• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제13권4호
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• pp.257-265
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• 2009

In this paper we find an explicit form of upper bound of Hausdorff distance between given cubic spline curve and its quadratic spline approximation. As an application the approximation of offset curve of cubic spline curve is presented using our explicit error analysis. The offset curve of quadratic spline curve is exact rational spline curve of degree six, which is also an approximation of the offset curve of cubic spline curve.

• 통합자연과학논문집
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• 제7권2호
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• pp.124-129
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• 2014

In this paper, we construct an logarithmic spiral-like curve using curvature-continuous quadratic spline and quadratic rational spline. The quadratic (rational) spline has self-similarity. We present some properties of the quadratic spline. Also using this $G^2$ quadratic spline, an approximation of logarithmic spiral is proposed and error analysis is obtained.

• 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.

• Journal of Computational Design and Engineering
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• 제2권1호
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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.

• Structural Engineering and Mechanics
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• 제18권2호
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• pp.247-262
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• 2004

In the earlier application of the spline finite strip method(FSM), the uniform B3-spline functions were used in the longitudinal direction while the conventional interpolation functions were used in the transverse direction to construct the displacement filed in a strip. To overcome the shortcoming of the uniform B3-spline, non-periodic B-spline was developed as the displacement function. The use of non-periodic B3-spline function requires no tangential vectors at both ends to interpolate the geometry of shell and the Kronecker delta property is also satisfied at the end boundaries. Recently, non-periodic spline FSM which was modified to have a multiple knots at the boundary was developed for the shell analysis and applied to the analysis of bridges. In the formulation of a non-symmetric spline finite strip method, the concepts of non-periodic B3-spline and a stress-resultant finite strip with drilling degrees of freedom for a shell are used. The introduction of non-symmetrically spaced knots in the longitudinal direction allows the selective local refinement to improve the accuracy of solution at the connections or at the location of concentrated load. A number of numerical tests were performed to prove the accuracy and efficiency of the present study.

• 한국CDE학회논문집
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• 제11권1호
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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.

• International Journal of Ocean Engineering and Technology Speciallssue:Selected Papers
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• 제5권1호
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• pp.40-45
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• 2002

The calculation of earthwork plays a major role in the planning and design phases of many civil engineering projects, such as seashore reclamation; thus, improving the accuracy of earthwork calculation has become very important. In this paper, we propose an algorithm for finding a cubic spline surface with the free boundary conditions, which interpolates the given three-dimensional data, by using B-spline and an accurate method to estimate pit-excavation volume. The proposed method should be of interest to surveyors, especially those concerned with accuracy of volume computations. The mathematical models of the conventional methods have a common drawback: the modeling curves form peak points at the joints. To avoid this drawback, the cubic spline polynomial is chosen as the mathematical model of the new method. In this paper, we propose an algorithm of finding a spline surface, which interpolates the given data, and an appropriate method to calculate the earthwork. We present some computational results that show the proposed method, of the Maple program, provides better accuracy than the method presented by Chen and Lin.

• 대한조선학회논문집
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• 제28권2호
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• pp.21-27
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• 1991

이 논문에서는 periodic 균일 knot vector 뿐만아니라 open 균일 knot vector를 사용하여 선체형상을 Bi-cubic B-spline곡면으로 수식화하는 방법을 보인다. B-spline곡면을 형성하기 위한 B-spline control vertex는 기본 함수의 pseudoinverse matrix를 사용하여 결정된다. 주어진 offset과 형성된 선체곡면을 비교한 결과 잘 일치하였다. 곡면의 순정을 검토하기 위하여 Gaussian곡률을 많은 작은 곡면조각에 대해 계산하여 흑백의 농도 차이를 이용하여 도시화하였다.

• Journal of Advanced Marine Engineering and Technology
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• 제21권4호
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• pp.381-386
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• 1997

The offsetting method using geometric properties of B-spline control polygon is more faster than using of general normal vector in offset processing. But this method itself does not solve the prob¬lems of loop removal in normal offsetting. Generally the distance between neighborhood spans of B-spline control polygon is greater than the offset distance, the loops are occurred in offsetting. For generating of the more precision tool-path in NC machining, the loops of offset must be removed. In this paper, two methods for loop removal are introduced in offsetting of B-spline curve. One is using the intersection of B-spline control span which being occurred of the loop. The other is using two B-spline curve divisions divided from original B-spline curve or its offset curve. After the inter¬section point of loop was searched, the loop being removed to cusp. Also the method for filleting of cusp is inspected to more precision cutting. It is shown that the offsetting using B-spline control polygon is more effective in the sculptured surface machining.

• 한국지능시스템학회논문지
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• 제21권5호
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• pp.653-659
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• 2011

심전도 신호는 일반적으로 200Hz 이상의 주파수로 표본화 하므로 장시간의 심전도 신호를 획득할 경우 데이터가 방대해진다. 이러한 신호를 저장 및 전송하기 위해서는 효율적인 신호 압축을 필요로 한다. 본 논문에서는 B-spline 근사화를 이용하여 심전도 신호를 압축하는 방법을 제안한다. B-spline 곡선의 국부적 제어성(local controllability) 특성으로 인하여 원신호를 부분적으로 근사화할 수 있으며, 이를 통하여 방대한 심전도 신호를 압축할 수 있다. 따라서 본 논문에서는 응용수학의 근사이론 및 기하학적 모델링에 널리 사용되고 있는 비균일 B-spline 근사화 기법으로 효율적인 압축 방안을 제시한다. 제안한 알고리즘의 유효성을 확인하기 위해 실제 심전도 임상 데이터인 MIT-BIH 데이터베이스를 이용하여 실험을 수행하며, 그 결과로부터 제안한 기법을 이용한 B-spline 근사화 압축 방법의 효용성을 입증한다.