• 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.

• Transactions of Materials Processing
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• v.12 no.2
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• pp.142-150
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• 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 Ship and Ocean Technology
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• v.10 no.2
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• pp.24-36
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• 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.

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

• Korean Journal of Computational Design and Engineering
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• v.4 no.1
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• pp.32-42
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• 1999

Approximate lofting or skinning is one of practical surface modeling techniques well used in CAD and reverse engineering applications. Presented in this paper is a method for approximately lofting a given set of curves wihin a specified tolereance. It is based on refitting input curves simultaneously on a common knot vector and interpolating them to get a resultant NURBS surface. A concept of reducing the number of interior knots of the common knot vector is well adopted to acquire more compact representation for the resultant surface. Energy minimization is newly introduced in curve refitting process to stabilize the solution of the fitting problem and get more fair curve. The proposed approximate lofting provides more smooth surface models and realizes more efficient data reduction expecially when the parameterization and compatibility of input curves are not good enough. The method has been successfully implemented in a new CAD/CAM product VX Vision? of Varimetrix Corporation.

• 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 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.

• Proceedings of the Society of Korea Industrial and System Engineering Conference
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• 2002.05a
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• pp.461-466
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• 2002

In many applications of computer aided geometric design and computer graphics, B-spline is one of the most popular representation for curves and surfaces, and the evaluation of B-spline curves and surfaces is the most frequently used operation. For the evaluation and others, the power form representation of the curves and surfaces is preferred because it is possible to speed-up the operation using Horner's rule. In this paper, we present a new algorithm for the above-mentioned conversion focusing on a dynamic case. Experiment shows that the proposed algorithm significantly outperforms the conventional approach when one or more control points of a B-spline curve and surface are dynamically moving.

• Transactions of Materials Processing
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• v.12 no.6
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• pp.572-581
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• 2003

In this paper, an automatic surface construction method based on B-spline surface and scalar field theory is proposed to generate the extrusion die surface of non-symmetric H-and U-shaped sections. The isothermal lines and stream lines designed in the scalar field are introduced to find the control points which are used in constructing B-spline surfaces. Intersected points between the isothermal lines and stream lines are used to construct B-spline surfaces. The inlet and outlet profiles are precisely described with B-spline curves by using the centripetal method for uniform parameterization. The extrusion die surface is generated by using the cubic curve interpolation in the u-and v-directions. A quantitative measure for the control of surface is suggested by introducing the tangential vectors at the inlet and outlet sections. To verify the validity of the proposed method, automatic surface generation is carried out for extrusion die of non-symmetric H-and U-shaped sections.

• Proceedings of the Korean Society for Technology of Plasticity Conference
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• 2003.10a
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• pp.318-321
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• 2003

In order to generate the extrusion die surface of non-symmetric H- and U-shaped sections, an automatic surface construction method based on B-spline surface and scalar field theory is proposed in this study. The isothermal lines and stream lines designed in the scalar field are introduced to find the control points which are used in constructing B-spline surfaces. Intersected points between the isothermal lines and stream lines are used to construct B-spline surfaces. The inlet and outlet profiles are precisely described with B-spline curves by using the centripetal method for uniform parameterization. The extrusion die surface is generated by using the cubic curve interpolation in the u- and v-directions. A quantitative measure for the control of surface is suggested by introducing the tangential vectors at the inlet and outlet sections.