• 한국CDE학회논문집
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• 제5권3호
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• pp.276-284
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• 2000

Usual practice of the transformation of a B-spline curve into a set of piecewise polynomial curves in a power form is done by either a knot refinement followed by basis conversions or applying a Taylor expansion on the B-spline curve for each knot span. Presented in this paper is a new algorithm, called a direct expansion algorithm, for the problem. The algorithm first locates the coefficients of all the linear terms that make up the basis functions in a knot span, and then the algorithm directly obtains the power form representation of basis functions by expanding the summation of products of appropriate linear terms. Then, a polynomial segment of a knot span can be easily obtained by the summation of products of the basis functions within the knot span with corresponding control points. Repeating this operation for each knot span, all of the polynomials of the B-spline curve can be transformed into a power form. The algorithm has been applied to both static and dynamic curves. It turns out that the proposed algorithm outperforms the existing algorithms for the conversion for both types of curves. Especially, the proposed algorithm shows significantly fast performance for the dynamic curves.

• 한국경영과학회:학술대회논문집
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• 한국경영과학회/대한산업공학회 2003년도 춘계공동학술대회
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• pp.474-479
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• 2003

This paper addresses the problem of B-spline surface interpolation to serial contours, where the number of points varies from contour to contour. A traditional lofting approach creates a set of B-spline curves via B-spline curve interpolation to each contour, makes them compatible via degree elevation and knot insertion, and performs B-spline surface lofting to get a B-spline surface interpolating them. The approach tends to result in an astonishing number of control points in the resulting B-spline surface. This situation arises mainly from the inevitable process of progressively merging different knot vectors to make the B-spline curves compatible. This paper presents a new approach for avoiding this troublesome situation. The approach includes a novel process of getting a set of compatible B-spline curves from the given contours. The process is based on the universal parameterization [1,2] allowing the knots to be selected freely but leading to a more stable linear system for B-spline curve interpolation. Since the number of control points in each compatible B-spline curve is equal to the highest number of contour points, the proposed approach can realize efficient data reduction and provide a compact representation of a B-spline surface while keeping the desired surface shape. Some experimental results demonstrate its usefulness and quality.

• 한국멀티미디어학회논문지
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• 제13권9호
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• pp.1373-1381
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• 2010

현재 항공기 조종사들이 사용하고 있는 항공기동 도해도 방법은 2차원 공간 표현만을 사용하여, 3차원 정보 입력 시 한계가 있고 이를 직관적으로 이해하는 것이 어렵다. 이를 위해 도입된 항공기동 애니메이션 저작도구들은 사용법이 복잡하고 중간에 비행경로를 수정하거나 다수 비행객체들의 전투 상황을 실시간으로 인터렉티브하게 다룰 수 없다. 본 연구는 항공기동 교육을 위한 애니메이션 시스템 중 3차원 항공경로 생성방법에 관한 것이다. 본 연구에서는 2D 도해도에 스케치된 초기 입력과 실제 항공기 추력을 계산하여 실제 비행과 유사한 3차원 선형 스플라인 곡선을 생성해 낸다. 제안하는 선형 스플라인 곡선 생성 방법을 이용하여 항공기동 브리핑 및 디브리핑 시에 비행경로를 실시간으로 생성 및 수정하는 것이 가능하고 이를 애니메이션으로 즉시에 표현할 수 있다.

• 한국정밀공학회지
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• 제13권12호
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• pp.99-105
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• 1996

Increasing demands on precision machining of free-form surfaces have necessitated the tool to move not only with position error as small as possible, but also with smoothly varying feedrates. In this paper, linear, circular and spline interpolators were developed in reference-pulse type using PC. M-SAM and M-DAM were designed by the comparison and analysis of previous interpolation methods. Spline interpolator was designed to follow the free-form curves. To apply to the real cutting process, constant feedrate compensation and acceleration-deceleration compensation were conceived. Finally, its performance was tested using retrofitted milling machine. As a result, new interpolation algorithm is favorable in precision machining of free-form curves.

• 한국CDE학회논문집
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• 제3권2호
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• pp.113-120
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• 1998

Calculation of intersection points by two curves is fundamental to computer aided geometric design. Bezier clipping is one of the well-known curve intersection algorithms. However, this algorithm is only applicable to Bezier curve representation. Therefore, the NURBS curves that can represent free from curves and conics must be decomposed into constituent Bezier curves to find the intersections using Bezier clipping. And the respective pairs of decomposed Bezier curves are considered to find the intersection points so that the computational overhead increases very sharply. In this study, extended Bezier clipping which uses the linear precision of B-spline curve and Grevill's abscissa can find the intersection points of two NURBS curves without initial decomposition. Especially the extended algorithm is more efficient than Bezier clipping when the number of intersection points is small and the curves are composed of many Bezier curve segments.

• Journal of applied mathematics & informatics
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• 제6권1호
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• pp.203-216
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• 1999

In this paper a rational cubic interpolant spline with linear denominator has been constructed and it is used to constrain interpolation curves to be bounded in the given region. Necessary and sufficient conditions for the interpolant to satisfy the constraint have been developed. The existence conditions are computationally efficient and easy to apply. Finally the approximation properties have been studied.

• 대한전기학회:학술대회논문집
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• 대한전기학회 2006년도 심포지엄 논문집 정보 및 제어부문
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• pp.27-29
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• 2006

In this paper, we propose a new method of automatic white balance which is one of the image signal processing techniques. Our method is conceptually based on gray world assumption. However, while previous methods generate linear results as multiplying pixel values by a gain, our method generates non-linear results using the feature of B-Spline curves. The two merits of deriving non-linear results are preventing AWB failure from transforming strong color of high level into wrong color and well preserving original contrast of an input image.

• Journal of applied mathematics & informatics
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• 제7권2호
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• pp.517-525
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• 2000

A constrained rational cubic spline with linear denominator was constructed in [1]. In the present paper, the sufficient condition for convex interpolation and some properties in error estimation are given.

• 대한기계학회논문집A
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• 제33권2호
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• pp.135-144
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• 2009

In this present work, spline FEA for the trimmed NURBS surface of the 2D linear elasticity problem is presented. The main benefit of the proposed method is that no additional efforts for modeling of trimmed NURBS surfaces are needed and the information of the trimming curves and trimmed surfaces exported from the CAD system can be directly used for analysis. For this, trimmed elements are searched by using NURBS projection scheme. The integration of the trimmed elements is performed by using the NURBS-enhanced integration scheme. The formulation of constructing stiffness matrix of trimmed elements is presented. In this formulation, the information of the trimming curve is used for calculating the Jacobian as well as for obtaining integration points. The robustness and effectiveness of the proposed method are investigated through various numerical examples.

• 대한기계학회:학술대회논문집
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• 대한기계학회 2003년도 추계학술대회
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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.