• 제목/요약/키워드: geometric continuity

검색결과 46건 처리시간 0.233초

ON THE CONSTRUCTION AND THE EXISTENCE OF PARAMETRIC CUBIC$g^2$ B-SPLINE

  • Kimn, Ha-Jine
    • 대한수학회논문집
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    • 제10권2호
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    • pp.483-490
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    • 1995
  • A parametric cubic spline interpolating at fixed number of nodes is constructed by formulating a parametric cubic $g^2$ B-splines $S_3(t)$ with not equally spaced parametric knots. Since the fact that each component is in $C^2$ class is not enough to provide the geometric smoothness of parametric curves, the existence of $S_3(t)$ oriented toward the modified second-order geometric continuity is focalized in our work.

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APPROXIMATION OF HELIX BY G2 CUBIC POLYNOMIAL CURVES

  • YOUNG JOON AHN
    • Journal of the Korean Society for Industrial and Applied Mathematics
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    • 제28권2호
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    • pp.59-70
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    • 2024
  • In this paper we present the approximation method of the circular helix by G2 cubic polynomial curves. The approximants are G1 Hermite interpolation of the circular helix and their approximation order is four. We obtain numerical examples to illustrate the geometric continuity and the approximation order of the approximants. The method presented in this paper can be extended to approximating the elliptical helix. Using the property of affine transformation invariance we show that the approximant has G2 continuity and the approximation order four. The numerical examples are also presented to illustrate our assertions.

A Geometric Characterization of Complete Continuity Property

  • Lim, Jong Sul;Eun, Gwang Sik;Yoon, Ju Han
    • 충청수학회지
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    • 제7권1호
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    • pp.217-226
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    • 1994
  • We introduce the notion of the mean Bocce dentable and provide the geometric characterization of the CCP. We show that X has the CCP if and only if every bounded subset of X is mean Bocce dentable.

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G2 Continuity Smooth Path Planning using Cubic Polynomial Interpolation with Membership Function

  • Chang, Seong-Ryong;Huh, Uk-Youl
    • Journal of Electrical Engineering and Technology
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    • 제10권2호
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    • pp.676-687
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    • 2015
  • Path planning algorithms are used to allow mobile robots to avoid obstacles and find ways from a start point to a target point. The general path planning algorithm focused on constructing of collision free path. However, a high continuous path can make smooth and efficiently movements. To improve the continuity of the path, the searched waypoints are connected by the proposed polynomial interpolation. The existing polynomial interpolation methods connect two points. In this paper, point groups are created with three points. The point groups have each polynomial. Polynomials are made by matching the differential values and simple matrix calculation. Membership functions are used to distribute the weight of each polynomial at overlapped sections. As a result, the path has $G^2$ continuity. In addition, the proposed method can analyze path numerically to obtain curvature and heading angle. Moreover, it does not require complex calculation and databases to save the created path.

Nonlinear finite element model of the beam-to-column connection for precast concrete frames with high ratio of the continuity tie bars

  • Sergio A. Coelho;Sergio A. Coelho
    • Computers and Concrete
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    • 제31권1호
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    • pp.53-69
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    • 2023
  • The rotational stiffness of a semi-rigid beam-to-column connection plays an important role in the reduction of the second-order effects in the precast concrete skeletal frames. The aim of this study is to present a detailed nonlinear finite element study to reproduce the experimental response of a semi-rigid precast beam-to-column connection composed by corbel, dowel bar and continuity tie bars available in the literature. A parametric study was carried using four arrangements of the reinforcing tie bars in the connection, including high ratio of the continuity tie bars passing around the column in the cast-in-place concrete. The results from the parametric study were compared to analytical equations proposed to evaluate the secant rotational stiffness of beam-to-column connections. The good agreement with the experimental results was obtained, demonstrating that the finite element model can accurately predict the structural behaviour of the beam-to-column connection despite its complex geometric configuration. The secant rotational stiffness of the connection was good evaluated by the analytical model available in the literature for ratio of the continuity tie bars of up to 0.69%. Precast beam-to-column connection with a ratio of the continuity tie bars higher than 1.4% had the secant stiffness overestimated. Therefore, an adjustment coefficient for the effective depth of the crack at the end of the beam was proposed for the analytical model, which is a function of the ratio of the continuity tie bars.

20세기 초 모더니즘 패션에 나타난 신고전주의 양식의 연속성과 불연속성 -형식의 명료성을 중심으로- (Continuity and Discontinuity of the Neoclassic Style in Early Twentieth Century Fashion Modernism)

  • 함연자;김민자
    • 복식
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    • 제56권4호
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    • pp.148-159
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    • 2006
  • The purpose of this study is to understand continuity and discontinuity of the neoclassic style in early twentieth century fashion modernism. Researching relations in fashion between eighteenth to nineteenth century and twentieth century, the theory of 'linked solution' suggested by Kubler and Broadsky has been accepted. The results of this study are as follows: In early twentieth century fashion, continuity of the neoclassic style is considered as presentation of geometric form based on anatomical truth of the human body and moderation of decoration. Also simple construction to present practical purpose of the dress in honesty were continued. On the other hand, discontinuity of the style is found in the imitation of men's classic tailored suits and standardization of sizes and styles. These are considered to reflect such early twentieth century sociocultural contexts as equality of the sexes and mechanical aesthetics. Hopefully this study will contribute to the broadening of insight in fashion connecting traditions.

Constructing $G^1$ Quadratic B$\acute{e}$zier Curves with Arbitrary Endpoint Tangent Vectors

  • Gu, He-Jin;Yong, Jun-Hai;Paul, Jean-Claude;Cheng, Fuhua (Frank)
    • International Journal of CAD/CAM
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    • 제9권1호
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    • pp.55-60
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    • 2010
  • Quadratic B$\acute{e}$zier curves are important geometric entities in many applications. However, it was often ignored by the literature the fact that a single segment of a quadratic B$\acute{e}$zier curve may fail to fit arbitrary endpoint unit tangent vectors. The purpose of this paper is to provide a solution to this problem, i.e., constructing $G^1$ quadratic B$\acute{e}$zier curves satisfying given endpoint (positions and arbitrary unit tangent vectors) conditions. Examples are given to illustrate the new solution and to perform comparison between the $G^1$ quadratic B$\acute{e}$zier cures and other curve schemes such as the composite geometric Hermite curves and the biarcs.

Isoparametric Curve of Quadratic F-Bézier Curve

  • Park, Hae Yeon;Ahn, Young Joon
    • 통합자연과학논문집
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    • 제6권1호
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    • pp.46-52
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    • 2013
  • In this thesis, we consider isoparametric curves of quadratic F-B$\acute{e}$zier curves. F-B$\acute{e}$zier curves unify C-B$\acute{e}$zier curves whose basis is {sint, cos t, t, 1} and H-B$\acute{e}$zier curves whose basis is {sinht, cosh t, t,1}. Thus F-B$\acute{e}$zier curves are more useful in Geometric Modeling or CAGD(Computer Aided Geometric Design). We derive the relation between the quadratic F-B$\acute{e}$zier curves and the quadratic rational B$\acute{e}$zier curves. We also obtain the geometric properties of isoparametric curve of the quadratic F-B$\acute{e}$zier curves at both end points and prove the continuity of the isoparametric curve.

Delaunay 삼각화 기법을 활용한 다중-블록 정렬 격자의 자동 생성 기법 (Automatic Multi-Block Grid Generation Technique Based on Delaunay Triangulation)

  • 김병수
    • 한국전산유체공학회:학술대회논문집
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    • 한국전산유체공학회 1999년도 추계 학술대회논문집
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    • pp.108-114
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    • 1999
  • In this paper. a new automatic multi=block grid generation technique for general 2D regions is introduced. According to this simple and robust method, the domain of interest is first triangulated by using Delaunay triangulation of boundary points, and then geometric information of those triangles is used to obtain block topology. Once block boundaries are obtained. structured grid for each block is generated such that grid lines have $C^0-continuity$ across inter-block boundaries. In the final step of the present method, an elliptic grid generation method is applied to smoothen grid distribution for each block and also to re-locale the inter-block boundaries, and eventually to achieve a globally smooth multi-block structured grid system with $C^1-continuity$.

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Mesh distortion sensitivity of 8-node plane elasticity elements based on parametric, metric, parametric-metric, and metric-parametric formulations

  • Rajendran, S.;Subramanian, S.
    • Structural Engineering and Mechanics
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    • 제17권6호
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    • pp.767-788
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    • 2004
  • The classical 8-node isoparametric serendipity element uses parametric shape functions for both test and trial functions. Although this element performs well in general, it yields poor results under severe mesh distortions. The distortion sensitivity is caused by the lack of continuity and/or completeness of shape functions used for test and trial functions. A recent element using parametric and metric shape functions for constructing the test and trial functions exhibits distortion immunity. This paper discusses the choice of parametric or metric shape functions as the basis for test and/or trial functions, satisfaction of continuity and completeness requirements, and their connection to distortion sensitivity. Also, the performances of four types of elements, viz., parametric, metric, parametric-metric, and metric-parametric, are compared for distorted meshes, and their merits and demerits are discussed.