• Korean Journal of Computational Design and Engineering
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• v.17 no.4
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• pp.282-293
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• 2012

This paper presents an error-bounded B-spline fitting technique to approximate unorganized data within a prescribed error tolerance. The proposed approach includes two main steps: leastsquares minimization and error-bounded approximation. A B-spline hypervolume is first described as a data representation model, which includes its mathematical definition and the data structure for implementation. Then we present the least-squares minimization technique for the generation of an approximate B-spline model from the given data set, which provides a unique solution to the problem: overdetermined, underdetermined, or ill-conditioned problem. We also explain an algorithm for the error-bounded approximation which recursively refines the initial base model obtained from the least-squares minimization until the Euclidean distance between the model and the given data is within the given error tolerance. The proposed approach is demonstrated with some examples to show its usefulness and a good possibility for various applications.

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

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.8 no.3
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• pp.1026-1039
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• 2014

We present a new method for generating sweep surfaces using bivariate B-spline motion. The sweep surface is defined as the trace of a single point under bivariate B-spline motion. Direct manipulation of the sweep surface is achieved by controlling its motion components while producing various editing effects. We demonstrate the effectiveness of our technique by modeling and deforming various three-dimensional shapes.

• 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.

• Journal of Korea Water Resources Association
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• v.35 no.6
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• pp.779-786
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• 2002

A boundary element method with a Lagrangian approach and B-spline technique is employed to investigate characteristics of solitary waves attacking on beach slopes. By comparing numerical solutions with available laboratory measurements, it is shown that the maximum run-up heights of the present model are more agreeable than those of the existing numerical model. Variations of run-up heights and velocity vectors for different slopes are also described. Characteristics of hydrodynamic pressure acting beach slopes are investigated in detail.

• Journal of the Korean Society of Fisheries and Ocean Technology
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• v.27 no.1
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• pp.75-82
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• 1991

The present paper describes a preliminary design method by using the computer graphics for creation of the fore and after body profiles of fishing vessel. It is well known that the Form Parameter design method has some merits at an early stage of design, and the B-spline curve generation technique has some prior properties in representing hull form with the computer graphic. The B-spline curve generation technique combined with the form parameter design method is employed to generate the profiles of fishing vessel. For fore body the stem profiles with bulbous bulb or without one are considered. And for after body the stern profiles of cruiser type and the transom type are generated with stern bulb or with shoe piece. Several examples will shown.

• International Journal of Precision Engineering and Manufacturing
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• v.6 no.1
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• pp.15-22
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• 2005

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

• Korean Journal of Computational Design and Engineering
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• v.13 no.6
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• pp.469-477
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• 2008

Physically-based rendering is an image synthesis technique based on simulation of physical interactions between light and surface materials. Since generated images are highly photorealistic, physically-based rendering has become an indispensable tool in advanced design visualization for manufacturing and architecture as well as in film VFX and animations. Especially, BRDF (bidirectional reflectance distribution function) is critical in realistic visualization of materials since it models how an incoming light is reflected on the surface in terms of intensity and outgoing angles. In this paper, we introduce techniques to represent BRDF as B-spline volumes and to utilize them in physically-based rendering. We show that B-spline volume BRDF (BVB) representation is suitable for measured BRDFs due to its compact size without quality loss in rendering. Moreover, various CAGD techniques can be applied to B-spline volume BRDFs for further controls such as refinement and blending.

• Journal of the Korean Society for Precision Engineering
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• v.16 no.5 s.98
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• pp.160-168
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• 1999

This paper describes one method of reverse engineering that machines a free form shape without descriptive model. A portable five-axes 3D CMM was used to digitize point data from physical model. After approximation by rational B-spline curve from digitized point data of a geometric shape, a surface was constructed by the skinning method of the cross-sectional design technique. Since a surface patch was segmented by fifteen part, surface merging was also implemented to assure the surface boundary continuity. Finally, composite surface was transferred to commercial CAD/CAM system through IFES translation in order to machine the modeled geometric shape.

• International Journal of CAD/CAM
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• v.7 no.1
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• pp.11-20
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• 2007

A topology optimization methodology, named "smooth boundary topology optimization," is proposed to overcome the shortcomings of cell-based methods. Material boundary is represented by B-spline curves and their control points are considered as design variables. The design is improved by either creating a hole or moving control points. To determine which is more beneficial, a selection criterion is defined. Once determined to create a hole, it is represented by a new B-spline and recognized as a new boundary. Because the proposed method deals with the control points of B-spline as design variables, their total number is much smaller than cell-based methods and it ensures smooth boundaries. Differences between our method and level set method are also discussed. It is shown that our method is a natural way of obtaining smooth boundary topology design effectively combining computer graphics technique and design sensitivity analysis.