• Title/Summary/Keyword: $G^1$ 곡면

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NURBS Surface Reconstruction from an Unstructured Point Cloud (비조직화된 점군으로부터 NURBS 곡면 모델의 생성)

  • Li, Ri-Xie;Kim, Seok-Il
    • Proceedings of the KSME Conference
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    • 2007.05a
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    • pp.1564-1569
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    • 2007
  • This study concerns an advanced NURBS surface reconstruction method, which is based on the NURBS surface model fitting to the unstructured point cloud measured from an arbitrary complex shape. The concept of generating a simple triangular mesh model was introduced to generate a quadrilateral mesh model well-representing the topological characteristics of point cloud. The NURBS surface reconstruction processes required the use of the various methodologies such as QEM algorithm, merging scheme of pair-wise triangular mesh, creation algorithm of $G^1$ continuous tensor product NURBS surface patch, and so on. The effectiveness and reliability of the proposed NURBS surface reconstruction method were validated through the simulation results for the geometrically and topologically complex shapes.

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On Constructing NURBS Surface Model from Scattered and Unorganized 3-D Range Data (정렬되지 않은 3차원 거리 데이터로부터의 NURBS 곡면 모델 생성 기법)

  • Park, In-Kyu;Yun, Il-Dong;Lee, Sang-Uk
    • Journal of the Institute of Electronics Engineers of Korea SP
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    • v.37 no.3
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    • pp.17-30
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    • 2000
  • In this paper, we propose an efficient algorithm to produce 3-D surface model from a set of range data, based on NURBS (Non-Uniform Rational B-Splines) surface fitting technique. It is assumed that the range data is initially unorganized and scattered 3-D points, while their connectivity is also unknown. The proposed algorithm consists of three steps: initial model approximation, hierarchical representation, and construction of the NURBS patch network. The mitral model is approximated by polyhedral and triangular model using K-means clustering technique Then, the initial model is represented by hierarchically decomposed tree structure. Based on this, $G^1$ continuous NURBS patch network is constructed efficiently. The computational complexity as well as the modeling error is much reduced by means of hierarchical decomposition and precise approximation of the NURBS control mesh Experimental results show that the initial model as well as the NURBS patch network are constructed automatically, while the modeling error is observed to be negligible.

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Representation of Sweep Surface in Bicubic Spline surface Form (쌍3차 스플라인곡면 식에 의한 이동곡면의 표현)

  • 전차수;조형래;박세형
    • Transactions of the Korean Society of Mechanical Engineers
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    • v.19 no.4
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    • pp.1005-1012
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    • 1995
  • This paper proposes a new approach for modeling sweep surfaces. The overall modeling procedure consists of following steps : (1)remeshing the section curves based on the curve lengths ; (2)remeshing the guide curve and the boundary curves based on a given sweeping rule ; (3)obtaining intermediate section curves at the remeshed points of the guide curve by blending the initial section curves ; (4)compensation of the intermediate section curves ; (5)interpolating the initial and intermediate curves using Hermite interpolant. The resulting sweep surface is expressed in a G$^{2}$ bicubic parametric spline surface.

3D Surface Approximation to Serial 2D Cross Sections (단면정보로부터 3차원 근사곡면의 생성)

  • 박형준;김광수
    • Proceedings of the Korean Society of Precision Engineering Conference
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    • 1994.10a
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    • pp.719-724
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    • 1994
  • This paper describes a hybrid surface-based method for smooth 3D surface approximation to a sequence of 2D cross sections. The resulting surface is a hybrid G $^{1}$ surface represented by a mesh of triangular and rectangular Bezier patches defined on skinning, branching, or capping regions. Each skinning region is approximated with a closed B_spline surface, which is transformed into a mesh of Bezier patches. Triangular G $^{1}$ surfaces are constructed over brabching and capping regions such that the transitions between each capping regions such that the transitions between each triangular surface and its neighboring skinning surfaces are G $^{1}$ continuous. Since each skinning region is represented by an approximated rectangular C $^{2}$ suface instead of an interpolated trctangular G $^{[-1000]}$ surface, the proposed method can provide more smooth surfaces and realize more efficient data reduction than triangular surfacebased method.

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Composite $G^{1}$ surface construction from 2D cross-sections (2차원 단면 데이터로부터 복합 $G^{1}$ 자유곡면 생성)

  • Park, Hyung-Jun;Na, Sang-Wook;Bae, Chae-Yeol
    • Proceedings of the Korean Operations and Management Science Society Conference
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    • 2004.05a
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    • pp.44-47
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    • 2004
  • This paper proposes an approach for composite surface reconstruction from 2D serial cross-sections, where the number of contours varies from section to section. In a triangular surface-based approach taken in most reconstruction methods, a triangular $G^{1}$ surface is constructed by stitching triangular patches over a triangular net generated from the compiled contours. In the proposed approach, the resulting surface is a composite $G^{1}$ surface consisting of three kinds of surfaces: skinned, surface is first represented by a B-spline surface approximating the serial contours of the skinned region and then serial contours of the skinned region and then transformed into a mesh of rectangular Bezier patches. On branched and capped regions, triangular $G^{1}$ surfaces are constructed so that the connections between the triangular surfaces and their neighboring surfaces are $G^{1}$ continuous. Since each skinned region is represented by an approximated rectangular $G^{2}$ surface instead of an interpolated triangular $G^{1}$ surface, the proposed approach can provide more visually pleasing surfaces and realize more efficient data reduction than the triangular surface-based approach. Some experimental results demonstrate its usefulness and quality.

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$VC^2$ Chord-Length Spline Surface Using Hermite Interpolant (허미트 보간을 이용한 곡률 연속 현길이 스플라인 곡면)

  • Jun, C.S.;Ju, S.Y.;Jeon, M.G.
    • Journal of Korean Institute of Industrial Engineers
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    • v.20 no.1
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    • pp.87-98
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    • 1994
  • This paper describes a method of constructing VC2 Chord-length spline surface from semi-evenly spaced 3D point array. The suface uses Hermite interpolant as Ferguson surface, and it is an extention of chord-length spline curve to surface The proposed surface may be widely used in interpolating smoothly 3D point data obtaind by measurement or engineering design.

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A Study of Triangular Surface Interpolant for Scattered 3D points (불규칙한 3차원 상의 점군들에 대한 삼각곡면 보간에 관한 연구)

  • Ju, Sang-Yoon
    • Journal of Korean Institute of Industrial Engineers
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    • v.19 no.2
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    • pp.75-82
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    • 1993
  • This paper deals with a systematic procedure for constructing a triangular composite surface which is interpolated from given scattered 3-D points. The procedure consists of a triangulation, construction of curve net, and interpolation of triangular patches. An obtained surface is composed of cubic triangular patches, which are $G^1$ continuous to adjacent other patches.

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Construction of curve-net interpolation surface considering trajectory of cross-section curves (단면곡선의 궤적을 고려한 곡선망 보간곡면 형성)

  • Yoo, Woo-Sik;Shin, Ha-Yong;Choi, Byoung-K.
    • Journal of Korean Institute of Industrial Engineers
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    • v.20 no.2
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    • pp.77-90
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    • 1994
  • Curve-net interpolation surface is one of the most popular method in engineering design. Therefore it is supported with many commercial CAD/CAM system. However, construction algorithm of curve-net interpolation surfaces is rarely opened to the public because of its copy-right. In this paper we establish a construction algorithm of curve-net interpolation surface so called sweeping surface which especially concentrates on trajectory of cross-section curve. We also show the method which can construct sweeping surfaces as NURB or Bezier mathematical models. Surfaces having the form of standard mathematical models are very useful for the application of joining, trimming, blending etc. The proposed surface interpolation scheme consists of four steps; (1) preparation of guide curves and section curves, (2) remeshing guide curves and section curves, (3) blending section curves after deformation, and (4) determination of control points for sweeping surface using gordon method. The proposed method guarantee $G^1$-continuety, and construct the surface salifying given section curves and trajectory of section curves.

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Addendum Surface Modeling in Draw Die Design for Stamping Automotive Panels (자동차 프레스 패널 성형을 위한 드로 금형의 어덴덤 곡면 모델링)

  • Chung, Yunchan
    • Journal of the Korean Society of Manufacturing Technology Engineers
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    • v.22 no.6
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    • pp.1018-1024
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    • 2013
  • In the process of draw die design for stamping automotive press panels, the addendum surfaces generated in metal forming simulation software cannot be used in downstream processes such as machining and making draw dies because simulation tools use simple discrete models for the surface geometry. The downstream processes require more precise and continuous geometric models such as NURBS surfaces. Generally, automotive die engineers manually regenerate the addendum surface geometry using the discrete model. This paper presents an automated geometric modeling process for generating addendum surfaces using draft surface models. The design parameters of the section curve for the addendum surfaces are extracted automatically from the draft geometry. Using the extracted design parameters, smooth addendum surfaces are generated automatically as NURBS surfaces. The generated surfaces are $G^1$ continuous with the part surface and the binder surface, and can be used in downstream processes.

Noncontact Type Three Dimensional Profile Measurement for CAD Modeling of Sculptured Surface (자유곡면의 CAD 모델링을 위한 비접촉식 삼차원 형상측정)

  • Park, H.G.;Park, Y.B.;Kim, S.W.
    • Journal of the Korean Society for Precision Engineering
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    • v.12 no.1
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    • pp.5-14
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    • 1995
  • An optical measurement method of three dimensional surface profiles which is named the slit beam projection is suggested and practically implemented. This method is intended especially for noncontact and fast digitization of sculptured surfaces for CAD modeling and die manufacturing. Its basic principles are based on geometric optics. Deatiled optical principles and an sub-pixel image processing technique to enhance the measuring resolutions are described in this study. The measuring performances of the slit beam projection are presented and discussed to demonstrate that an actual measuring accuracy of below .+-. 0.2mm can be achived over the whole measuring range(500mm*300mm*200mm)

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