• Kyungpook Mathematical Journal
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• v.58 no.1
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• pp.117-135
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• 2018

The orthogonal trajectories of the first tangents of the curve are called the involutes of x. The hyperspheres which have higher order contact with a curve x are known osculating hyperspheres of x. The centers of osculating hyperspheres form a curve which is called generalized evolute of the given curve x in n-dimensional Euclidean space ${\mathbb{E}}^n$. In the present study, we give a characterization of involute curves of order k (resp. evolute curves) of the given curve x in n-dimensional Euclidean space ${\mathbb{E}}^n$. Further, we obtain some results on these type of curves in ${\mathbb{E}}^3$ and ${\mathbb{E}}^4$, respectively.

• Bulletin of the Korean Mathematical Society
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• v.59 no.2
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• pp.407-417
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• 2022

Archimedes proved that for a point P on a parabola X and a chord AB of X parallel to the tangent of X at P, the area of the region bounded by the parabola X and the chord AB is four thirds of the area of the triangle ∆ABP. This property was proved to be a characteristic of parabolas, so called the Archimedean characterization of parabolas. In this article, we study strictly convex curves in the plane ℝ². As a result, first using a functional equation we establish a characterization theorem for quadrics. With the help of this characterization we give another proof of the Archimedean characterization of parabolas. Finally, we present two related conditions which are necessary and sufficient for a strictly convex curve in the plane to be an open arc of a parabola.

• Honam Mathematical Journal
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• v.36 no.1
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• pp.113-129
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• 2014

In this study, we have investigated the possibility of whether any Frenet plane of a given space curve in a 3-dimensional Euclidean space $\mathbb{E}_3$ also is any Frenet plane of another space curve in the same space. We have obtained some characterizations of a given space curve by considering nine possible case.

• Honam Mathematical Journal
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• v.44 no.3
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• pp.391-401
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• 2022

In this study, we investigate the explicit characterization of spherical curves using the Flc (Frenet like curve) frame in Euclidean 3-space. Firstly, the axis of curvature and the osculating sphere of a polynomial space curve are calculated using Flc frame invariants. It is then shown that the axis of curvature is on a straight line. The position vector of a spherical curve is expressed with curvatures connected to the Flc frame. Finally, a differential equation is obtained from the third order, which characterizes a spherical curve.

• 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.

• Journal of the Institute of Electronics Engineers of Korea SP
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• v.41 no.6
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• pp.33-41
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• 2004

This paper proposes a color matching 3D look-up table simplifying the complex color matching procedure between a monitor and a mobile display device. In other to perform color matching, it is necessary to process color of image in the device independent color space like CIEXYZ or CIELAB. To obtain the data of the device independent color space from that of the device dependent RGB color space, we must perform display characterizations. LCD characterization error using S-curve model is larger than tolerance error since LCD is more nonlinear than CRT. This paper improves the S-curve model to have smaller characterization error than tolerance error using the electro-optical transfer functions of X, Y, and Z value. We obtained images having higher color fidelity on mobile display devices through color matching experiments between monitor and mobile display devices. As a result of this experiments, we concluded that the color matching look-up table with 64(4${\times}$4${\times}$4) is the smallest size allowing characterization error to be acceptable.

• Korean Journal of Computational Design and Engineering
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• v.3 no.3
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• pp.183-191
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• 1998

There are many available algorithms based on the different approaches to solve the intersection problems between two curves. Among them, the implicitization method is frequently used since it computes precise solutions fast and is robust in lower degrees. However, once the degrees of curves to be intersected are higher than cubics, its computation time increases rapidly and the numerical stability gets worse. From this observation, it is natural to transform the original problem into a set of easier ones. Therefore, curves are subdivided appropriately depending on their geometric behavior and approximated by a set of rational quadratic Bezier cures. Then, the implicitization method is applied to compute the intersections between approximated ones. Since the solutions of the implicitization method are intersections between approximated curves, a numerical process such as Newton-Raphson iteration should be employed to find true intersection points. As the seeds of numerical process are close to a true solution through the mix-and-match process, the experimental results illustrates that the proposed algorithm is superior to other algorithms.

• Proceedings of the IEEK Conference
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• 2003.11a
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• pp.15-18
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• 2003

This paper proposes a color matching 3D look-up table simplifying the complex color matching procedure between a monitor and a mobile display device. In order to perform color matching, it is necessary to process color of image in the device independent color space like CIEXYZ or CIELAB. We improved the S-curve model to have smaller characterization error than tolerance error. Also, as a result of the experiments, we concluded that the color matching look-up table with 64(4$\times$4$\times$4) is the smallest size allowing characterization error to be acceptable.

• Journal of applied mathematics & informatics
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• v.19 no.1_2
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• pp.241-251
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• 2005

In this paper, we introduce a new algebraic method to characterize rational PH plane curves. And using this method, we study the algebraic characterization of generic strongly regular rational plane PH curves expressed in the complex formalism which is introduced by R.T. Farouki. We prove that generic strongly semi-regular rational PH plane curves are completely characterized by solving a simple functional equation H(f, g) = $h^2$ where h is a complex polynomial and H is a bi-linear operator defined by H(f, g) = f'g - fg' for complex polynomials f,g.

• Journal of Ocean Engineering and Technology
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• v.12 no.1
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• pp.65-75
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• 1998

The fracture resistance curve is one of most important and design techniques employed in nuclear pressure vessel structures. This study is to evaluate the J-R curve characteristics for the SA508C-3 by the unloading compliance method and load rato analysis. The effect of strain aging for the exponential correlation of the J-R curve in this metal are investigated at room temperature, 20$0^{\circ}C$ and 30$0^{\circ}C$. The load ratio analysis method can evaluate the J-R curve by using the simple tension load-displacement curve only without the repeat of the unloading and loading. Therefore, the analysis by the proposed load ratio method has a merit, in comparison with the unloading compliance method, which can measure the crack length without the precision measurement equipment.