• Title, Summary, Keyword: CAGD

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A Brief History of Study on the Bound for Derivative of Rational Curves in CAGD (CAGD에서 유리 곡선의 미분과 그 상한에 관한 연구의 흐름)

  • Park, Yunbeom
    • Journal for History of Mathematics
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    • v.27 no.5
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    • pp.329-345
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    • 2014
  • CAGD(Computer Aided Geometric Design) is a branch of applied mathematics concerned with algorithms for the design of smooth curves and surfaces and for their efficient mathematical representation. The representation is used for the computation of the curves and surfaces, as well as geometrical quantities of importance such as curvatures, intersection curves between two surfaces and offset surfaces. The $B\acute{e}zier$ curves, B-spline, rational $B\acute{e}zier$ curves and NURBS(Non-Uniform Rational B-Spline) are basically and widely used in CAGD. The definitions and properties of these curves are presented in this paper. And a brief history of study on the bound for derivative of rational curves in CAGD is also presented.

A Study on the Shape and Thickness Optimizations of Shells Using CAGD through Minimization of Strain Energy with Volume Constraint (CAGD를 사용한 쉘의 형상 및 두께 최적화에 관한 연구 (부피 제약조건을 사용한 변형에너지의 최소화))

  • 이상진;한상을
    • Journal of the Computational Structural Engineering Institute of Korea
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    • v.12 no.4
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    • pp.551-561
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    • 1999
  • 본 논문에서는 쉘 최적화에 대한 연구 결과를 기술하였다. 본 연구의 주목적은 쉘 구조물의 최적형상과 두께 분포를 찾는데 있다. 쉘의 변형에너지를 목적함수로 사용하고 초기 쉘의 부피를 제약조건을 고려하였다. 본 연구에서는 Computer-Aided Geometric Design (CAGD) 기법을 이용하여 쉘의 형상과 그 두께 분포를 표현하였고 쉘의 변형에너지를 측정하기 위해서 가변형 도를 채용한 퇴화 쉘 요소(Degenerated Shell Element)를 도입하였다. 최적 값을 구하기 위해서 세 가지 수학적 프로그래밍 기법을 제공하는 프로그램 DOT를 사용하였다. 마지막으로 새로이 개발된 쉘 최적화시스템의 효율성을 최적화예제로써 증명하였다.

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GEOMETRIC CONIC SPLINE APPROXIMATION IN CAGD

  • Ahn, Young-Joon
    • Communications of the Korean Mathematical Society
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    • v.17 no.2
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    • pp.331-347
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    • 2002
  • We characterize the best geometric conic approximation to regular plane curve and verify its uniqueness. Our characterization for the best geometric conic approximation can be applied to degree reduction, offset curve approximation or convolution curve approximation which are very frequently occurred in CAGD (Computer Aided Geometric Design). We also present the numerical results for these applications.

Automatic FE Mesh Generation Technique using Computer Aided Geometric Design for Free-form Discrete Spatial Structure (CAGD를 이용한 프리폼 이산화 공간구조물의 유한요소망 자동생성기법)

  • Lee, Sang-Jin
    • Journal of Korean Association for Spatial Structures
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    • v.10 no.2
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    • pp.77-86
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    • 2010
  • This paper provides background theories and numerical results of automatic finite element (FE) mesh generation for freeform discrete structures. The present method adopts the computer aided geometric design (CAGD) technique to overcome the limitation of case-sensitive traditional automatic FE mesh generator. The present technique involves two steps. The first one is to represent the shape of the structure using the geometric model based on the CAGD and the second one is to generate the discrete FE mesh of spatial structures over the geometric model. From numerical results, it is found to be that the present technique is very easy to produce the FE mesh for free-form spatial structures and it can also reuse some features of traditional automatic mesh generator in the process. Furthermore, it shows the possibility to be used for the shape optimization of large spatial structures.

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SDL: A New CAGD Library for Conputer-Aided Ship Design

  • Koras, George D.;Kaklis, Panagiotis D.;Papanikolaou, Apostolos D.
    • Journal of Ship and Ocean Technology
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    • v.5 no.4
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    • pp.1-18
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    • 2001
  • Software written in academic environments is rarely integrated and/or reused. Moreover, typical academic software products do not communicate with commercial CAD packages, consequently functionality that is readily available to industry is not available do academic researchers. The Surface Design Library (SDL) is a library serving as a framework under which, CAGD software, intended for research or educational use, can be written in such a manner that it becomes a reusable part of a useful CAGD system. Moreover SDL is equipped with an IGES translator so that it communicates with commercial CAD packages, This paper gives a brief overview to SDL and presents examples of using it for high quality fairing performed on a naval ship hull, before employing commercial CAD packages for further design and analysis.

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On the Contents and Curriculum for University geometry course focused on applications (대학수학교육에서 기하학의 응용과 교과내용의 구성방안)

  • Jeon, Myung-Jin;Cho, Min-Shik
    • Communications of Mathematical Education
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    • v.19 no.4
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    • pp.621-631
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    • 2005
  • The purpose of this study is to consider how to restructure the university geometry curriculum and contents in terms of applications to theoretical computer science. We analyzed various topics from computer graphics, CAGD(computer aided geometric design) and computational geometry suitable for geometry students interested in applications. Moreover we discussed about selections of topics for several cases.

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Study on approximating subdivision schemes for the application to CAD/CAE (CAD/CAE 적응을 위한 근사 서브디비전 방법의 고찰)

  • 서홍석;조맹효
    • Proceedings of the Computational Structural Engineering Institute Conference
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    • pp.237-243
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    • 2002
  • Recently, in computer-aided geometric modeling(CAGD), subdivision surfaces are frequently employed to construct free-form surface. Subdivision schemes have been very popular in computer graphics and animation community, but the community of CAGD adopts this tool only recently to handle surface geometry. In the present study, Loop scheme and Catmull-Clark scheme are applied to generate smooth surfaces. To be consistent with the limit points of target surface, the initial sampling points are properly rearranged. The pointwise curvature errors and coordinate value errors between the points in the sequence of subdivision process and the points on the target surface are evaluated In the numerical examples in both Loop scheme & Catmull-Clark subdivision scheme.

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Approximate Conversion of Rational Bézier Curves

  • Lee, Byung-Gook;Park, Yunbeom
    • Journal of the Korean Society for Industrial and Applied Mathematics
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    • v.2 no.1
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    • pp.88-93
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    • 1998
  • It is frequently important to approximate a rational B$\acute{e}$zier curve by an integral, i.e., polynomial one. This need will arise when a rational B$\acute{e}$zier curve is produced in one CAD system and is to be imported into another system, which can only handle polynomial curves. The objective of this paper is to present an algorithm to approximate rational B$\acute{e}$zier curves with polynomial curves of higher degree.

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A Form-finding Technique for Three-dimensional Spatial Structures

  • Lee, Sang Jin
    • Architectural research
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    • v.15 no.4
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    • pp.207-214
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    • 2013
  • A form-finding technique is proposed for three-dimensional spatial structures. Two-step discrete finite element (FE) mesh generator based on computer aided geometric design (CAGD) is introduced and used to control the shape of three-dimensional spatial structures. Mathematical programming technique is adopted to search new forms (or shapes) of spatial structures. For this purpose, the strain energy is introduced as the objective function to be minimized and the initial volume (or the initial weight) is considered as constraint function. Numerical examples are carried out to test the capability of the proposed form-finding techniques and provided as benchmark tests.

STUDY ON BCN AND BAN RULED SURFACES IN 𝔼3

  • Abd-Ellah, Hamdy N.;Omran, Abdelrahim Khalifa
    • Korean Journal of Mathematics
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    • v.25 no.4
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    • pp.513-535
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    • 2017
  • As a continuation to the study in [8, 12, 15, 17], we construct bi-conservative central normal (BCN) and bi-conservative asymptomatic normal (BAN) ruled surfaces in Euclidean 3-space ${\mathbb{E}}^3$. For such surfaces, local study is given and some examples are constructed using computer aided geometric design (CAGD).