• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.13 no.4
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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.

• Journal of Integrative Natural Science
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• v.7 no.2
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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.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 2003.05a
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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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• 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.

• Structural Engineering and Mechanics
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• v.18 no.2
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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.

• 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.

• International Journal of Ocean Engineering and Technology Speciallssue:Selected Papers
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• v.5 no.1
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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.

• Journal of the Society of Naval Architects of Korea
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• v.28 no.2
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• pp.21-27
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• 1991

This paper outlines the method of formulating the bi-cubic B-spline surface of ship hull, employing the open uniform knot vector as well as the periodic uniform knot vector. An appropriate set of B-spline control vertices to generate the B-spline surface is determined by obtaining the pseudoinverse matrix of basis functions. The comparison between the given offsets and the resulting coordinates from the generated ship hull surface shows a good agreement. To check the fairness of the surface Gaussian curvature is calculated on many small subpatches and displayed on the black-and-white plot of the isoparametric net of the surface.

• Journal of Advanced Marine Engineering and Technology
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• v.21 no.4
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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.

• Journal of the Korean Institute of Intelligent Systems
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• v.21 no.5
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• pp.653-659
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• 2011

In general, electrocardiogram(ECG) signals are sampled with a frequency over 200Hz and stored for a long time. It is required to compress data efficiently for storing and transmitting them. In this paper, a method for compression of ECG data is proposed, using by Non Uniform B-spline approximation, which has been widely used to approximation theory of applied mathematics and geometric modeling. ECG signals are compressed and reconstructed using B-spline basis function which curve has local controllability and control a shape and curve in part. The proposed method selected additional knot with each step for minimizing reconstruction error and reduced time complexity. It is established that the proposed method using B-spline approximation has good compression ratio and reconstruct besides preserving all feature point of ECG signals, through the experimental results from MIT-BIH Arrhythmia database.