• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.20 no.2
• /
• pp.151-161
• /
• 2016

In this paper, we present a $C^3$ quartic B-spline approximation of circular arcs. The Hausdorff distance between the $C^3$ quartic B-spline curve and the circular arc is obtained in closed form. Using this error analysis, we show that the approximation order of our approximation method is six. For a given circular arc and error tolerance we find the $C^3$ quartic B-spline curve having the minimum number of control points within the tolerance. The algorithm yielding the $C^3$ quartic B-spline approximation of a circular arc is also presented.

• Journal of Ship and Ocean Technology
• /
• v.10 no.2
• /
• pp.24-36
• /
• 2006

Ship hullform is usually designed with a curve network, and smooth hullform surfaces are supposed to be generated by filling in (or interpolating) the curve network with appropriate surface patches. Tensor-product surfaces such as B-spline and $B\'{e}zier$ patches are typical representations to this interpolating problem. However, they have difficulties in representing the surfaces of irregular topological type which are frequently appeared in the fore- and after-body of ship hullform curve network. In this paper, we proposed a method that can automatically generate discrete $G^1$ continuous B-spline surfaces interpolating given curve network of ship hullform. This method consists of three steps. In the first step, given curve network is reorganized to be of two types: boundary curves and reference curves of surface patches. Especially, the boundary curves are specified for their surface patches to be rectangular or triangular topological type that can be represented with tensor-product (or degenerate) B-spline surface patches. In the second step, surface fitting points and cross boundary derivatives are estimated by constructing virtual iso-parametric curves at discrete parameters. In the last step, discrete $G^1$ continuous B-spline surfaces are generated by surface fitting algorithm. Finally, several examples of resulting smooth hullform surfaces generated from the curve network data of actual ship hullform are included to demonstrate the quality of the proposed method.

• Transactions of Materials Processing
• /
• v.12 no.2
• /
• pp.142-150
• /
• 2003

To construct the extrusion die surface, a B-Spline surface scheme based on the cubic B-Spline curve interpolation method is proposed in the present work. The inlet and outlet profiles are described with B-Spline curves by using the centripetal method for uniform parameterization. The interior control points of surface are generated using the derivative characteristics of B-Spline curve. A complete B-Spline surface is constructed by using appropriate coordinate transformation and knot deletion. In the present study, a quantitative measure for the control of surface is suggested by introducing the tangential vector and inclination angles at the inlet and outlet sections. To verify the validity of the proposed method, automatic surface generation is carried out for the various types of extrusion die surface.

• Journal of the Korean Society for Precision Engineering
• /
• v.16 no.10
• /
• pp.126-131
• /
• 1999

Up until now, it is said that no satisfactory computer solutions have been found for synthesizing four-bar linkage based on the prescribed coupler link curve. In our study, an algorithm has been developed to improve the design synthesis of four-bar linkage automatically generating prescribed path by using B-spline interpolation. The suggested algorithm generates the desired coupler curve by using B-spline interpolation, and hence the generated curve approximates as closely as to the desired curve representing coupler link trajectory. Also, when comparing each generated polygon with the control polygon, rapid comparison by applying convex hull concept. finally, optimization process using ADS is incorporated into the algorithm based on the 5 precision point method to reduce the total optimization process time. As for examples, three different four-bar linkages were tested and the results showed the effectiveness of the algorithm.

• Journal of Ocean Engineering and Technology
• /
• v.12 no.3 s.29
• /
• pp.96-102
• /
• 1998

This paper presents to create a SAC(Sectional Area Curve) using an ANFIS(Adaptive-Network-based Fuzzy Inference System). First, it defines SACs of parent ships by using a B-spline approximation and a genetic algorithm and accumulates a database about SAC's control points. Second, it learns an ANFIS from parent ship data, which are related with principal dimensions and SAC's control points. This process is to model an ANFIS for SAC inferreice. When an ANFIS modeling is completed, we can determine a SAC through an ANFIS inferring.

• Journal of the Korea Computer Graphics Society
• /
• v.17 no.3
• /
• pp.33-42
• /
• 2011

We present a new technique for removing interior knots of parametric B-spline curves. An initial curve is constructed by continuous $L_{\infty}$ approximation proposed by Eck and Hadenfeld. We employ Hausdorff distance to measure the shape difference between the original curve and the initial one. The final curve is obtained by minimizing their Hausdorff distance. We demonstrate the effectiveness of our technique with experimental results on various types of planar and spatial curves.

• Proceedings of the KSME Conference
• /
• 2003.11a
• /
• pp.1334-1339
• /
• 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 Korea Computer Graphics Society
• /
• v.16 no.4
• /
• pp.41-50
• /
• 2010

We present a new technique for multilevel editing of hierarchical B-spline curves. At each level, control points of a displacement function are expressed in the rotation minimizing frames (RMFs) [1] which are computed on nodal points of the curve at previous level. When the curve is edited at previous level, the corresponding RMFs are updated and the control points of the displacement function at current level are applied to the new RMFs, which maintains the relative details of the curve at current level to those of previous level. We demonstrate the effectiveness and robustness of the proposed technique using several experimental results.

• Journal of Computational Design and Engineering
• /
• v.3 no.1
• /
• pp.14-23
• /
• 2016

The problem of fitting B-spline curves to planar point clouds is studied in this paper. A novel method is proposed to deal with the most challenging case where multiple intersecting curves or curves with self-intersection are necessary for shape representation. A method based on Delauney Triangulation of data points is developed to identify connected components which is also capable of removing outliers. A skeleton representation is utilized to represent the topological structure which is further used to create a weighted graph for deciding the merging of curve segments. Different to existing approaches which utilize local shape information near intersections, our method considers shape characteristics of curve segments in a larger scope and is thus capable of giving more satisfactory results. By fitting each group of data points with a B-spline curve, we solve the problems of curve structure reconstruction from point clouds, as well as the vectorization of simple line drawing images by drawing lines reconstruction.

• Journal of the Society of Naval Architects of Korea
• /
• v.34 no.4
• /
• pp.127-138
• /
• 1997

In this study, a new technique is presented, by which one can define ship hull form with full fairness from the input data of lines. For curve modeling, the de Casteljau Algorithm and Bezier control points are used to express free curves and to establish the unified curve modeling technique which enables one to convert non-uniform B-spline (NUB) curve or cubic spline curve into composite Bezier curves. For surface modeling, the mesh curve net which is required to define surface of ship hull form is interpolated by the method of the unified curve modeling, and the boundary curve segments of Gregory surface patches are generated by remeshing(rearranging) the given mesh curve net. From these boundary information, composite Gregory surfaces of good quality in fairness can be formulated.