• 대한수학회지
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• 제39권6호
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• pp.821-879
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• 2002

Let U, V and W be complex vector spaces of dimensions 3, 3 and 4 respectively. The reductive algebraic group G = PGL(U) $\times$ PGL(W) $\times$ PGL(W) acts linearly on the projective tensor product space (equation omitted). In this paper, we show that the G-equivalence classes of the projective tensors are in one-to-one correspondence with the PGL(3)-equivalence classes of unordered configurations of six points on the projective plane.

• 한국정밀공학회:학술대회논문집
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• 한국정밀공학회 1994년도 추계학술대회 논문집
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• pp.298-302
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• 1994

A three dimensional FE mesh generation scheme based on mapping approach is proposed in this study. A volume in Euclcdian space is represented by composite hyperpatches which are piecewise cubic functions with parameters u,v,w. A key idea in the proposed approach is that sampled grid data points only on the boundary surfaces are needed for the shape representation. Inner points which are necessary of form a hyperpatch are internally generated by Coons patches. This approach is most appropriate for the shapes which are compositions of hexahedron-like shapes and also severely curved.

• Journal of information and communication convergence engineering
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• 제9권4호
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• pp.424-427
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• 2011

The paper is devoted to problem of spline approximation. A new method of nodes location for curves and surfaces computer construction by means of B-splines, of Reyabenko's splines and results of simulink-modeling is presented. The advantages of this paper is that we comprise the basic spline with classical polynomials both on accuracy, as well as degree of paralleling calculations are also show's.

• Journal of the Optical Society of Korea
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• 제6권2호
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• pp.21-26
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• 2002

Interferometric metrology with a null CGH(computer-generated hologram) is presented for measuring highly aspheric surfaces used in a large screen projection television system with high accuracy. The cubic spline surface model which works in a single-pass configuration with a refractive index of object space 0 is used for designing a null CGH. A hybrid null corrector with plano-concave lens in front of a CGH is presented to make the CGH easier to fabricate. Experimental results are presented to demonstrate the validity of the proposed technique.

• 한국소성가공학회:학술대회논문집
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• 한국소성가공학회 2003년도 추계학술대회논문집
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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.

• 한국소성가공학회:학술대회논문집
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• 한국소성가공학회 2003년도 추계학술대회논문집
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• pp.197-200
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• 2003

An automatic surface construction method based on B-spline surface and scalar field theory is proposed to generate the extrusion die surface of complicated sections in this paper. 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.

• International Journal of Precision Engineering and Manufacturing
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• 제3권1호
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• pp.49-56
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• 2002

The Z-map is a special farm of discrete non-parametric representation in which the height values at grid points on the xy-plane are stored as a 2D array z[ij]. While the z-map is the simplest farm of representing sculptured surfaces and is the most versatile scheme for modeling non-parametric objects, its practical application in industry (eg, tool-path generation) has aroused much controversy over its weaknesses, namely its inaccuracy, singularity (eg, vertical wall), and some excessive storage needs. Much research or the application of the z-map can be found in various articles, however, research on the systematic analysis of sculptured surface shape representation via the z-map model is rather rare. Presented in this paper are the following: shape modeling power of the simple z-map model, exact (within tolerance) z-map representation of sculptured surfaces which have some feature-shapes such as vertical-walls and real sharp-edges by adopting some complementary z-map models, and some application examples.

• 소성∙가공
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• 제12권6호
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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.

• Journal of applied mathematics & informatics
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• 제23권1_2호
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• pp.397-410
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• 2007

Visualization of 2D and 3D data, which arises from some scientific phenomena, physical model or mathematical formula, in the form of curve or surface view is one of the important topics in Computer Graphics. The problem gets critically important when data possesses some inherent shape feature. For example, it may have positive feature in one instance and monotone in the other. This paper is concerned with the solution of similar problems when data has convex shape and its visualization is required to have similar inherent features to that of data. A rational cubic function [5] has been used for the review of visualization of 2D data. After that it has been generalized for the visualization of 3D data. Moreover, simple sufficient constraints are made on the free parameters in the description of rational bicubic functions to visualize the 3D convex data in the view of convex surfaces.

• 대한조선학회논문집
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• 제29권3호
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• pp.15-20
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• 1992

이 논문에서는 화가의(Painter's) 알고리듬을 사용하여 3차원 자유형상곡면(Three dimensional free form surface)을 가시화하는 방법을 개발하였고, 특히 선체형상은 Open 균일 B-Spline 곡면으로 정의하였다. 컴퓨터그래픽스를 응용하여 와이어프레임, 숨은면제거, 묘영등의 가시화를 위한 프로그램을 완성하였다. 또한 선체곡면의 순정을 검토하기 위해 Gaussian 곡률값을 15등급으로 구분하여 등급별 색(color)처리 하였다.