• Journal of Korean Ophthalmic Optics Society
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• v.8 no.2
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• pp.77-83
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• 2003

To investigate the influence of the variation of conic coefficient of the front surface on the RMS SD(Root Mean Square Spot Diameter) in a back focal plane, we use programs which are Cove V and LOSA 2.0. We consider a spectacle lens with back vertex power of -4.00D, diameter of 70 mm, the front surface powers which are 2.00D, 4.00D, 6.00D, and 8.00D, and the indices which are $n_d$=1.498, 1.523, 1.586, and 1.660, respectively. The RMS SD in the back focal plane and the thickness of an aspherical tens having the optimized conic constant are smaller than those of a spherical lens. The RMS SD in the back focal plane decreases as the front surface power decreases. From these results, we determine the optimized conic constant to improve the optical image quality and decrease RMS SD in the back focal plane.

• Journal of Satellite, Information and Communications
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• v.5 no.2
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• pp.50-56
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• 2010

Most mission trajectory design technologies for space exploration have been utilized the Patched Conic Approximation which is based on Hohmann transfer in two-body problem. The Hohmann transfer trajectory is basically an elliptic trajectory, and Patched Conic Approximation consists of Hohmann transfer trajectories in which each trajectory are patched to the next one. This technology is the most efficient method when considering only one major planet at each patch trajectory design. The disadvantages of the conventional Patched Conic Approach are more fuel (or mass) needed and only conic trajectories are designed. Recent space exploration missions need to satisfy more various scientific or engineering goals, and mission utilizing smaller satellites are needed for cost reduction. The geometrical characteristics of three-body dynamics could change the paradigm of the conventional solar system. In this theoretical concept, one can design a trajectory connecting around the solar system with comparably very small energy. In this paper, the basic three-body dynamics are introduced and a spacecraft mission trajectory is designed utilizing the three-body dynamics.

• Journal of Institute of Control, Robotics and Systems
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• v.5 no.4
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• pp.437-445
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• 1999

Most autonomous mobile robots view only things in front of then, and as a result, they may collide with objects moving from the side or behind. To overcome this problem, an active omni-directional range sensor system has been built that can obtain an omni-directional depth map through the use of a laser conic plane and a conic mirror. In the navigation of the mobile robot, the proposed sensor system produces a laser conic plane by rotating the laser point source at high speed: this creates a two-dimensional depth map, in real time, once an image is captured. The results obtained from experiment show that the proposed sensor system is very efficient, and can be utilized for navigation of mobile robot in an unknown environment.

• 제어로봇시스템학회:학술대회논문집
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• 1996.10b
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• pp.824-827
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• 1996

Most autonomous mobile robots view things only in front of them. As a result, they may collide against objects moving from the side or behind. To overcome the problem we have built an Active Omni-directional Range Sensor that can obtain omnidirectional depth data by a laser conic plane and a conic mirror. In the navigation of the mobile robot, the proposed sensor system makes a laser conic plane by rotating the laser point source at high speed and achieves two dimensional depth map, in real time, once an image capture. The experimental results show that the proposed sensor system provides the best potential for navigation of the mobile robot in uncertain environment.

• The Pure and Applied Mathematics
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• v.22 no.1
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• pp.25-34
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• 2015

In this paper we characterize the isogonal and isotomic conjugates of conic. Every conic can be expressed by a quadratic rational B$\acute{e}$zier curve having control polygon $b_0b_1b_2$ with weight w > 0. We show that the isotomic conjugate of parabola and hyperbola with respect to ${\Delta}b_0b_1b_2$ is ellipse, and that the isotomic conjugate of ellipse with the weight $w={\frac{1}{2}}$ is identical. We also find all cases of the isogonal conjugate of conic with respect to ${\Delta}b_0b_1b_2$. Our characterizations are derived easily due to the expression of conic by the quadratic rational B$\acute{e}$ezier curve in standard form.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.44 no.6
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• pp.468-476
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• 2016

In this study, the conic winglet which is made by rotating wing tip airfoil by each 3 axis is applied to the dual type combined fan to reduce the wing tip leakage loss. Computational Fluid Dynamics is used to calculate the loss and optimum technique is used to get minimum loss. Optimization results shows that total pressure loss coefficient was reduced by 3.4 %, and optimization model was a bended shape at the end of wing forward to pressure side.

• Journal for History of Mathematics
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• v.25 no.4
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• pp.83-99
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• 2012

The conic sections are defined as algebraic expressions using the focus and the directrix in the high school curriculum. However it is difficult that students understand the conic sections without environment which they can manipulate the conic sections. To make up for this weak point, we have found the evidence for generating method of a conic section through a sundial and investigated the history of terms 'focus', 'directrix' and the tool of drawing them continuously.

• Journal of Science Education
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• v.47 no.3
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• pp.263-272
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• 2023

We consider how a pre-service teacher can understand and utilize various concepts of Euclidean geometry by learning conic sections using mathematical definitions in non-Euclidean geometry. In a third-grade class of D University, we used mathematical definitions to demonstrate that learning conic sections in non-Euclidean space, such as taxicab geometry and Minkowski distance space, can aid pre-service teachers by enhancing their ability to acquire and accept new geometric concepts. As a result, learning conic sections using mathematical definitions in taxicab geometry and Minkowski distance space is expected to contribute to enhancing the education of pre-service teachers for Euclidean geometry expertise by fostering creative and flexible thinking.

• Communications of the Korean Mathematical Society
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• v.17 no.4
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• pp.741-754
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• 2002

In this paper we present an error bound for cubic spline approximation of conic section curve. We compare it to the error bound proposed by Floater [1]. The error estimating function proposed in this paper is sharper than Floater's at the mid-point of parameter, which means the overall error bound is sharper than Floater's if the estimating function has the maximum at the midpoint.

• Communications of the Korean Mathematical Society
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• v.20 no.4
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• pp.861-873
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• 2005

In this paper we approximate a cylindrical helix by bi-conic and bi-quadratic Bezier curves. Each approximation method is $G^1$ end-points interpolation of the helix. We present a sharp upper bound of the Hausdorff distance between the helix and each approximation curve. We also show that the error bound has the approximation order three and monotone increases as the length of the helix increases. As an illustration we give some numerical examples.