function, that are designed to take advantage of the contour of the previous slice. The test results show that the proposed method extracts contour of individual object successfully from the complex image sequence. We validate the algorithm by false-positive/negative errors and relative amounts of agreements.

• Korean Journal of Computational Design and Engineering
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• v.11 no.1
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• pp.1-10
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• 2006

This paper addresses B-spline curve approximation of a set of ordered points to a specified toterance. The important issue in this problem is to reduce the number of control points while keeping the desired accuracy in the resulting B-spline curve. In this paper we propose a new method for error-bounded B-spline curve approximation based on adaptive selection of dominant points. The method first selects from the given points initial dominant points that govern the overall shape of the point set. It then computes a knot vector using the dominant points and performs B-spline curve fitting to all the given points. If the fitted B-spline curve cannot approximate the points within the tolerance, the method selects more points as dominant points and repeats the curve fitting process. The knots are determined in each step by averaging the parameters of the dominant points. The resulting curve is a piecewise B-spline curve of order (degree+1) p with $C^{(p-2)}$ continuity at each knot. The shape index of a point set is introduced to facilitate the dominant point selection during the iterative curve fitting process. Compared with previous methods for error-bounded B-spline curve approximation, the proposed method requires much less control points to approximate the given point set with the desired shape fidelity. Some experimental results demonstrate its usefulness and quality.

• Journal of Computational Design and Engineering
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• v.2 no.1
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• pp.1-15
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• 2015

Measured bidirectional reflectance distribution function (BRDF) data have been used to represent complex interaction between lights and surface materials for photorealistic rendering. However, their massive size makes it hard to adopt them in practical rendering applications. In this paper, we propose an adaptive method for B-spline volume representation of measured BRDF data. It basically performs approximate B-spline volume lofting, which decomposes the problem into three sub-problems of multiple B-spline curve fitting along u-, v-, and w-parametric directions. Especially, it makes the efficient use of knots in the multiple B-spline curve fitting and thereby accomplishes adaptive knot placement along each parametric direction of a resulting B-spline volume. The proposed method is quite useful to realize efficient data reduction while smoothing out the noises and keeping the overall features of BRDF data well. By applying the B-spline volume models of real materials for rendering, we show that the B-spline volume models are effective in preserving the features of material appearance and are suitable for representing BRDF data.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.3 no.1
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• pp.81-98
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• 1999

In spite of the well developed theory and the practical use of the univariate B-spline, the theory of multivariate B-spline is very new and waits its practical use. We compare in this article the multivariate B-spline approximation with the polynomial approximation for the surface fitting. The graphical and numerical comparisons show that the multivariate B-spline approximation gives much better fitting than the polynomial one, especially for the surfaces which vary very rapidly.

• 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.

• Proceedings of the KSME Conference
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• 2003.11a
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• pp.1334-1339
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• 2003

An efficient method is developed for the shape optimization of 2-D structures. The sequential linear programming is used for minimization problems. Selected set of master nodes are employed as design variables and assigned to move towards the normal direction. After adapting the nodes on the design boundary, the B-spline curves and mesh smoothing schemes are used to maintain the finite element in good quality. Finally, a numerical implementation of optimum design of an automobile torque converter piston subjected to pressure and centrifugal loads is presented. The results shows additional weight up to 13% may be saved after the shape optimization.

• Journal of the Society of Naval Architects of Korea
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• v.46 no.1
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• pp.87-95
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• 2009

The applicability of optimization techniques for hull surface fitting has been important in the ship design process. In this research, the Genetic Algorithm has been used as a searching technique for solving surface fitting problem and minimizing errors between B-spline surface and the ship's offset data. The encoded design variables are the location of the vertex points and parametric values. The sufficient accuracy in surface fitting implies not only various techniques for computer-aided design, but also the future production design.

• Korean Journal of Computational Design and Engineering
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• v.17 no.4
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• pp.282-293
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• 2012

This paper presents an error-bounded B-spline fitting technique to approximate unorganized data within a prescribed error tolerance. The proposed approach includes two main steps: leastsquares minimization and error-bounded approximation. A B-spline hypervolume is first described as a data representation model, which includes its mathematical definition and the data structure for implementation. Then we present the least-squares minimization technique for the generation of an approximate B-spline model from the given data set, which provides a unique solution to the problem: overdetermined, underdetermined, or ill-conditioned problem. We also explain an algorithm for the error-bounded approximation which recursively refines the initial base model obtained from the least-squares minimization until the Euclidean distance between the model and the given data is within the given error tolerance. The proposed approach is demonstrated with some examples to show its usefulness and a good possibility for various applications.

• Transactions of the Korean Society of Machine Tool Engineers
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• v.12 no.2
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• pp.79-85
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• 2003

An algorithm for fitting with Least Square is a traditional and an effective method in processing with experimental data. Due to the lack of definite representation, it is difficult to fit measured data with free curves or surfaces. B-Spline is usefully utilized to express free curves and surfaces with a few parameters. This paper presents the combination of these two techniques to process the point data measured from CMM and other similar instruments. This research shows tests and comparison of the simulation results from two techniques.

• Korean Journal of Computational Design and Engineering
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• v.4 no.1
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• pp.32-42
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• 1999

Approximate lofting or skinning is one of practical surface modeling techniques well used in CAD and reverse engineering applications. Presented in this paper is a method for approximately lofting a given set of curves wihin a specified tolereance. It is based on refitting input curves simultaneously on a common knot vector and interpolating them to get a resultant NURBS surface. A concept of reducing the number of interior knots of the common knot vector is well adopted to acquire more compact representation for the resultant surface. Energy minimization is newly introduced in curve refitting process to stabilize the solution of the fitting problem and get more fair curve. The proposed approximate lofting provides more smooth surface models and realizes more efficient data reduction expecially when the parameterization and compatibility of input curves are not good enough. The method has been successfully implemented in a new CAD/CAM product VX Vision? of Varimetrix Corporation.