• Journal of the Korean Society of Manufacturing Process Engineers
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• v.10 no.3
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• pp.33-38
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• 2011

A cubic spline trajectory planner with arc-length parameter is formulated with estimation by summing up to the 3rd order in Taylor's expansion. The PVAJT motion planning is presented to reduce trajectory calculation time at every cycle time of servo control loop so that it is able to generate cubic spline trajectory in real time. This method can be used to more complex spline trajectory. Several case studies are executed with different values of cycle time and sampling time, and showed the advantages of the PVAJT motion planner. A DSP-based motion controller is designed to implement the PVAJT motion planning.

• Bulletin of the Society of Naval Architects of Korea
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• v.22 no.3
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• pp.19-26
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• 1985

This paper deals with the representation and fairing of ship hull using a B-spline surface which is known as a 3-D model in computer aided free-form design. The first part of this paper is devoted to the fundamental concepts of B-spline theory and its geometrical characteristics. In its second part are described the facillities for efficient application, fast rendering of B-spline surface, and intersection of B-spline surfaces. The examples are presented with actual application to a real ship in the last part. And also a new concept of evaluating the surface fairness by the Gaussian curvature isolines is briefly discussed and its examples are presented.

• Journal of computational fluids engineering
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• v.3 no.2
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• pp.1-8
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• 1998

We make use of cubic B-spline interpolation function in two cases: heat conduction and fluid flow problems. Cubic B-spline test function is employed because it is superior to approximation of linear and non-linear problems. We investigated the accuracy of the numerical formulation and focused on the position of the breakpoints within the computational domain. When the domain is divided by partitions of equal space, the results show poor accuracy. For the case of a heat conduction problem this partition can not reflect the temperature gradient which is rapidly changed near the wall. To correct the problem, we have more grid points near the wall or the region which has a rapid change of variables. When we applied the unequally spaced breakpoints, the results show high accuracy. Based on the comparison of the linear problem, we extended to the highly non-linear fluid flow problems.

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

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2001.04a
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• pp.18-25
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• 2001

Analysis of prestressed box-girder bridges using the spline finite strip method is presented. In the present study, the spline finite strip method(FSM) is modified using the non-periodic B-spline interpolation. In the analysis of the prestressed box girder bridges, each tendon force is evaluated by summation of the adjacent segment forces. Once the equivalent forces acting on the structure at the tendon points are found, they are transformed into statically equivalent forces at the adjacent node or joints. Several examples were analyzed to verify the performance of present method using the non-periodic B-spline FSM. Good agreements were obtained when compared with the previous study.

• Journal of the Society of Naval Architects of Korea
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• v.29 no.3
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• pp.1-14
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• 1992

Using form parameters representing geometric characteristics of the form, this paper attempts the generation of 3-D free surface given in terms of B-spline surface equation. This is achieved by coupling the form parameter decision, Coons surface of the form parameters, and B-spline. To check the validing of the present method, a analogous surface to the bulbous bow was generated.

• Journal of the Korean Society for Precision Engineering
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• v.20 no.10
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• pp.156-163
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• 2003

This research presents modeling of a functional surface which is a constructed free-formed surface. The modeling introduced in this paper adopts modified B-spline that is utilizing approximating technique. The modified B-Spline is constructed with altered control vertices. It is applied to measure points on a surface of an impeller blade. This research builds a surface-modeler accepting inputs of measured points. Generation of cutter-paths for NC machining employs the model of the constructed surfaces. The machined surfaces which is generated in several cases are compared in the aspect of machining accuracy.

• Korean Journal of Geomatics
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• v.2 no.1
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• pp.25-29
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• 2002

The calculation of earthwork plays a major role in plan or design of many civil engineering projects, and thus it has become very important to improve the accuracy of earthwork calculation. 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 concerned with accuracy of volume computations. We present some computational results showing that our proposed method provides good accuracy.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2012.05a
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• pp.287-288
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• 2012

• The Pure and Applied Mathematics
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• v.10 no.4
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• pp.255-263
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• 2003

We compare the computing times on the bicubic B-spline dueing to the algorithms.