• Title, Summary, Keyword: Curve

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ON TIMELIKE BERTRAND CURVES IN MINKOWSKI 3-SPACE

  • Ucum, Ali;Ilarslan, Kazim
    • Honam Mathematical Journal
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    • v.38 no.3
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    • pp.467-477
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    • 2016
  • In this paper, we study the timelike Bertrand curves in Minkowski 3-space. Since the principal normal vector of a timelike curve is spacelike, the Bertrand mate curve of this curve can be a timelike curve, a spacelike curve with spacelike principal normal or a Cartan null curve, respectively. Thus, by considering these three cases, we get the necessary and sufficient conditions for a timelike curve to be a Bertrand curve. Also we give the related examples.

SOME INTEGRAL CURVES ASSOCIATED WITH A TIMELIKE FRENET CURVE IN MINKOWSKI 3-SPACE

  • Duldul, Bahar Uyar
    • Honam Mathematical Journal
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    • v.39 no.4
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    • pp.603-616
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    • 2017
  • In this paper, we give some relations related with a spacelike principal-direction curve and a spacelike binormal-direction curve of a timelike Frenet curve. The Darboux-direction curve and the Darboux-rectifying curve of a timelike Frenet curve in Minkowski 3-space $E^3_1$ are introduced and some characterizations related with these associated curves are given. Later we define the spacelike V-direction curve which is associated with a timelike curve lying on a timelike oriented surface in $E^3_1$ and present some results together with the relationships between the curvatures of this associated curve.

EXPLICIT ERROR BOUND FOR QUADRATIC SPLINE APPROXIMATION OF CUBIC SPLINE

  • Kim, Yeon-Soo;Ahn, Young-Joon
    • Journal of the Korean Society for Industrial and Applied Mathematics
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    • v.13 no.4
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    • pp.257-265
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    • 2009
  • In this paper we find an explicit form of upper bound of Hausdorff distance between given cubic spline curve and its quadratic spline approximation. As an application the approximation of offset curve of cubic spline curve is presented using our explicit error analysis. The offset curve of quadratic spline curve is exact rational spline curve of degree six, which is also an approximation of the offset curve of cubic spline curve.

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A Study on the Optimized Biarc Curve Fitting of Involute Curve (인벌류트 곡선의 Biarc Curve Fitting 최적화에 관한 연구)

  • Cho, Seung-Rae;Lee, Choon-Man
    • Journal of the Korean Society for Precision Engineering
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    • v.16 no.4
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    • pp.71-78
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    • 1999
  • The determination of the optimum biarc curve passing through a given set of points along involute curve is studied. The method adopted is that of finding the optimum number of span and the optimum length of the span such that error between the biarc curve and involute curve minimum. Iterative method is effectively used to find the optimim number and length of the span on involute curve with reduced length of NC-code.

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DIRECTIONAL ASSOCIATED CURVES OF A NULL CURVE IN MINKOWSKI 3-SPACE

  • Qian, Jinhua;Kim, Young Ho
    • Bulletin of the Korean Mathematical Society
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    • v.52 no.1
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    • pp.183-200
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    • 2015
  • In this paper, we define the directional associated curve and the self-associated curve of a null curve in Minkowski 3-space. We study the properties and relations between the null curve, its directional associated curve and its self-associated curve. At the same time, by solving certain differential equations, we get the explicit representations of some null curves.

A Tessellation of a Polynomial Curve by a Sequential Method (다항식곡선으로부터 순차적 방법에 의한 점열의 생성)

  • Ju S.Y.
    • Korean Journal of Computational Design and Engineering
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    • v.11 no.3
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    • pp.205-210
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    • 2006
  • Curve tessellation, which generates a sequence of points from a curve, is very important for curves rendering on a computer screen and for NC machining. For the most case the sequence of discrete points is used rather than a continuous curve. This paper deals with a method of tessellation by calculating the maximal deviation of a curve. The maximal deviation condition is introduced to find the point with the maximal chordal deviation on a curve segment. In the previous research a curve tessellation was tried by the subdivision method, that is, a curve is subdivided until the maximal chordal deviation is less than the given tolerance. On the other hand, a curve tessellation by sequential method is tried in this paper, that is, points are generated successively by using the local property of a curve. The sequential method generates relatively much less points than the subdivision method. Besides, the sequential method can generate a sequence of points from a spatial curve by approximation to a planar curve. The proposed method can be applied for high-accuracy curve tessellation and NC tool-path generation.

Analysis for the Concept of Smooth Curve by Velocity (속도의 관점에서 매끄러운 곡선의 의미 분석)

  • Choi, Myeong-Suk;Jeong, Da-Rae;Kim, Jun-Seok
    • Journal of Educational Research in Mathematics
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    • v.22 no.1
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    • pp.23-38
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    • 2012
  • The purpose of this paper is to describe the true meaning of smooth curve and to let people understand the smooth curve by way of velocity. It is true that it is not easy for us to perceive smooth curve because when there are no cups in the curve and the shape of the curve looks smooth, we often perceive it is smooth curve. However, even when the shape of curve looks smooth, it happens that it is not smooth curve. When the particle moves on the curve, depending on the velocity, it can be smooth curve or not. That is, even though the shape looks smooth, when the velocity is discontinuous or it is 0, it is not smooth curve. Therefore, this paper shows that it is important to understand and to teach smooth curve by way of velocity. In other words, when parameter of path for the smooth curve is taught in the calculus of high school, it needs to be understood by way of velocity. Finally, this paper tries to suggest that we need to shift our paradigm in teaching of smooth curve from fixed curve to dynamic curve.

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Bezier Control Points for the Image of a Domain Curve on a Bezier Surface (베지어 곡면의 도메인 곡선의 이미지 곡선에 대한 베지어 조정점의 계산)

  • 신하용
    • Korean Journal of Computational Design and Engineering
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    • v.1 no.2
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    • pp.158-162
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    • 1996
  • Algorithms to find the Bezier control points of the image of a Bezier domain curve on a Bezier surface are described. The diagonal image curve is analysed and the general linear case is transformed to the diagonal case. This proposed algorithm gives the closed form solution to find the control points of the image curve of a linear domain curve. If the domain curve is not linear, the image curve can be obtained by solving the system of linear equations.

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Study for Prediction of Ride Comfort on the Curve Track by Predictive Curve Detection (사전틸팅제어의 곡선부 주행 승차감 평가 연구)

  • Ko, Tae-Hwan;Lee, Duk-Sang
    • Proceedings of the KSR Conference
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    • pp.69-74
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    • 2011
  • In the curving detection method by using an accelerometer, the ride comfort in the first car is worse than one in the others due to spend the time to calculate the tilting command and drive the tilting mechanism after entering in the curve. In order to enhance the ride comfort in the first car, the preditive curve detection method which predicts the distance from a train to the starting point of curve by using the GPS, Tachometer, Ground balise and position DB for track. In this study, we predicted and evaluated the ride comfort for predictive curve detection method in transient curves according to the shape and dimension of transient curve and the various driving speed. Also, we predicted the improvement of the ride comfort for predictive curve detection method by comparing with the result of the ride comfort for predictive curve detection method and for curve detection method using an accelerometer in the short transient curve.

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A Tessellation of a Planar Polynomial Curve and Its Offset (평면곡선과 오프셋곡선의 점열화)

  • Ju, S.Y.;Chu, H.
    • Korean Journal of Computational Design and Engineering
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    • v.9 no.2
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    • pp.158-163
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    • 2004
  • Curve tessellation, which generates a sequence of points from a curve, is very important for curve rendering on a computer screen and for NC machining. For the most case the sequence of discrete points is used rather than a continuous curve. This paper deals with a method of tessellation by calculating the maximal deviation of a curve. The maximal deviation condition is introduced to find the point with the maximal deviation. Our approach has two merits. One is that it guarantees satisfaction of a given tolerance, and the other is that it can be applied in not only a polynomial curve but its offset. Especially the point sequence generated from an original curve can cause over-cutting in NC machining. This problem can be solved by using the point sequence generated from the offset curve. The proposed method can be applied for high-accuracy curve tessellation and NC tool-path generation.